Semantic search

Jump to: navigation, search
Search

Edit query Show embed code

The query [[Satisfies property::Finite group]] was answered by the SMWSQLStore3 in 0.0088 seconds.


Results 1 – 344    (Previous 500 | Next 500)   (20 | 50 | 100 | 250 | 500)   (JSON | CSV | RSS | RDF)
 GAP IDArithmetic function value
Alternating group:A412 (3)Order of a group (12)
Exponent of a group (6)
Derived length (2)
Frattini length (1)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Max-length of a group (3)
Composition length (3)
Chief length (2)
Number of conjugacy classes (4)
Number of orbits under automorphism group (3)
Number of equivalence classes under real conjugacy (3)
Number of equivalence classes under rational conjugacy (3)
Number of conjugacy classes of real elements (2)
Number of conjugacy classes of rational elements (2)
Number of conjugacy classes of subgroups (5)
Number of subgroups (10)
Alternating group:A560 (5)Order of a group (60)
Exponent of a group (30)
Frattini length (1)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Max-length of a group (4)
Composition length (1)
Chief length (1)
Number of subgroups (59)
Number of conjugacy classes (5)
Number of conjugacy classes of subgroups (9)
Alternating group:A6360 (118)Order of a group (360)
Exponent of a group (60)
Frattini length (1)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Max-length of a group (5)
Number of subgroups (501)
Number of conjugacy classes (7)
Number of conjugacy classes of subgroups (22)
Automorphism group of alternating group:A61,440 (5841)Order of a group (1,440)
Number of conjugacy classes (13)
Binary octahedral group48 (28)Order of a group (48)
Exponent of a group (24)
Derived length (4)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Max-length of a group (5)
Number of conjugacy classes (8)
Number of subgroups (35)
Number of conjugacy classes of subgroups (13)
Burnside group:B(3,3)2,187 (4487)Underlying prime of p-group (3)
Order of a group (2,187)
Prime-base logarithm of order (7)
Max-length of a group (7)
Chief length (7)
Composition length (7)
Exponent of a group (3)
Prime-base logarithm of exponent (1)
Nilpotency class (3)
Derived length (2)
Central product of D16 and Z432 (42)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Central product of D8 and Q832 (50)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (1)
Central product of D8 and Z1248 (47)
Central product of D8 and Z1664 (185)
Central product of D8 and Z416 (13)Underlying prime of p-group (2)
Order of a group (16)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (1)
Central product of D8 and Z832 (38)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (2)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (1)
Central product of M16 and Z8 over common Z264 (86)
Central product of SL(2,3) and Z448 (33)Order of a group (48)
Central product of SL(2,5) and Z4240 (93)Order of a group (240)
Central product of UT(3,3) and Z981 (14)Order of a group (81)
Prime-base logarithm of order (4)
Exponent of a group (9)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Fitting length (1)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (1)
Central product of UT(3,p) and Zp^2
Central product of Z9 and wreath product of Z3 and Z3243 (55)
Cyclic group of prime-cube orderPrime-base logarithm of order (3)
Max-length of a group (3)
Chief length (3)
Composition length (3)
Prime-base logarithm of exponent (3)
Frattini length (3)
Minimum size of generating set (1)
Subgroup rank of a group (1)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Cyclic group of prime-square orderPrime-base logarithm of order (2)
Max-length of a group (2)
Chief length (2)
Composition length (2)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (1)
Subgroup rank of a group (1)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Cyclic group:Z1010 (2)Order of a group (10)
Exponent of a group (10)
Cyclic group:Z1212 (2)Order of a group (12)
Exponent of a group (12)
Nilpotency class (1)
Derived length (1)
Frattini length (2)
Fitting length (1)
Cyclic group:Z128128 (1)Underlying prime of p-group (2)
Order of a group (128)
Prime-base logarithm of order (7)
Max-length of a group (7)
Chief length (7)
Composition length (7)
Exponent of a group (128)
Prime-base logarithm of exponent (7)
Frattini length (7)
Minimum size of generating set (1)
Subgroup rank of a group (1)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Cyclic group:Z1616 (1)Underlying prime of p-group (2)
Order of a group (16)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (16)
Prime-base logarithm of exponent (4)
Frattini length (4)
Minimum size of generating set (1)
Subgroup rank of a group (1)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Cyclic group:Z1818 (2)Order of a group (18)
Exponent of a group (18)
Frattini length (2)
Cyclic group:Z22 (1)Underlying prime of p-group (2)
Order of a group (2)
Prime-base logarithm of order (1)
Max-length of a group (1)
Chief length (1)
Composition length (1)
Exponent of a group (2)
Prime-base logarithm of exponent (1)
Frattini length (1)
Minimum size of generating set (1)
Subgroup rank of a group (1)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Number of conjugacy classes (2)
Number of subgroups (2)
Number of conjugacy classes of subgroups (2)
Number of equivalence classes under real conjugacy (2)
Number of equivalence classes under rational conjugacy (2)
Cyclic group:Z2020 (2)Order of a group (20)
Exponent of a group (20)
Frattini length (2)
Fitting length (1)
Derived length (1)
Cyclic group:Z2424 (2)Order of a group (24)
Exponent of a group (24)
Nilpotency class (1)
Derived length (1)
Cyclic group:Z243243 (1)Order of a group (243)
Prime-base logarithm of order (5)
Exponent of a group (243)
Prime-base logarithm of exponent (5)
Minimum size of generating set (1)
Subgroup rank of a group (1)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Derived length (1)
Nilpotency class (1)
Frattini length (5)
Cyclic group:Z2727 (1)Underlying prime of p-group (3)
Order of a group (27)
Prime-base logarithm of order (3)
Max-length of a group (3)
Chief length (3)
Composition length (3)
Exponent of a group (27)
Prime-base logarithm of exponent (3)
Frattini length (3)
Minimum size of generating set (1)
Subgroup rank of a group (1)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Cyclic group:Z33 (1)Underlying prime of p-group (3)
Order of a group (3)
Prime-base logarithm of order (1)
Max-length of a group (1)
Chief length (1)
Composition length (1)
Exponent of a group (3)
Prime-base logarithm of exponent (1)
Frattini length (1)
Minimum size of generating set (1)
Subgroup rank of a group (1)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Cyclic group:Z3232 (1)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (32)
Prime-base logarithm of exponent (5)
Frattini length (5)
