,"GAP ID","Arithmetic function value"
"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","1440; 5841","Order of a group; 1440,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)","2187; 4487","Underlying prime of p-group; 3,Order of a group; 2187,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","3125; 30","Order of a group; 3125,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","3125; 33","Order of a group; 3125,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)","1320; 133","Order of a group; 1320"
"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)","1092; 25","Order of a group; 1092,Exponent of a group; 546,Frattini length; 1,Chief length; 1,Composition length; 1,Number of conjugacy classes; 9,Number of equivalence classes under rational conjugacy; 6,Number of conjugacy classes of subgroups; 16,Number of subgroups; 942"
"Projective special linear group:PSL(2,8)","504; 156","Order of a group; 504,Exponent of a group; 126,Number of conjugacy classes; 9,Number of conjugacy classes of subgroups; 12,Number of subgroups; 386"
"Projective special linear group:PSL(2,Z9)","324; 160","Order of a group; 324,Exponent of a group; 18,Derived length; 3,Frattini length; 1,Fitting length; 3,Number of conjugacy classes; 13,Number of conjugacy classes of subgroups; 32,Number of subgroups; 340"
"Projective special linear group:PSL(3,2)","168; 42","Order of a group; 168,Exponent of a group; 84,Frattini length; 1,Minimum size of generating set; 2,Subgroup rank of a group; 2,Max-length of a group; 5,Number of subgroups; 179,Number of conjugacy classes; 6,Number of conjugacy classes of subgroups; 15"
"Quaternion group","8; 4","Underlying prime of p-group; 2,Order of a group; 8,Prime-base logarithm of order; 3,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2,Frattini length; 2,Minimum size of generating set; 2,Subgroup rank of a group; 2,Rank of a p-group; 1,Normal rank of a p-group; 1,Characteristic rank of a p-group; 1,Number of conjugacy classes; 5,Number of equivalence classes under real conjugacy; 5,Number of conjugacy classes of real elements; 5,Number of equivalence classes under rational conjugacy; 5,Number of conjugacy classes of rational elements; 5,Number of subgroups; 6,Number of conjugacy classes of subgroups; 6,Number of normal subgroups; 6,Number of automorphism classes of subgroups; 4"
"Ree group:Ree(3)","1512; 779","Order of a group; 1512,Exponent of a group; 126,Number of conjugacy classes; 11,Number of conjugacy classes of subgroups; 25,Number of subgroups; 1154"
"Semidihedral group:SD128","128; 162","Underlying prime of p-group; 2,Order of a group; 128,Prime-base logarithm of order; 7,Max-length of a group; 7,Chief length; 7,Composition length; 7,Exponent of a group; 64,Prime-base logarithm of exponent; 6,Nilpotency class; 6,Derived length; 2,Frattini length; 6,Minimum size of generating set; 2,Subgroup rank of a group; 2,Rank of a p-group; 2,Normal rank of a p-group; 1,Characteristic rank of a p-group; 1"
"Semidihedral group:SD16","16; 8","Underlying prime of p-group; 2,Order of a group; 16,Prime-base logarithm of order; 4,Max-length of a group; 4,Chief length; 4,Composition length; 4,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 3,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Subgroup rank of a group; 2,Rank of a p-group; 2,Normal rank of a p-group; 1,Characteristic rank of a p-group; 1,Number of conjugacy classes; 7,Number of equivalence classes under rational conjugacy; 6,Number of conjugacy classes of rational elements; 5"
"Semidihedral group:SD256","256; 540","Underlying prime of p-group; 2,Order of a group; 256,Prime-base logarithm of order; 8,Max-length of a group; 8,Chief length; 8,Composition length; 8,Exponent of a group; 128,Prime-base logarithm of exponent; 7,Nilpotency class; 7,Derived length; 2,Frattini length; 7,Minimum size of generating set; 2,Subgroup rank of a group; 2,Rank of a p-group; 2,Normal rank of a p-group; 1,Characteristic rank of a p-group; 1"
"Semidihedral group:SD32","32; 19","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Max-length of a group; 5,Chief length; 5,Composition length; 5,Exponent of a group; 16,Prime-base logarithm of exponent; 4,Nilpotency class; 4,Derived length; 2,Frattini length; 4,Minimum size of generating set; 2,Subgroup rank of a group; 2,Rank of a p-group; 2,Normal rank of a p-group; 1,Characteristic rank of a p-group; 1"
