| Alternating group:A4 | 12 (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:A5 | 60 (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:A6 | 360 (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:A6 | 1,440 (5841) | Order of a group (1,440)
Number of conjugacy classes (13) |
| Binary octahedral group | 48 (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 Z4 | 32 (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 Q8 | 32 (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 Z12 | 48 (47) | |
| Central product of D8 and Z16 | 64 (185) | |
| Central product of D8 and Z8 | 32 (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 Z2 | 64 (86) | |
| Central product of SL(2,3) and Z4 | 48 (33) | Order of a group (48) |
| Central product of SL(2,5) and Z4 | 240 (93) | Order of a group (240) |
| Central product of UT(3,3) and Z9 | 81 (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 Z3 | 243 (55) | |
| Cyclic group of prime-cube order | | Prime-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 order | | Prime-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:Z10 | 10 (2) | Order of a group (10)
Exponent of a group (10) |
| Cyclic group:Z12 | 12 (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:Z128 | 128 (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:Z16 | 16 (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:Z18 | 18 (2) | Order of a group (18)
Exponent of a group (18)
Frattini length (2) |
| Cyclic group:Z2 | 2 (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:Z20 | 20 (2) | Order of a group (20)
Exponent of a group (20)
Frattini length (2)
Fitting length (1)
Derived length (1) |
| Cyclic group:Z24 | 24 (2) | Order of a group (24)
Exponent of a group (24)
Nilpotency class (1)
Derived length (1) |
| Cyclic group:Z243 | 243 (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:Z27 | 27 (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:Z3 | 3 (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:Z32 | 32 (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:Z36 | 36 (2) | |
| Cyclic group:Z4 | 4 (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:Z40 | 40 (2) | |
| Cyclic group:Z5 | 5 (1) | Order of a group (5)
Exponent of a group (5)
Derived length (1)
Frattini length (1)
Fitting length (1) |
| Cyclic group:Z64 | 64 (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:Z7 | 7 (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:Z8 | 8 (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:Z81 | 81 (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:Z9 | 9 (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:Dic12 | 12 (1) | |
| Dicyclic group:Dic20 | 20 (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:Dic24 | 24 (4) | Order of a group (24)
Exponent of a group (12)
Derived length (2) |
| Dihedral group:D10 | 10 (1) | Order of a group (10)
Exponent of a group (10)
Fitting length (2)
Frattini length (1)
Derived length (2) |
| Dihedral group:D12 | 12 (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:D128 | 128 (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:D14 | 14 (1) | |
| Dihedral group:D16 | 16 (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:D18 | 18 (1) | |
| Dihedral group:D20 | 20 (4) | Order of group (20)
Order of a group (10)
Frattini length (1)
Fitting length (1)
Derived length (2) |