Minimum size of generating set (1)
Subgroup rank of a group (1)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Cyclic group:Z3636 (2)
Cyclic group:Z44 (1)Underlying prime of p-group (2)
Order of a group (4)
Prime-base logarithm of order (2)
Max-length of a group (2)
Chief length (2)
Composition length (2)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (1)
Subgroup rank of a group (1)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Cyclic group:Z4040 (2)
Cyclic group:Z55 (1)Order of a group (5)
Exponent of a group (5)
Derived length (1)
Frattini length (1)
Fitting length (1)
Cyclic group:Z6464 (1)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (64)
Prime-base logarithm of exponent (6)
Frattini length (6)
Minimum size of generating set (1)
Subgroup rank of a group (1)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Cyclic group:Z77 (1)Order of a group (7)
Exponent of a group (7)
Frattini length (1)
Fitting length (1)
Subgroup rank of a group (1)
Rank of a p-group (1)
Cyclic group:Z88 (1)Underlying prime of p-group (2)
Order of a group (8)
Prime-base logarithm of order (3)
Max-length of a group (3)
Chief length (3)
Composition length (3)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Frattini length (3)
Minimum size of generating set (1)
Subgroup rank of a group (1)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Cyclic group:Z8181 (1)Underlying prime of p-group (3)
Order of a group (81)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (81)
Prime-base logarithm of exponent (4)
Frattini length (4)
Minimum size of generating set (1)
Subgroup rank of a group (1)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Cyclic group:Z99 (1)Order of a group (9)
Exponent of a group (9)
Derived length (1)
Frattini length (2)
Fitting length (1)
Subgroup rank of a group (1)
Dicyclic group:Dic1212 (1)
Dicyclic group:Dic2020 (1)Order of a group (20)
Exponent of a group (10)
Frattini length (2)
Derived length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Dicyclic group:Dic2424 (4)Order of a group (24)
Exponent of a group (12)
Derived length (2)
Dihedral group:D1010 (1)Order of a group (10)
Exponent of a group (10)
Fitting length (2)
Frattini length (1)
Derived length (2)
Dihedral group:D1212 (4)Order of a group (12)
Exponent of a group (6)
Derived length (2)
Frattini length (1)
Fitting length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Max-length of a group (3)
Dihedral group:D128128 (161)Underlying prime of p-group (2)
Order of a group (128)
Prime-base logarithm of order (7)
Max-length of a group (7)
Chief length (7)
Composition length (7)
Exponent of a group (64)
Prime-base logarithm of exponent (6)
Nilpotency class (6)
Derived length (2)
Frattini length (6)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Dihedral group:D1414 (1)
Dihedral group:D1616 (7)Underlying prime of p-group (2)
Order of a group (16)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Number of conjugacy classes (7)
Number of equivalence classes under rational conjugacy (6)
Number of conjugacy classes of rational elements (5)
Dihedral group:D1818 (1)
Dihedral group:D2020 (4)Order of group (20)
Order of a group (10)
Frattini length (1)
Fitting length (1)
Derived length (2)
Dihedral group:D2424 (6)
Dihedral group:D256256 (539)Underlying prime of p-group (2)
Order of a group (256)
Prime-base logarithm of order (8)
Max-length of a group (8)
Chief length (8)
Composition length (8)
Exponent of a group (128)
Prime-base logarithm of exponent (7)
Nilpotency class (7)
Derived length (2)
Frattini length (7)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Dihedral group:D3232 (18)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (16)
Prime-base logarithm of exponent (4)
Nilpotency class (4)
Derived length (2)
Frattini length (4)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Dihedral group:D6464 (52)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (32)
Prime-base logarithm of exponent (5)
Nilpotency class (5)
Derived length (2)
Frattini length (5)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Dihedral group:D88 (3)Underlying prime of p-group (2)
Order of a group (8)
Prime-base logarithm of order (3)
Max-length of a group (3)
Chief length (3)
Composition length (3)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Fitting length (1)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (1)
Number of conjugacy classes (5)
Number of equivalence classes under real conjugacy (5)
Number of conjugacy classes of real elements (5)
Number of equivalence classes under rational conjugacy (5)
Number of conjugacy classes of rational elements (5)
Number of subgroups (10)
Number of conjugacy classes of subgroups (8)
Number of normal subgroups (6)
Number of automorphism classes of subgroups (6)
Number of characteristic subgroups (4)
Direct product of A4 and A4144 (184)
Direct product of A4 and D896 (197)Order of a group (96)
Exponent of a group (12)
Derived length (2)
Minimum size of generating set (2)
Direct product of A4 and E896 (228)Order of a group (96)
Exponent of a group (6)
Derived length (2)
Minimum size of generating set (2)
Direct product of A4 and Q896 (199)Order of a group (96)
Exponent of a group (12)
Derived length (2)
Minimum size of generating set (2)
Direct product of A4 and S372 (44)Order of a group (72)
Exponent of a group (6)
Derived length (2)
Direct product of A4 and V448 (49)
Direct product of A4 and Z224 (13)Order of a group (24)
Exponent of a group (12)
Derived length (2)
Frattini length (1)
Minimum size of generating set (2)
Subgroup rank of a group (3)
Direct product of A4 and Z336 (11)
Direct product of A4 and Z448 (31)
Direct product of A4 and Z4 and Z296 (196)Order of a group (96)
Exponent of a group (12)
Minimum size of generating set (2)
Derived length (2)
Direct product of A4 and Z560 (9)Order of a group (60)
Exponent of a group (30)
Minimum size of generating set (2)
Derived length (2)
Direct product of A4 and Z896 (73)Order of a group (96)
Exponent of a group (24)
Derived length (2)
Minimum size of generating set (2)
Direct product of A5 and V4240 (190)Order of a group (240)
Direct product of A5 and Z2120 (35)Order of a group (120)
Exponent of a group (30)
Composition length (2)
Chief length (2)
Max-length of a group (5)
Frattini length (1)
Direct product of A5 and Z4240 (92)Order of a group (240)
Exponent of a group (60)
Composition length (3)
Chief length (3)
Minimum size of generating set (2)
Direct product of A5 and Z7420 (13)
Direct product of A6 and Z2720 (766)Order of a group (720)
Exponent of a group (60)
Direct product of D12 and Z224 (14)
Direct product of D12 and Z336 (12)
Direct product of D16 and V464 (250)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Direct product of D16 and Z232 (39)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Direct product of D16 and Z348 (25)