"Semidihedral group:SD64","64; 53","Underlying prime of p-group; 2,Order of a group; 64,Prime-base logarithm of order; 6,Max-length of a group; 6,Chief length; 6,Composition length; 6,Exponent of a group; 32,Prime-base logarithm of exponent; 5,Nilpotency class; 5,Derived length; 2,Frattini length; 5,Minimum size of generating set; 2,Subgroup rank of a group; 2,Rank of a p-group; 2,Normal rank of a p-group; 1,Characteristic rank of a p-group; 1"
"Semidirect product of Z16 and Z4 of M-type","64; 27",
"Semidirect product of Z16 and Z4 of dihedral type","64; 47",
"Semidirect product of Z16 and Z4 of semidihedral type","64; 48",
"Semidirect product of Z16 and Z4 via cube map","64; 46",
"Semidirect product of Z16 and Z4 via fifth power map","64; 28",
"Semidirect product of Z3 and D8 with action kernel V4","24; 8","Order of a group; 24,Exponent of a group; 12,Derived length; 2,Fitting length; 2,Frattini length; 2,Minimum size of generating set; 2"
"Semidirect product of Z5 and Z8 via inverse map","40; 1",
"Semidirect product of Z5 and Z8 via square map","40; 3",
"Semidirect product of Z8 and Z4 of M-type","32; 4","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Max-length of a group; 5,Chief length; 5,Composition length; 5,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 2,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Subgroup rank of a group; 2,Rank of a p-group; 2,Normal rank of a p-group; 2,Characteristic rank of a p-group; 2"
"Semidirect product of Z8 and Z4 of dihedral type","32; 14","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 3,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Subgroup rank of a group; 2,Rank of a p-group; 2,Normal rank of a p-group; 2,Characteristic rank of a p-group; 2"
"Semidirect product of Z8 and Z4 of semidihedral type","32; 13","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 3,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Subgroup rank of a group; 2,Rank of a p-group; 2,Normal rank of a p-group; 2,Characteristic rank of a p-group; 2"
"Semidirect product of Z8 and Z8 of M-type","64; 3",
"Semidirect product of Z8 and Z8 of dihedral type","64; 16",
"Semidirect product of Z8 and Z8 of semidihedral type","64; 15",
"Semidirect product of cyclic group of prime-cube order and cyclic group of prime order",,
"SmallGroup(128,1015)","128; 1015","Underlying prime of p-group; 2,Order of a group; 128,Prime-base logarithm of order; 7,Max-length of a group; 7,Chief length; 7,Composition length; 7,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2,Frattini length; 2,Minimum size of generating set; 4,Rank of a p-group; 4,Normal rank of a p-group; 4,Characteristic rank of a p-group; 4"
"SmallGroup(16,3)","16; 3","Underlying prime of p-group; 2,Order of a group; 16,Prime-base logarithm of order; 4,Max-length of a group; 4,Chief length; 4,Composition length; 4,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2,Frattini length; 2,Minimum size of generating set; 2,Subgroup rank of a group; 3,Rank of a p-group; 3,Normal rank of a p-group; 3,Characteristic rank of a p-group; 3,Number of conjugacy classes; 10,Number of conjugacy classes of subgroups; 17"
"SmallGroup(243,16)","243; 16","Underlying prime of p-group; 3,Order of a group; 243,Prime-base logarithm of order; 5,Exponent of a group; 27,Prime-base logarithm of exponent; 3,Nilpotency class; 3,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Rank of a p-group; 3,Normal rank of a p-group; 3"
"SmallGroup(243,19)","243; 19","Underlying prime of p-group; 3,Order of a group; 243,Prime-base logarithm of order; 5,Exponent of a group; 27,Prime-base logarithm of exponent; 3,Nilpotency class; 3,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Rank of a p-group; 2,Normal rank of a p-group; 2"
"SmallGroup(243,20)","243; 20","Underlying prime of p-group; 3,Order of a group; 243,Prime-base logarithm of order; 5,Exponent of a group; 27,Prime-base logarithm of exponent; 3,Nilpotency class; 3,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Rank of a p-group; 2,Normal rank of a p-group; 2"
