C₃₁×#3586 #16843519

order	3968
nilpotency class	3
isoclinism	isoclinic class of #3585
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₃₁×#3586

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₃₁
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₁ ◁ C₂×#41×C₃₁ ◁ G

1412 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 992

A minimal faithful permutation representation — 5 generators on 63 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)(32,33)(34,42)(35,39)(36,48)(37,40)(38,44)(41,50)(43,56)(45,55)(46,53)(47,60)(49,52)(51,58)(54,59)(57,63)(61,62);(32,34,37,45)(33,38,40,52)(35,43,46,57)(36,49,50,44)(39,51,53,62)(41,55,48,42)(47,61,59,58)(54,63,60,56);(32,35)(33,39)(34,43)(36,47)(37,46)(38,51)(40,53)(41,54)(42,56)(44,58)(45,57)(48,60)(49,61)(50,59)(52,62)(55,63);(35,46)(39,53)(43,57)(47,59)(51,62)(54,60)(56,63)(58,61);(33,40)(38,52)(39,53)(41,48)(42,55)(51,62)(54,60)(56,63)

Conjugacy classes & character table

1271 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#23873, C₃₁×#23875, C₃₁×#23884, …
maximal normal subgroup of	C₃₁×#23873, C₃₁×#23875, C₃₁×#23884, …
maximal quotient of	C₃₁×#60088, C₃₁×#60089, C₃₁×#60109, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2318);

C31×#3586 #16843519