Direct product of D16 and Z464 (118)Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Direct product of D32 and Z264 (186)
Direct product of D8 and D864 (226)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (2)
Direct product of D8 and E864 (261)
Direct product of D8 and Q864 (230)
Direct product of D8 and S348 (38)
Direct product of D8 and V432 (46)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (3)
Direct product of D8 and Z216 (11)Underlying prime of p-group (2)
Order of a group (16)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Fitting length (1)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (2)
Direct product of D8 and Z324 (10)Order of a group (24)
Exponent of a group (12)
Frattini length (2)
Fitting length (1)
Derived length (2)
Nilpotency class (2)
Direct product of D8 and Z432 (25)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (2)
Direct product of D8 and Z4 and Z264 (196)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (3)
Direct product of D8 and Z540 (10)
Direct product of D8 and Z648 (45)
Direct product of D8 and Z756 (9)
Direct product of Dic12 and Z224 (7)Order of a group (24)
Exponent of a group (12)
Fitting length (2)
Frattini length (2)
Derived length (2)
Minimum size of generating set (2)
Direct product of E16 and Z464 (260)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (5)
Subgroup rank of a group (5)
Rank of a p-group (5)
Normal rank of a p-group (5)
Characteristic rank of a p-group (5)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of E8 and Z324 (15)Order of a group (24)
Exponent of a group (6)
Frattini length (3)
Direct product of E8 and Z432 (45)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (4)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of M16 and V464 (247)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (2)
Derived length (2)
Frattini length (3)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (4)
Direct product of M16 and Z232 (37)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (2)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Direct product of M16 and Z348 (24)
Direct product of M16 and Z464 (85)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (2)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Direct product of M27 and Z381 (13)
Direct product of M32 and Z264 (184)
Direct product of Mp^3 and Zp
Direct product of Q16 and V464 (252)
Direct product of Q16 and Z232 (41)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Direct product of Q16 and Z348 (27)
Direct product of Q16 and Z464 (120)Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Direct product of Q32 and Z264 (188)
Direct product of Q8 and Q864 (239)
Direct product of Q8 and S348 (40)
Direct product of Q8 and V432 (47)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Direct product of Q8 and Z216 (12)Underlying prime of p-group (2)
Order of a group (16)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Direct product of Q8 and Z324 (11)Order of a group (24)
Exponent of a group (12)
Nilpotency class (2)
Derived length (2)
Fitting length (1)
Frattini length (2)
Direct product of Q8 and Z432 (26)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Direct product of Q8 and Z540 (11)
Direct product of S3 and S336 (10)Order of a group (36)
Exponent of a group (6)
Frattini length (1)
Derived length (2)
Minimum size of generating set (2)
Direct product of S3 and Z318 (3)
Direct product of S3 and Z424 (5)Order of a group (24)
Exponent of a group (12)
Derived length (2)
Fitting length (2)
Frattini length (2)
Minimum size of generating set (2)
Direct product of S4 and V496 (226)Order of a group (96)
Exponent of a group (12)
Derived length (3)
Minimum size of generating set (2)
Direct product of S4 and Z248 (48)
Direct product of S4 and Z372 (42)Order of a group (72)
Direct product of S4 and Z496 (186)Order of a group (96)
Exponent of a group (12)
Minimum size of generating set (2)
Direct product of S4 and Z5120 (37)Order of a group (120)
Exponent of a group (60)
Minimum size of generating set (2)
Derived length (3)
Direct product of S5 and Z2240 (189)
Direct product of SD16 and V464 (251)
Direct product of SD16 and Z232 (40)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Direct product of SD16 and Z348 (26)
Direct product of SD16 and Z464 (119)Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Direct product of SD32 and Z264 (187)
Direct product of SL(2,3) and V496 (198)Order of a group (96)
Exponent of a group (12)
Derived length (3)
Direct product of SL(2,3) and Z248 (32)Order of a group (48)
Exponent of a group (12)
Derived length (3)
Direct product of SL(2,3) and Z372 (25)Order of a group (72)
Direct product of SL(2,3) and Z496 (69)Order of a group (96)
Exponent of a group (12)
Derived length (3)
Direct product of SL(2,5) and Z2240 (94)Order of a group (240)
Direct product of SmallGroup(16,13) and V464 (263)
Direct product of SmallGroup(16,13) and Z232 (48)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (2)
Direct product of SmallGroup(16,13) and Z464 (198)
Direct product of SmallGroup(16,3) and V464 (193)
Direct product of SmallGroup(16,3) and Z232 (22)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (4)
Direct product of SmallGroup(16,3) and Z348 (21)
Direct product of SmallGroup(16,3) and Z464 (58)
Direct product of SmallGroup(16,4) and V464 (194)
Direct product of SmallGroup(16,4) and Z232 (23)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Direct product of SmallGroup(16,4) and Z464 (59)
Direct product of SmallGroup(32,12) and Z264 (103)
Direct product of SmallGroup(32,13) and Z264 (106)
Direct product of SmallGroup(32,14) and Z264 (107)
Direct product of SmallGroup(32,2) and Z264 (56)
Direct product of SmallGroup(32,24) and Z264 (195)
Direct product of SmallGroup(32,27) and Z264 (202)
Direct product of SmallGroup(32,33) and Z264 (209)
Direct product of SmallGroup(32,4) and Z264 (84)
Direct product of SmallGroup(32,49) and Z264 (264)
Direct product of SmallGroup(32,50) and Z264 (265)
Direct product of Z10 and Z220 (5)Order of a group (20)
Exponent of a group (10)
Frattini length (1)
Fitting length (1)
Derived length (1)
Minimum size of generating set (2)
Direct product of Z16 and V464 (183)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (16)
Prime-base logarithm of exponent (4)
Frattini length (4)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z16 and Z232 (16)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (16)
Prime-base logarithm of exponent (4)
Frattini length (4)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z16 and Z464 (26)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (16)
Prime-base logarithm of exponent (4)
Frattini length (4)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z27 and E9243 (48)Order of a group (243)
Prime-base logarithm of order (5)
Exponent of a group (27)
