| Braid group:B3 | | |
| 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) |
| 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) |
| Dihedral group:D10 | 10 (1) | Order of a group (10)
Exponent of a group (10)
Fitting length (2)
Frattini length (1)
Derived length (2) |
| Direct product of A4 and Z2 | 24 (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 D8 and Z2 | 16 (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 Z3 | 24 (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 E8 and Z4 | 32 (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 Z16 and V4 | 64 (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 Z27 and Z3 | 81 (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 Z4 and Z2 | 8 (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 Z8 and V4 | 32 (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 Z2 | 16 (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 Z8 | 64 (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 Z9 and Z9 | 81 (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) |
| Elementary abelian group:E64 | 64 (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:E8 | 8 (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:E9 | 9 (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) |
| Free group:F2 | | |
| Group of rational numbers modulo integers | | |
| Group of rational numbers with square-free denominators | | |
| Klein four-group | 4 (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) |
| Quotient of profinite completion of the integers by the integers | | |
| 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(32,35) | 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) |
| Sylow subgroup of holomorph of Z27 | 243 (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) |
