C₃₁×#3560 #16843493

order	3968
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₁×#3560

Subgroups

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

1056 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)(34,38)(40,41)(42,45)(43,48)(44,49)(46,50)(47,52)(51,53)(54,55);(33,36)(37,39)(41,42)(43,50)(47,49)(51,55);(32,33)(34,37)(35,36)(38,39)(40,42,45,41)(43,48,50,46)(44,49,52,47)(51,54,55,53);(32,34,35,38)(33,37,36,39)(40,43)(41,46)(42,48)(44,51)(45,50)(47,53)(49,54)(52,55);(40,44)(41,47)(42,49)(43,51)(45,52)(46,53)(48,54)(50,55)

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#8489, C₃₁×#18248, C₃₁×#18249, …
maximal normal subgroup of	C₃₁×#8489, C₃₁×#18248, C₃₁×#18249, …
maximal quotient of	C₃₁×#34381, C₃₁×#34388, C₃₁×#34401, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2292);

C31×#3560 #16843493