Prime-base logarithm of exponent (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Derived length (1)
Nilpotency class (1)
Frattini length (3)
Direct product of Z27 and Z381 (5)Underlying prime of p-group (3)
Order of a group (81)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (27)
Prime-base logarithm of exponent (3)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z27 and Z9243 (10)Order of a group (243)
Prime-base logarithm of order (5)
Exponent of a group (27)
Prime-base logarithm of exponent (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Derived length (1)
Nilpotency class (1)
Frattini length (3)
Direct product of Z32 and Z264 (50)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (32)
Prime-base logarithm of exponent (5)
Frattini length (5)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z4 and V416 (10)Underlying prime of p-group (2)
Order of a group (16)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z4 and Z28 (2)Underlying prime of p-group (2)
Order of a group (8)
Prime-base logarithm of order (3)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z4 and Z416 (2)Underlying prime of p-group (2)
Order of a group (16)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z4 and Z4 and V464 (192)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (4)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z4 and Z4 and Z232 (21)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z4 and Z4 and Z464 (55)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z6 and Z212 (5)Order of a group (12)
Exponent of a group (6)
Nilpotency class (1)
Derived length (1)
Frattini length (1)
Fitting length (1)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Direct product of Z6 and Z318 (5)Order of a group (18)
Exponent of a group (6)
Derived length (1)
Nilpotency class (1)
Direct product of Z6 and Z424 (9)
Direct product of Z8 and D864 (115)Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (2)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (2)
Direct product of Z8 and E864 (246)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Frattini length (3)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (4)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z8 and V432 (36)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z8 and Z216 (5)Underlying prime of p-group (2)
Order of a group (16)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z8 and Z432 (3)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z8 and Z4 and V4128 (1601)Underlying prime of p-group (2)
Order of a group (128)
Prime-base logarithm of order (7)
Max-length of a group (7)
Chief length (7)
Composition length (7)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Frattini length (3)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (4)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z8 and Z4 and Z264 (83)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z8 and Z864 (2)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z81 and Z3243 (23)Order of a group (243)
Prime-base logarithm of order (5)
Exponent of a group (81)
Prime-base logarithm of exponent (4)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Derived length (1)
Nilpotency class (1)
Frattini length (4)
Direct product of Z9 and E27243 (61)Order of a group (243)
Prime-base logarithm of order (5)
Exponent of a group (9)
Prime-base logarithm of exponent (2)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (4)
Derived length (1)
Nilpotency class (1)
Direct product of Z9 and E981 (11)Underlying prime of p-group (3)
Order of a group (81)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (9)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z9 and Z327 (2)Underlying prime of p-group (3)
Order of a group (27)
Prime-base logarithm of order (3)
Exponent of a group (9)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z9 and Z981 (2)Underlying prime of p-group (3)
Order of a group (81)
Prime-base logarithm of order (4)
Exponent of a group (9)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of Z9 and Z9 and Z3243 (31)Order of a group (243)
Prime-base logarithm of order (5)
Exponent of a group (9)
Prime-base logarithm of exponent (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Derived length (1)
Nilpotency class (1)
Frattini length (2)
Direct product of cyclic group of prime-cube order and cyclic group of prime orderPrime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Prime-base logarithm of exponent (3)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of cyclic group of prime-square order and cyclic group of prime orderPrime-base logarithm of order (3)
Max-length of a group (3)
Chief length (3)
Composition length (3)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of cyclic group of prime-square order and cyclic group of prime-square orderPrime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of cyclic group of prime-square order and elementary abelian group of prime-square orderPrime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Prime-base logarithm of exponent (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Direct product of holomorph of Z8 and Z264 (254)
Direct product of prime-cube order group:U(3,3) and Z381 (12)
Double cover of symmetric group:S5 of minus type240 (89)Order of a group (240)
Double cover of symmetric group:S5 of plus type240 (90)Order of a group (240)
Elementary abelian group of prime-cube orderPrime-base logarithm of order (3)
Max-length of a group (3)
Chief length (3)
Composition length (3)
Prime-base logarithm of exponent (1)
Frattini length (1)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Elementary abelian group of prime-square orderPrime-base logarithm of order (2)
Max-length of a group (2)
Chief length (2)
Composition length (2)
Prime-base logarithm of exponent (1)
Frattini length (1)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Elementary abelian group:E1616 (14)Underlying prime of p-group (2)
Order of a group (16)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (2)
Prime-base logarithm of exponent (1)
Frattini length (1)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (4)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Elementary abelian group:E243243 (67)Order of a group (243)
Prime-base logarithm of order (5)
Exponent of a group (3)
Prime-base logarithm of exponent (1)
Minimum size of generating set (5)
Subgroup rank of a group (5)
Rank of a p-group (5)
Normal rank of a p-group (5)
Characteristic rank of a p-group (5)
Derived length (1)
Frattini length (1)
Nilpotency class (1)
Elementary abelian group:E2727 (5)Underlying prime of p-group (3)
Order of a group (27)
Prime-base logarithm of order (3)
Max-length of a group (3)
Chief length (3)
Composition length (3)
Exponent of a group (3)
Prime-base logarithm of exponent (1)