"SmallGroup(256,27799)","256; 27799",
"SmallGroup(256,29626)","256; 29626",
"SmallGroup(256,6745)","256; 6745","Underlying prime of p-group; 2,Order of a group; 256,Prime-base logarithm of order; 8,Max-length of a group; 8,Chief length; 8,Composition length; 8,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2"
"SmallGroup(32,10)","32; 10","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 3,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Subgroup rank of a group; 3,Rank of a p-group; 2,Normal rank of a p-group; 2,Characteristic rank of a p-group; 2"
"SmallGroup(32,15)","32; 15","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Max-length of a group; 5,Chief length; 5,Composition length; 5,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 3,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Subgroup rank of a group; 2,Rank of a p-group; 2,Normal rank of a p-group; 2,Characteristic rank of a p-group; 2"
"SmallGroup(32,2)","32; 2","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Max-length of a group; 5,Chief length; 5,Composition length; 5,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Frattini length; 2,Nilpotency class; 2,Derived length; 2,Minimum size of generating set; 2,Subgroup rank of a group; 3,Rank of a p-group; 3,Normal rank of a p-group; 3,Characteristic rank of a p-group; 3"
"SmallGroup(32,24)","32; 24","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2,Frattini length; 2,Minimum size of generating set; 3,Subgroup rank of a group; 3,Rank of a p-group; 3,Normal rank of a p-group; 3,Characteristic rank of a p-group; 3"
"SmallGroup(32,27)","32; 27","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2,Frattini length; 2,Minimum size of generating set; 3,Subgroup rank of a group; 4,Rank of a p-group; 4,Normal rank of a p-group; 4,Characteristic rank of a p-group; 4"
"SmallGroup(32,28)","32; 28","Underlying prime; 2,Order of a group; 32,Prime-base logarithm of order; 5,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2,Frattini length; 2,Minimum size of generating set; 3,Subgroup rank of a group; 3,Rank of a p-group; 3,Normal rank of a p-group; 3,Characteristic rank of a p-group; 3"
"SmallGroup(32,29)","32; 29","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2,Frattini length; 2,Minimum size of generating set; 3,Subgroup rank of a group; 3,Rank of a p-group; 3,Normal rank of a p-group; 3,Characteristic rank of a p-group; 3"
"SmallGroup(32,30)","32; 30","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Max-length of a group; 5,Chief length; 5,Composition length; 5,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2,Frattini length; 2,Minimum size of generating set; 3,Subgroup rank of a group; 3,Rank of a p-group; 3,Normal rank of a p-group; 3,Characteristic rank of a p-group; 3"
"SmallGroup(32,31)","32; 31","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Max-length of a group; 5,Chief length; 5,Composition length; 5,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2,Frattini length; 2,Fitting length; 1,Minimum size of generating set; 3,Subgroup rank of a group; 3,Rank of a p-group; 3,Normal rank of a p-group; 3,Characteristic rank of a p-group; 2"
"SmallGroup(32,32)","32; 32","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2,Frattini length; 2,Minimum size of generating set; 3,Subgroup rank of a group; 3,Rank of a p-group; 2,Normal rank of a p-group; 2,Characteristic rank of a p-group; 2"
"SmallGroup(32,33)","32; 33","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Max-length of a group; 5,Chief length; 5,Composition length; 5,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2,Frattini length; 2,Fitting length; 1,Minimum size of generating set; 3,Subgroup rank of a group; 3,Rank of a p-group; 3,Normal rank of a p-group; 3,Characteristic rank of a p-group; 3"
"SmallGroup(32,35)","32; 35","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Max-length of a group; 5,Chief length; 5,Composition length; 5,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2,Frattini length; 2,Minimum size of generating set; 3,Subgroup rank of a group; 3,Rank of a p-group; 2,Normal rank of a p-group; 2,Characteristic rank of a p-group; 2"
