C₃₁×#2865 #16842798

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₁×#2865

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₁
prime radical	C₂⁴×C₃₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 1984

A minimal faithful permutation representation — 4 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)(41,44)(42,46)(49,51)(53,54);(40,41)(42,45)(43,44)(46,47)(48,49,52,51)(50,53,55,54);(32,33,35,36)(34,37,38,39)(40,41)(42,45)(43,44)(46,47)(48,50,52,55)(49,53,51,54);(32,34)(33,37)(35,38)(36,39)(40,42,43,46)(41,45,44,47)(48,51,52,49)(50,54,55,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#35027, C₃₁×#35028, C₃₁×#35040, …
maximal normal subgroup of	C₃₁×#35027, C₃₁×#35028, C₃₁×#35040, …
maximal quotient of	C₃₁×#14690, C₃₁×#14701, C₃₁×#14704, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1597);

C31×#2865 #16842798