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 | | |

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) |