,"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",