Frattini length (1)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Elementary abelian group:E3232 (51)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (2)
Prime-base logarithm of exponent (1)
Frattini length (1)
Minimum size of generating set (5)
Subgroup rank of a group (5)
Rank of a p-group (5)
Normal rank of a p-group (5)
Characteristic rank of a p-group (5)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Elementary abelian group:E6464 (267)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (2)
Prime-base logarithm of exponent (1)
Frattini length (1)
Minimum size of generating set (6)
Subgroup rank of a group (6)
Rank of a p-group (6)
Normal rank of a p-group (6)
Characteristic rank of a p-group (6)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Elementary abelian group:E88 (5)Underlying prime of p-group (2)
Order of a group (8)
Prime-base logarithm of order (3)
Max-length of a group (3)
Chief length (3)
Composition length (3)
Exponent of a group (2)
Prime-base logarithm of exponent (1)
Frattini length (1)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Elementary abelian group:E8181 (15)Underlying prime of p-group (3)
Order of a group (81)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (3)
Prime-base logarithm of exponent (1)
Frattini length (1)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (4)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Elementary abelian group:E99 (2)Underlying prime of p-group (3)
Order of a group (9)
Prime-base logarithm of order (2)
Max-length of a group (2)
Chief length (2)
Composition length (2)
Exponent of a group (3)
Prime-base logarithm of exponent (1)
Frattini length (1)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
Faithful semidirect product of E8 and Z432 (6)Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (3)
Derived length (2)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Free product of class two of two Klein four-groups256 (8935)
General affine group:GA(1,5)20 (3)Order of a group (20)
Exponent of a group (20)
Frattini length (1)
Fitting length (2)
Derived length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
General affine group:GA(1,7)42 (1)Order of a group (42)
Exponent of a group (42)
Frattini length (1)
Fitting length (2)
Derived length (2)
Subgroup rank of a group (2)
Minimum size of generating set (2)
General affine group:GA(1,8)56 (11)Order of a group (56)
Exponent of a group (14)
Frattini length (1)
Fitting length (2)
Derived length (2)
Minimum size of generating set (2)
Subgroup rank of a group (3)
General affine group:GA(1,9)72 (39)Order of a group (72)
Exponent of a group (24)
Frattini length (1)
Fitting length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
General affine group:GA(2,3)432 (734)Order of a group (432)
Number of conjugacy classes (11)
General linear group:GL(2,3)48 (29)Order of a group (48)
Exponent of a group (24)
Derived length (4)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Max-length of a group (5)
Composition length (5)
Chief length (4)
Number of subgroups (55)
Number of conjugacy classes (8)
Number of conjugacy classes of subgroups (16)
General linear group:GL(2,4)180 (19)Order of a group (180)
Exponent of a group (30)
Frattini length (1)
Subgroup rank of a group (5)
Number of subgroups (148)
Number of conjugacy classes (15)
Number of conjugacy classes of subgroups (21)
Composition length (2)
General linear group:GL(2,Z4)96 (195)Order of a group (96)
Exponent of a group (12)
Derived length (3)
General semiaffine group:GammaA(1,9)144 (182)Order of a group (144)
Number of conjugacy classes (9)
General semilinear group:GammaL(1,8)21 (1)Order of a group (21)
Exponent of a group (21)
Derived length (2)
Fitting length (2)
Frattini length (1)
Number of conjugacy classes (5)
Generalized dihedral group for E918 (4)Order of a group (18)
Exponent of a group (6)
Derived length (2)
Frattini length (1)
Fitting length (2)
Generalized dihedral group for direct product of Z4 and Z432 (34)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (2)
Generalized quaternion group:Q1616 (9)Underlying prime of p-group (2)
Order of a group (16)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Number of conjugacy classes (7)
Number of equivalence classes under rational conjugacy (6)
Number of conjugacy classes of rational elements (5)
Generalized quaternion group:Q3232 (20)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (16)
Prime-base logarithm of exponent (4)
Nilpotency class (4)
Derived length (2)
Frattini length (4)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Generalized quaternion group:Q6464 (54)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (32)
Prime-base logarithm of exponent (5)
Nilpotency class (5)
Derived length (2)
Frattini length (5)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Holomorph of D864 (134)
Holomorph of Z832 (43)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Holomorph of Z954 (6)Order of a group (54)
Exponent of a group (18)
Frattini length (2)
Fitting length (2)
Derived length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Inner automorphism group of wreath product of Z2 and A496 (70)
Inner automorphism group of wreath product of Z2 and A5960 (11358)
Inner automorphism group of wreath product of Z5 and Z53,125 (30)Order of a group (3,125)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (5)
Prime-base logarithm of exponent (1)
Nilpotency class (4)
Derived length (2)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (4)
Inner holomorph of D832 (49)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (1)
Klein four-group4 (2)Underlying prime of p-group (2)
Order of a group (4)
Prime-base logarithm of order (2)
Max-length of a group (2)
Chief length (2)
Composition length (2)
Exponent of a group (2)
Prime-base logarithm of exponent (1)
Frattini length (1)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nilpotency class (1)
Derived length (1)
Fitting length (1)
M1616 (6)Underlying prime of p-group (2)
Order of a group (16)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (2)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
M2727 (4)Order of a group (27)
Underlying prime of p-group (3)
Prime-base logarithm of order (3)
Exponent of a group (9)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
M3232 (17)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (16)
Prime-base logarithm of exponent (4)
Nilpotency class (2)
Derived length (2)
Frattini length (4)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
M6464 (51)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (32)
Prime-base logarithm of exponent (5)
Nilpotency class (2)
Derived length (2)
Frattini length (5)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
M8181 (6)Order of a group (81)
Exponent of a group (27)
Frattini length (3)
Derived length (2)
Nilpotency class (2)
Subgroup rank of a group (2)