"SmallGroup(32,44)","32; 44","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Max-length of a group; 5,Chief length; 5,Composition length; 5,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 3,Derived length; 2,Frattini length; 3,Minimum size of generating set; 3,Subgroup rank of a group; 3,Rank of a p-group; 2,Normal rank of a p-group; 2,Characteristic rank of a p-group; 2"
"SmallGroup(32,5)","32; 5","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 2,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Subgroup rank of a group; 3,Rank of a p-group; 3,Normal rank of a p-group; 3,Characteristic rank of a p-group; 3"
"SmallGroup(32,7)","32; 7","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 3,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Subgroup rank of a group; 3,Rank of a p-group; 3,Normal rank of a p-group; 3,Characteristic rank of a p-group; 2"
"SmallGroup(32,8)","32; 8","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Max-length of a group; 5,Chief length; 5,Composition length; 5,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Frattini length; 3,Nilpotency class; 3,Derived length; 2,Minimum size of generating set; 2,Subgroup rank of a group; 3,Rank of a p-group; 2,Normal rank of a p-group; 2,Characteristic rank of a p-group; 2"
"SmallGroup(32,9)","32; 9","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 3,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Subgroup rank of a group; 3,Rank of a p-group; 3,Normal rank of a p-group; 2,Characteristic rank of a p-group; 2"
"SmallGroup(64,113)","64; 113","Underlying prime of p-group; 2,Order of a group; 64,Prime-base logarithm of order; 6,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 2,Derived length; 2,Frattini length; 3,Minimum size of generating set; 3,Rank of a p-group; 3,Normal rank of a p-group; 3"
"SmallGroup(64,114)","64; 114","Underlying prime of p-group; 2,Order of a group; 64,Prime-base logarithm of order; 6,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 2,Derived length; 2,Frattini length; 3,Minimum size of generating set; 3,Rank of a p-group; 3,Normal rank of a p-group; 3"
"SmallGroup(64,17)","64; 17","Underlying prime of p-group; 2,Order of a group; 64,Prime-base logarithm of order; 6,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 2,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Rank of a p-group; 3,Normal rank of a p-group; 3"
"SmallGroup(64,210)","64; 210","Underlying prime of p-group; 2,Order of a group; 64,Prime-base logarithm of order; 6,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2,Frattini length; 2,Minimum size of generating set; 4,Rank of a p-group; 3,Normal rank of a p-group; 3"
"SmallGroup(64,248)","64; 248",
"SmallGroup(64,25)","64; 25","Order of a group; 64,Prime-base logarithm of order; 6,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 3,Derived length; 2,Frattini length; 3"
"SmallGroup(64,57)","64; 57",
"SmallGroup(81,3)","81; 3","Order of a group; 81,Exponent of a group; 9,Frattini length; 2,Fitting length; 1,Derived length; 2,Nilpotency class; 2,Minimum size of generating set; 2,Rank of a p-group; 3,Normal rank of a p-group; 3,Characteristic rank of a p-group; 3,Number of conjugacy classes; 33,Number of subgroups; 41,Number of conjugacy classes of subgroups; 23"
"SmallGroup(81,8)","81; 8","Order of a group; 81,Exponent of a group; 9,Prime-base logarithm of order; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 3,Derived length; 2,Frattini length; 2,Minimum size of generating set; 2,Rank of a p-group; 2,Normal rank of a p-group; 2"
"SmallGroup(81,9)","81; 9","Order of a group; 81,Exponent of a group; 9,Prime-base logarithm of order; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 3,Derived length; 2,Frattini length; 2,Minimum size of generating set; 2,Rank of a p-group; 2,Normal rank of a p-group; 2"
"Special affine group:SA(2,3)","216; 153","Order of a group; 216,Number of conjugacy classes; 10"
"Special linear group:SL(2,11)","1320; 13","Order of a group; 1320,Number of conjugacy classes; 15"
