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 Z4 | 16 (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 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) |

Dihedral group:D24 | 24 (6) | |

Dihedral group:D256 | 256 (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:D32 | 32 (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:D64 | 64 (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:D8 | 8 (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 A4 | 144 (184) | |

Direct product of A4 and D8 | 96 (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 E8 | 96 (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 Q8 | 96 (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 S3 | 72 (44) | Order of a group (72) Exponent of a group (6) Derived length (2) |

Direct product of A4 and V4 | 48 (49) | |

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 A4 and Z3 | 36 (11) | |

Direct product of A4 and Z4 | 48 (31) | |

Direct product of A4 and Z4 and Z2 | 96 (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 Z5 | 60 (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 Z8 | 96 (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 V4 | 240 (190) | Order of a group (240) |

Direct product of A5 and Z2 | 120 (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 Z4 | 240 (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 Z7 | 420 (13) | |

Direct product of A6 and Z2 | 720 (766) | Order of a group (720) Exponent of a group (60) |

Direct product of D12 and Z2 | 24 (14) | |

Direct product of D12 and Z3 | 36 (12) | |

Direct product of D16 and V4 | 64 (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 Z2 | 32 (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 Z3 | 48 (25) | |

Direct product of D16 and Z4 | 64 (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 Z2 | 64 (186) | |

Direct product of D8 and D8 | 64 (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 E8 | 64 (261) | |

Direct product of D8 and Q8 | 64 (230) | |

Direct product of D8 and S3 | 48 (38) | |

Direct product of D8 and V4 | 32 (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 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 D8 and Z4 | 32 (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 Z2 | 64 (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 Z5 | 40 (10) | |

Direct product of D8 and Z6 | 48 (45) | |

Direct product of D8 and Z7 | 56 (9) | |

Direct product of Dic12 and Z2 | 24 (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 Z4 | 64 (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 Z3 | 24 (15) | Order of a group (24) Exponent of a group (6) Frattini length (3) |

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 M16 and V4 | 64 (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 Z2 | 32 (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 Z3 | 48 (24) | |

Direct product of M16 and Z4 | 64 (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 Z3 | 81 (13) | |

Direct product of M32 and Z2 | 64 (184) | |

Direct product of Mp^3 and Zp | | |

Direct product of Q16 and V4 | 64 (252) | |

Direct product of Q16 and Z2 | 32 (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 Z3 | 48 (27) | |

Direct product of Q16 and Z4 | 64 (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 Z2 | 64 (188) | |

Direct product of Q8 and Q8 | 64 (239) | |

Direct product of Q8 and S3 | 48 (40) | |

Direct product of Q8 and V4 | 32 (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 Z2 | 16 (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 Z3 | 24 (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 Z4 | 32 (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 Z5 | 40 (11) | |

Direct product of S3 and S3 | 36 (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 Z3 | 18 (3) | |

Direct product of S3 and Z4 | 24 (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 V4 | 96 (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 Z2 | 48 (48) | |

Direct product of S4 and Z3 | 72 (42) | Order of a group (72) |

Direct product of S4 and Z4 | 96 (186) | Order of a group (96) Exponent of a group (12) Minimum size of generating set (2) |

Direct product of S4 and Z5 | 120 (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 Z2 | 240 (189) | |

Direct product of SD16 and V4 | 64 (251) | |

Direct product of SD16 and Z2 | 32 (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 Z3 | 48 (26) | |

Direct product of SD16 and Z4 | 64 (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 Z2 | 64 (187) | |

Direct product of SL(2,3) and V4 | 96 (198) | Order of a group (96) Exponent of a group (12) Derived length (3) |

Direct product of SL(2,3) and Z2 | 48 (32) | Order of a group (48) Exponent of a group (12) Derived length (3) |

Direct product of SL(2,3) and Z3 | 72 (25) | Order of a group (72) |

Direct product of SL(2,3) and Z4 | 96 (69) | Order of a group (96) Exponent of a group (12) Derived length (3) |

