C₃₁×#3540 #16843473

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

Aliases

direct product

C₃₁×#3540

Subgroups

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

1058 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)(42,49)(43,46)(44,52)(45,48)(47,53)(50,54)(51,55);(33,36)(37,39)(40,42,45,43)(41,46,48,49)(44,50,53,51)(47,54,52,55);(32,33)(34,37)(35,36)(38,39)(40,43,45,42)(41,46,48,49)(44,51,53,50)(47,54,52,55);(32,34)(33,37)(35,38)(36,39)(40,41)(42,49)(43,46)(44,47)(45,48)(50,55)(51,54)(52,53);(40,44,45,53)(41,47,48,52)(42,50,43,51)(46,54,49,55)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#12756, C₃₁×#12758, C₃₁×#33555, …
maximal normal subgroup of	C₃₁×#12756, C₃₁×#12758, C₃₁×#33555, …
maximal quotient of	C₃₁×#34361, C₃₁×#34391, C₃₁×#34411, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2272);

C31×#3540 #16843473