Minimum size of generating set (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Mathieu group:M10720 (765)Order of a group (720)
Exponent of a group (120)
Frattini length (1)
Mathieu group:M972 (41)Order of a group (72)
Exponent of a group (12)
Derived length (3)
Frattini length (1)
Fitting length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Max-length of a group (5)
Number of subgroups (68)
Number of conjugacy classes (6)
Number of conjugacy classes of subgroups (14)
Maximal unipotent subgroup of symplectic group:Sp(4,p)
Nontrivial semidirect product of Z3 and Z824 (1)Order of a group (24)
Exponent of a group (24)
Derived length (2)
Frattini length (3)
Fitting length (2)
Minimum size of generating set (2)
Nontrivial semidirect product of Z4 and Z1664 (44)
Nontrivial semidirect product of Z4 and Z416 (4)Underlying prime of p-group (2)
Order of a group (16)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Number of subgroups (15)
Number of conjugacy classes of subgroups (13)
Number of conjugacy classes (10)
Nontrivial semidirect product of Z4 and Z832 (12)Underlying prime (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (2)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Nontrivial semidirect product of Z7 and Z963 (1)Order of a group (63)
Exponent of a group (63)
Derived length (2)
Frattini length (2)
Fitting length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Nontrivial semidirect product of Z9 and Z981 (4)Order of a group (81)
Prime-base logarithm of order (4)
Exponent of a group (9)
Prime-base logarithm of exponent (2)
Frattini length (2)
Derived length (2)
Nilpotency class (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Panferov Lie group for 53,125 (33)Order of a group (3,125)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (5)
Prime-base logarithm of exponent (1)
Nilpotency class (4)
Derived length (2)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Projective general linear group:PGL(2,11)1,320 (133)Order of a group (1,320)
Projective general linear group:PGL(2,7)336 (208)
Projective general linear group:PGL(2,9)720 (764)Order of a group (720)
Projective general linear group:PGL(2,Z9)648 (703)
Projective special linear group:PSL(2,11)660 (13)Order of a group (660)
Exponent of a group (330)
Frattini length (1)
Chief length (1)
Composition length (1)
Number of conjugacy classes (8)
Number of equivalence classes under rational conjugacy (6)
Number of conjugacy classes of subgroups (16)
Number of subgroups (620)
Number of automorphism classes of subgroups (14)
Projective special linear group:PSL(2,13)1,092 (25)Order of a group (1,092)
Exponent of a group (546)
Frattini length (1)
Chief length (1)
Composition length (1)
Number of conjugacy classes (9)
Number of equivalence classes under rational conjugacy (6)
Number of conjugacy classes of subgroups (16)
Number of subgroups (942)
Projective special linear group:PSL(2,8)504 (156)Order of a group (504)
Exponent of a group (126)
Number of conjugacy classes (9)
Number of conjugacy classes of subgroups (12)
Number of subgroups (386)
Projective special linear group:PSL(2,Z9)324 (160)Order of a group (324)
Exponent of a group (18)
Derived length (3)
Frattini length (1)
Fitting length (3)
Number of conjugacy classes (13)
Number of conjugacy classes of subgroups (32)
Number of subgroups (340)
Projective special linear group:PSL(3,2)168 (42)Order of a group (168)
Exponent of a group (84)
Frattini length (1)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Max-length of a group (5)
Number of subgroups (179)
Number of conjugacy classes (6)
Number of conjugacy classes of subgroups (15)
Quaternion group8 (4)Underlying prime of p-group (2)
Order of a group (8)
Prime-base logarithm of order (3)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (1)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Number of conjugacy classes (5)
Number of equivalence classes under real conjugacy (5)
Number of conjugacy classes of real elements (5)
Number of equivalence classes under rational conjugacy (5)
Number of conjugacy classes of rational elements (5)
Number of subgroups (6)
Number of conjugacy classes of subgroups (6)
Number of normal subgroups (6)
Number of automorphism classes of subgroups (4)
Ree group:Ree(3)1,512 (779)Order of a group (1,512)
Exponent of a group (126)
Number of conjugacy classes (11)
Number of conjugacy classes of subgroups (25)
Number of subgroups (1,154)
Semidihedral group:SD128128 (162)Underlying prime of p-group (2)
Order of a group (128)
Prime-base logarithm of order (7)
Max-length of a group (7)
Chief length (7)
Composition length (7)
Exponent of a group (64)
Prime-base logarithm of exponent (6)
Nilpotency class (6)
Derived length (2)
Frattini length (6)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Semidihedral group:SD1616 (8)Underlying prime of p-group (2)
Order of a group (16)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Number of conjugacy classes (7)
Number of equivalence classes under rational conjugacy (6)
Number of conjugacy classes of rational elements (5)
Semidihedral group:SD256256 (540)Underlying prime of p-group (2)
Order of a group (256)
Prime-base logarithm of order (8)
Max-length of a group (8)
Chief length (8)
Composition length (8)
Exponent of a group (128)
Prime-base logarithm of exponent (7)
Nilpotency class (7)
Derived length (2)
Frattini length (7)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Semidihedral group:SD3232 (19)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (16)
Prime-base logarithm of exponent (4)
Nilpotency class (4)
Derived length (2)
Frattini length (4)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Semidihedral group:SD6464 (53)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (32)
Prime-base logarithm of exponent (5)
Nilpotency class (5)
Derived length (2)
Frattini length (5)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (1)
Characteristic rank of a p-group (1)
Semidirect product of Z16 and Z4 of M-type64 (27)
Semidirect product of Z16 and Z4 of dihedral type64 (47)
Semidirect product of Z16 and Z4 of semidihedral type64 (48)
Semidirect product of Z16 and Z4 via cube map64 (46)
Semidirect product of Z16 and Z4 via fifth power map64 (28)
Semidirect product of Z3 and D8 with action kernel V424 (8)Order of a group (24)
Exponent of a group (12)
Derived length (2)
Fitting length (2)
Frattini length (2)
Minimum size of generating set (2)
Semidirect product of Z5 and Z8 via inverse map40 (1)
Semidirect product of Z5 and Z8 via square map40 (3)
Semidirect product of Z8 and Z4 of M-type32 (4)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (2)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Semidirect product of Z8 and Z4 of dihedral type32 (14)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Semidirect product of Z8 and Z4 of semidihedral type32 (13)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Semidirect product of Z8 and Z8 of M-type64 (3)