Direct product of SL(2,5) and Z2 | 240 (94) | Order of a group (240) |

Direct product of SmallGroup(16,13) and V4 | 64 (263) | |

Direct product of SmallGroup(16,13) and Z2 | 32 (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 Z4 | 64 (198) | |

Direct product of SmallGroup(16,3) and V4 | 64 (193) | |

Direct product of SmallGroup(16,3) and Z2 | 32 (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 Z3 | 48 (21) | |

Direct product of SmallGroup(16,3) and Z4 | 64 (58) | |

Direct product of SmallGroup(16,4) and V4 | 64 (194) | |

Direct product of SmallGroup(16,4) and Z2 | 32 (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 Z4 | 64 (59) | |

Direct product of SmallGroup(32,12) and Z2 | 64 (103) | |

Direct product of SmallGroup(32,13) and Z2 | 64 (106) | |

Direct product of SmallGroup(32,14) and Z2 | 64 (107) | |

Direct product of SmallGroup(32,2) and Z2 | 64 (56) | |

Direct product of SmallGroup(32,24) and Z2 | 64 (195) | |

Direct product of SmallGroup(32,27) and Z2 | 64 (202) | |

Direct product of SmallGroup(32,33) and Z2 | 64 (209) | |

Direct product of SmallGroup(32,4) and Z2 | 64 (84) | |

Direct product of SmallGroup(32,49) and Z2 | 64 (264) | |

Direct product of SmallGroup(32,50) and Z2 | 64 (265) | |

Direct product of Z10 and Z2 | 20 (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 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 Z16 and Z2 | 32 (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 Z4 | 64 (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 E9 | 243 (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 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 Z27 and Z9 | 243 (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 Z2 | 64 (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 V4 | 16 (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 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 Z4 and Z4 | 16 (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 V4 | 64 (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 Z2 | 32 (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 Z4 | 64 (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 Z2 | 12 (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 Z3 | 18 (5) | Order of a group (18) Exponent of a group (6) Derived length (1) Nilpotency class (1) |

Direct product of Z6 and Z4 | 24 (9) | |

Direct product of Z8 and D8 | 64 (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 E8 | 64 (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 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 Z4 | 32 (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 V4 | 128 (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 Z2 | 64 (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 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 Z81 and Z3 | 243 (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 E27 | 243 (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 E9 | 81 (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 Z3 | 27 (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 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) |

Direct product of Z9 and Z9 and Z3 | 243 (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 order | | Prime-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 order | | Prime-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 order | | Prime-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 order | | Prime-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 Z2 | 64 (254) | |

Direct product of prime-cube order group:U(3,3) and Z3 | 81 (12) | |

Double cover of symmetric group:S5 of minus type | 240 (89) | Order of a group (240) |

Double cover of symmetric group:S5 of plus type | 240 (90) | Order of a group (240) |

Elementary abelian 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 (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 order | | Prime-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:E16 | 16 (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:E243 | 243 (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:E27 | 27 (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:E32 | 32 (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: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:E81 | 81 (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: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) |

Faithful semidirect product of E8 and Z4 | 32 (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-groups | 256 (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 E9 | 18 (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 Z4 | 32 (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:Q16 | 16 (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:Q32 | 32 (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:Q64 | 64 (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 D8 | 64 (134) | |

Holomorph of Z8 | 32 (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 Z9 | 54 (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 A4 | 96 (70) | |

Inner automorphism group of wreath product of Z2 and A5 | 960 (11358) | |

Inner automorphism group of wreath product of Z5 and Z5 | 3,125 (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 D8 | 32 (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-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) |

M16 | 16 (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) |

M27 | 27 (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) |

M32 | 32 (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) |

M64 | 64 (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) |

M81 | 81 (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:M10 | 720 (765) | Order of a group (720) Exponent of a group (120) Frattini length (1) |

Mathieu group:M9 | 72 (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 Z8 | 24 (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 Z16 | 64 (44) | |

Nontrivial semidirect product of Z4 and Z4 | 16 (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 Z8 | 32 (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 Z9 | 63 (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 Z9 | 81 (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 5 | 3,125 (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) |