C₃₁×#2428 #16842361

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₃₁×#2428

Subgroups

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

832 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1984

A minimal faithful permutation representation — 4 generators on 43 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)(33,34)(40,41,42,43);(32,33,35,34)(37,39)(40,41,42,43);(36,37)(38,39)(40,41)(42,43);(32,34,35,33)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#25148, C₃₁×#25153, C₃₁×#25159, …
maximal normal subgroup of	C₃₁×#25148, C₃₁×#25153, C₃₁×#25159, …
maximal quotient of	C₃₁×#13876, C₃₁×#13920, C₃₁×#13970, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1160);

C31×#2428 #16842361