Semidirect product of Z8 and Z8 of dihedral type64 (16)
Semidirect product of Z8 and Z8 of semidihedral type64 (15)
Semidirect product of cyclic group of prime-cube order and cyclic group of prime order
SmallGroup(128,1015)128 (1015)Underlying prime of p-group (2)
Order of a group (128)
Prime-base logarithm of order (7)
Max-length of a group (7)
Chief length (7)
Composition length (7)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (4)
SmallGroup(16,3)16 (3)Underlying prime of p-group (2)
Order of a group (16)
Prime-base logarithm of order (4)
Max-length of a group (4)
Chief length (4)
Composition length (4)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Number of conjugacy classes (10)
Number of conjugacy classes of subgroups (17)
SmallGroup(243,16)243 (16)Underlying prime of p-group (3)
Order of a group (243)
Prime-base logarithm of order (5)
Exponent of a group (27)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Rank of a p-group (3)
Normal rank of a p-group (3)
SmallGroup(243,19)243 (19)Underlying prime of p-group (3)
Order of a group (243)
Prime-base logarithm of order (5)
Exponent of a group (27)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
SmallGroup(243,20)243 (20)Underlying prime of p-group (3)
Order of a group (243)
Prime-base logarithm of order (5)
Exponent of a group (27)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
SmallGroup(256,27799)256 (27799)
SmallGroup(256,29626)256 (29626)
SmallGroup(256,6745)256 (6745)Underlying prime of p-group (2)
Order of a group (256)
Prime-base logarithm of order (8)
Max-length of a group (8)
Chief length (8)
Composition length (8)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
SmallGroup(32,10)32 (10)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (3)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
SmallGroup(32,15)32 (15)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
SmallGroup(32,2)32 (2)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Frattini length (2)
Nilpotency class (2)
Derived length (2)
Minimum size of generating set (2)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
SmallGroup(32,24)32 (24)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
SmallGroup(32,27)32 (27)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (4)
SmallGroup(32,28)32 (28)Underlying prime (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
SmallGroup(32,29)32 (29)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
SmallGroup(32,30)32 (30)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
SmallGroup(32,31)32 (31)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Fitting length (1)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (2)
SmallGroup(32,32)32 (32)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
SmallGroup(32,33)32 (33)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Fitting length (1)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
SmallGroup(32,35)32 (35)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
SmallGroup(32,44)32 (44)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Subgroup rank of a group (3)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
SmallGroup(32,5)32 (5)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (2)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
SmallGroup(32,7)32 (7)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (2)
SmallGroup(32,8)32 (8)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Max-length of a group (5)
Chief length (5)
Composition length (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Frattini length (3)
Nilpotency class (3)
Derived length (2)
Minimum size of generating set (2)
Subgroup rank of a group (3)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
SmallGroup(32,9)32 (9)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (3)
Rank of a p-group (3)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
SmallGroup(64,113)64 (113)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (2)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
SmallGroup(64,114)64 (114)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (2)
Derived length (2)
Frattini length (3)
Minimum size of generating set (3)
Rank of a p-group (3)
Normal rank of a p-group (3)
SmallGroup(64,17)64 (17)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (2)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Rank of a p-group (3)
Normal rank of a p-group (3)
SmallGroup(64,210)64 (210)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (4)
Rank of a p-group (3)
Normal rank of a p-group (3)
SmallGroup(64,248)64 (248)
SmallGroup(64,25)64 (25)Order of a group (64)
Prime-base logarithm of order (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
SmallGroup(64,57)64 (57)
SmallGroup(81,3)81 (3)Order of a group (81)
Exponent of a group (9)
Frattini length (2)
Fitting length (1)
Derived length (2)
Nilpotency class (2)
Minimum size of generating set (2)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Number of conjugacy classes (33)
Number of subgroups (41)
Number of conjugacy classes of subgroups (23)
SmallGroup(81,8)81 (8)Order of a group (81)
Exponent of a group (9)
Prime-base logarithm of order (4)
Prime-base logarithm of exponent (2)
Nilpotency class (3)
Derived length (2)
Frattini length (2)
Minimum size of generating set (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
SmallGroup(81,9)81 (9)Order of a group (81)
Exponent of a group (9)
Prime-base logarithm of order (4)
Prime-base logarithm of exponent (2)
Nilpotency class (3)
Derived length (2)
Frattini length (2)
Minimum size of generating set (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Special affine group:SA(2,3)216 (153)Order of a group (216)
Number of conjugacy classes (10)
Special linear group:SL(2,11)1,320 (13)Order of a group (1,320)
Number of conjugacy classes (15)
Special linear group:SL(2,3)24 (3)Order of a group (24)
Exponent of a group (12)
Derived length (3)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Max-length of a group (4)
Composition length (4)
Chief length (3)
Number of conjugacy classes (7)
Number of equivalence classes under rational conjugacy (5)
Number of conjugacy classes of rational elements (3)
Number of subgroups (15)
Number of conjugacy classes of subgroups (7)
Special linear group:SL(2,5)120 (5)Order of a group (120)
Exponent of a group (60)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Max-length of a group (5)
Composition length (2)
Number of conjugacy classes (9)
Number of equivalence classes under rational conjugacy (7)
Number of conjugacy classes of rational elements (5)
Number of conjugacy classes of subgroups (12)
Number of subgroups (76)
Special linear group:SL(2,7)336 (114)Order of a group (336)