"Special linear group:SL(2,3)","24; 3","Order of a group; 24,Exponent of a group; 12,Derived length; 3,Frattini length; 2,Minimum size of generating set; 2,Subgroup rank of a group; 2,Max-length of a group; 4,Composition length; 4,Chief length; 3,Number of conjugacy classes; 7,Number of equivalence classes under rational conjugacy; 5,Number of conjugacy classes of rational elements; 3,Number of subgroups; 15,Number of conjugacy classes of subgroups; 7"
"Special linear group:SL(2,5)","120; 5","Order of a group; 120,Exponent of a group; 60,Frattini length; 2,Minimum size of generating set; 2,Subgroup rank of a group; 2,Max-length of a group; 5,Composition length; 2,Number of conjugacy classes; 9,Number of equivalence classes under rational conjugacy; 7,Number of conjugacy classes of rational elements; 5,Number of conjugacy classes of subgroups; 12,Number of subgroups; 76"
"Special linear group:SL(2,7)","336; 114","Order of a group; 336,Exponent of a group; 168,Frattini length; 2,Number of conjugacy classes; 11,Number of conjugacy classes of subgroups; 19,Number of subgroups; 224"
"Special linear group:SL(2,9)","720; 409","Order of a group; 720,Exponent of a group; 120,Frattini length; 2,Minimum size of generating set; 2,Number of conjugacy classes; 13,Number of equivalence classes under rational conjugacy; 10,Number of subgroups; 588,Number of conjugacy classes of subgroups; 27"
"Special linear group:SL(2,Z4)","48; 30","Order of a group; 48,Exponent of a group; 12,Derived length; 3,Frattini length; 2,Number of conjugacy classes; 10"
"Special linear group:SL(2,Z9)","648; 641","Order of a group; 648,Exponent of a group; 36,Derived length; 3,Frattini length; 2,Fitting length; 3,Number of conjugacy classes; 25,Number of conjugacy classes of subgroups; 48,Number of subgroups; 456"
"Sylow subgroup of holomorph of 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"
"Symmetric group:S3","6; 1","Order of a group; 6,Exponent of a group; 6,Derived length; 2,Minimum size of generating set; 2,Subgroup rank of a group; 2,Max-length of a group; 2,Number of conjugacy classes; 3,Number of equivalence classes under real conjugacy; 3,Number of conjugacy classes of real elements; 3,Number of equivalence classes under rational conjugacy; 3,Number of conjugacy classes of rational elements; 3,Number of subgroups; 6,Number of conjugacy classes of subgroups; 4,Number of normal subgroups; 3,Number of automorphism classes of subgroups; 4"
"Symmetric group:S4","24; 12","Order of a group; 24,Exponent of a group; 12,Derived length; 3,Frattini length; 1,Minimum size of generating set; 2,Subgroup rank of a group; 2,Max-length of a group; 4,Composition length; 4,Chief length; 3,Number of subgroups; 30,Number of conjugacy classes; 5,Number of conjugacy classes of subgroups; 11"
"Symmetric group:S5","120; 34","Order of a group; 120,Exponent of a group; 60,Frattini length; 1,Minimum size of generating set; 2,Subgroup rank of a group; 2,Max-length of a group; 5,Number of subgroups; 156,Number of conjugacy classes; 7,Number of conjugacy classes of subgroups; 19"
"Symmetric group:S6","720; 763","Order of a group; 720,Exponent of a group; 60,Frattini length; 1,Minimum size of generating set; 2,Subgroup rank of a group; 3,Max-length of a group; 6,Composition length; 2,Chief length; 2,Number of conjugacy classes; 11,Number of conjugacy classes of subgroups; 56,Number of subgroups; 1455"
"Triple cover of alternating group:A6","1080; 260","Order of a group; 1080,Exponent of a group; 60,Number of conjugacy classes; ?"
"Trivial group","1; 1","Order of a group; 1,Exponent of a group; 1,Nilpotency class; 0,Derived length; 0,Frattini length; 0,Minimum size of generating set; 0,Subgroup rank of a group; 0"
"Unitriangular matrix group of degree three over quotient of polynomial ring over F2 by square of indeterminate","64; 215","Underlying prime of p-group; 2,Order of a group; 64,Prime-base logarithm of order; 6,Max-length of a group; 6,Chief length; 6,Composition length; 6,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 2,Derived length; 2,Frattini length; 2,Minimum size of generating set; 4,Rank of a p-group; 4,Normal rank of a p-group; 4,Number of conjugacy classes; 22,Number of conjugacy classes of subgroups; 173,Number of subgroups; 321"
