C₃₁×#3521 #16843454

order	3968
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₁×#3521

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ G

1042 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 992

A minimal faithful permutation representation — 5 generators on 55 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)(33,36)(37,39)(40,41)(42,48)(43,51)(44,45)(46,50)(47,52)(49,53)(54,55);(41,45)(46,48)(47,51)(53,54);(32,33)(34,37)(35,36)(38,39)(40,42,44,50)(41,46,45,48)(43,49,52,55)(47,53,51,54);(40,41)(42,46)(43,47)(44,45)(48,50)(49,53)(51,52)(54,55);(32,34,35,38)(33,37,36,39)(40,43)(41,47)(42,49)(44,52)(45,51)(46,53)(48,54)(50,55)

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#61486, C₃₁×#61487, C₃₁×#61500, …
maximal normal subgroup of	C₃₁×#61486, C₃₁×#61487, C₃₁×#61500, …
maximal quotient of	C₃₁×#34195, C₃₁×#34234, C₃₁×#34237, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2253);

C31×#3521 #16843454