Exponent of a group (168)
Frattini length (2)
Number of conjugacy classes (11)
Number of conjugacy classes of subgroups (19)
Number of subgroups (224)
Special linear group:SL(2,9)720 (409)Order of a group (720)
Exponent of a group (120)
Frattini length (2)
Minimum size of generating set (2)
Number of conjugacy classes (13)
Number of equivalence classes under rational conjugacy (10)
Number of subgroups (588)
Number of conjugacy classes of subgroups (27)
Special linear group:SL(2,Z4)48 (30)Order of a group (48)
Exponent of a group (12)
Derived length (3)
Frattini length (2)
Number of conjugacy classes (10)
Special linear group:SL(2,Z9)648 (641)Order of a group (648)
Exponent of a group (36)
Derived length (3)
Frattini length (2)
Fitting length (3)
Number of conjugacy classes (25)
Number of conjugacy classes of subgroups (48)
Number of subgroups (456)
Sylow subgroup of holomorph of Z27243 (22)Order of a group (243)
Exponent of a group (27)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Fitting length (1)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Number of conjugacy classes (35)
Symmetric group:S36 (1)Order of a group (6)
Exponent of a group (6)
Derived length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Max-length of a group (2)
Number of conjugacy classes (3)
Number of equivalence classes under real conjugacy (3)
Number of conjugacy classes of real elements (3)
Number of equivalence classes under rational conjugacy (3)
Number of conjugacy classes of rational elements (3)
Number of subgroups (6)
Number of conjugacy classes of subgroups (4)
Number of normal subgroups (3)
Number of automorphism classes of subgroups (4)
Symmetric group:S424 (12)Order of a group (24)
Exponent of a group (12)
Derived length (3)
Frattini length (1)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Max-length of a group (4)
Composition length (4)
Chief length (3)
Number of subgroups (30)
Number of conjugacy classes (5)
Number of conjugacy classes of subgroups (11)
Symmetric group:S5120 (34)Order of a group (120)
Exponent of a group (60)
Frattini length (1)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Max-length of a group (5)
Number of subgroups (156)
Number of conjugacy classes (7)
Number of conjugacy classes of subgroups (19)
Symmetric group:S6720 (763)Order of a group (720)
Exponent of a group (60)
Frattini length (1)
Minimum size of generating set (2)
Subgroup rank of a group (3)
Max-length of a group (6)
Composition length (2)
Chief length (2)
Number of conjugacy classes (11)
Number of conjugacy classes of subgroups (56)
Number of subgroups (1,455)
Triple cover of alternating group:A61,080 (260)Order of a group (1,080)
Exponent of a group (60)
Number of conjugacy classes (?)
Trivial group1 (1)Order of a group (1)
Exponent of a group (1)
Nilpotency class (0)
Derived length (0)
Frattini length (0)
Minimum size of generating set (0)
Subgroup rank of a group (0)
Unitriangular matrix group of degree three over quotient of polynomial ring over F2 by square of indeterminate64 (215)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (2)
Derived length (2)
Frattini length (2)
Minimum size of generating set (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Number of conjugacy classes (22)
Number of conjugacy classes of subgroups (173)
Number of subgroups (321)
Unitriangular matrix group:UT(3,3)27 (3)Underlying prime of p-group (3)
Order of a group (27)
Prime-base logarithm of order (3)
Exponent of a group (3)
Prime-base logarithm of exponent (1)
Frattini length (2)
Derived length (2)
Nilpotency class (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (1)
Unitriangular matrix group:UT(3,4)64 (242)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Frattini length (2)
Nilpotency class (2)
Derived length (2)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (4)
Unitriangular matrix group:UT(3,7)343 (3)
Unitriangular matrix group:UT(3,9)729 (469)Underlying prime of p-group (3)
Order of a group (729)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (3)
Prime-base logarithm of exponent (1)
Frattini length (2)
Nilpotency class (2)
Derived length (2)
Minimum size of generating set (4)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (2)
Unitriangular matrix group:UT(3,Z4)64 (18)Underlying prime of p-group (2)
Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (2)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Number of conjugacy classes (22)
Number of conjugacy classes of subgroups (47)
Number of subgroups (77)
Unitriangular matrix group:UT(3,Z9)729 (24)
Unitriangular matrix group:UT(4,2)64 (138)Order of a group (64)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (4)
Prime-base logarithm of exponent (2)
Nilpotency class (3)
Derived length (2)
Frattini length (2)
Number of conjugacy classes (16)
Number of conjugacy classes of subgroups (99)
Number of subgroups (225)
Unitriangular matrix group:UT(4,3)729 (307)Order of a group (729)
Prime-base logarithm of order (6)
Max-length of a group (6)
Chief length (6)
Composition length (6)
Exponent of a group (9)
Prime-base logarithm of exponent (2)
Nilpotency class (3)
Derived length (2)
Frattini length (2)
Wreath product of A4 and Z2288 (1025)Order of a group (288)
Wreath product of D8 and Z2128 (928)Underlying prime of p-group (2)
Order of a group (128)
Prime-base logarithm of order (7)
Max-length of a group (7)
Chief length (7)
Composition length (7)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Minimum size of generating set (3)
Subgroup rank of a group (4)
Rank of a p-group (4)
Normal rank of a p-group (4)
Characteristic rank of a p-group (2)
Wreath product of S3 and Z272 (40)Order of a group (72)
Wreath product of Z2 and A4192 (201)Order of a group (192)
Exponent of a group (12)
Minimum size of generating set (2)
Wreath product of Z2 and A51,920 (240997)Order of a group (1,920)
Exponent of a group (60)
Minimum size of generating set (2)
Wreath product of Z2 and Z464 (32)
Wreath product of Z3 and S3162 (10)Order of a group (162)
Wreath product of Z3 and Z381 (7)Order of a group (81)
Exponent of a group (9)
Nilpotency class (3)
Derived length (2)
Fitting length (1)
Frattini length (2)
Minimum size of generating set (2)
Subgroup rank of a group (2)
Rank of a p-group (3)
Normal rank of a p-group (3)
Characteristic rank of a p-group (3)
Wreath product of Z4 and Z232 (11)Underlying prime of p-group (2)
Order of a group (32)
Prime-base logarithm of order (5)
Exponent of a group (8)
Prime-base logarithm of exponent (3)
Nilpotency class (3)
Derived length (2)
Frattini length (3)
Minimum size of generating set (2)
Subgroup rank of a group (3)
Rank of a p-group (2)
Normal rank of a p-group (2)
Characteristic rank of a p-group (2)
Wreath product of Z5 and Z250 (3)Order of a group (50)
Exponent of a group (10)
Wreath product of Z6 and Z272 (30)Order of a group (72)