"Unitriangular matrix group:UT(3,3)","27; 3","Underlying prime of p-group; 3,Order of a group; 27,Prime-base logarithm of order; 3,Exponent of a group; 3,Prime-base logarithm of exponent; 1,Frattini length; 2,Derived length; 2,Nilpotency class; 2,Minimum size of generating set; 2,Subgroup rank of a group; 2,Rank of a p-group; 2,Normal rank of a p-group; 2,Characteristic rank of a p-group; 1"
"Unitriangular matrix group:UT(3,4)","64; 242","Underlying prime of p-group; 2,Order of a group; 64,Prime-base logarithm of order; 6,Max-length of a group; 6,Chief length; 6,Composition length; 6,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Frattini length; 2,Nilpotency class; 2,Derived length; 2,Minimum size of generating set; 4,Subgroup rank of a group; 4,Rank of a p-group; 4,Normal rank of a p-group; 4,Characteristic rank of a p-group; 4"
"Unitriangular matrix group:UT(3,7)","343; 3",
"Unitriangular matrix group:UT(3,9)","729; 469","Underlying prime of p-group; 3,Order of a group; 729,Prime-base logarithm of order; 6,Max-length of a group; 6,Chief length; 6,Composition length; 6,Exponent of a group; 3,Prime-base logarithm of exponent; 1,Frattini length; 2,Nilpotency class; 2,Derived length; 2,Minimum size of generating set; 4,Subgroup rank of a group; 4,Rank of a p-group; 4,Normal rank of a p-group; 4,Characteristic rank of a p-group; 2"
"Unitriangular matrix group:UT(3,Z4)","64; 18","Underlying prime of p-group; 2,Order of a group; 64,Prime-base logarithm of order; 6,Max-length of a group; 6,Chief length; 6,Composition length; 6,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 2,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Rank of a p-group; 3,Normal rank of a p-group; 3,Characteristic rank of a p-group; 3,Number of conjugacy classes; 22,Number of conjugacy classes of subgroups; 47,Number of subgroups; 77"
"Unitriangular matrix group:UT(3,Z9)","729; 24",
"Unitriangular matrix group:UT(4,2)","64; 138","Order of a group; 64,Prime-base logarithm of order; 6,Max-length of a group; 6,Chief length; 6,Composition length; 6,Exponent of a group; 4,Prime-base logarithm of exponent; 2,Nilpotency class; 3,Derived length; 2,Frattini length; 2,Number of conjugacy classes; 16,Number of conjugacy classes of subgroups; 99,Number of subgroups; 225"
"Unitriangular matrix group:UT(4,3)","729; 307","Order of a group; 729,Prime-base logarithm of order; 6,Max-length of a group; 6,Chief length; 6,Composition length; 6,Exponent of a group; 9,Prime-base logarithm of exponent; 2,Nilpotency class; 3,Derived length; 2,Frattini length; 2"
"Wreath product of A4 and Z2","288; 1025","Order of a group; 288"
"Wreath product of D8 and Z2","128; 928","Underlying prime of p-group; 2,Order of a group; 128,Prime-base logarithm of order; 7,Max-length of a group; 7,Chief length; 7,Composition length; 7,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Minimum size of generating set; 3,Subgroup rank of a group; 4,Rank of a p-group; 4,Normal rank of a p-group; 4,Characteristic rank of a p-group; 2"
"Wreath product of S3 and Z2","72; 40","Order of a group; 72"
"Wreath product of Z2 and A4","192; 201","Order of a group; 192,Exponent of a group; 12,Minimum size of generating set; 2"
"Wreath product of Z2 and A5","1920; 240997","Order of a group; 1920,Exponent of a group; 60,Minimum size of generating set; 2"
"Wreath product of Z2 and Z4","64; 32",
"Wreath product of Z3 and S3","162; 10","Order of a group; 162"
"Wreath product of Z3 and Z3","81; 7","Order of a group; 81,Exponent of a group; 9,Nilpotency class; 3,Derived length; 2,Fitting length; 1,Frattini length; 2,Minimum size of generating set; 2,Subgroup rank of a group; 2,Rank of a p-group; 3,Normal rank of a p-group; 3,Characteristic rank of a p-group; 3"
"Wreath product of Z4 and Z2","32; 11","Underlying prime of p-group; 2,Order of a group; 32,Prime-base logarithm of order; 5,Exponent of a group; 8,Prime-base logarithm of exponent; 3,Nilpotency class; 3,Derived length; 2,Frattini length; 3,Minimum size of generating set; 2,Subgroup rank of a group; 3,Rank of a p-group; 2,Normal rank of a p-group; 2,Characteristic rank of a p-group; 2"
"Wreath product of Z5 and Z2","50; 3","Order of a group; 50,Exponent of a group; 10"
"Wreath product of Z6 and Z2","72; 30","Order of a group; 72"