C₃₁×#3484 #16843417

order	3968
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₃₁×#3484

Subgroups

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

1900 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 496

A minimal faithful permutation representation — 5 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)(33,35)(36,37)(38,42)(39,40)(41,43);(37,40)(41,42);(32,33)(34,35);(36,37)(38,41)(39,40)(42,43);(36,38)(37,41)(39,43)(40,42)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#8453, C₃₁×#8534, C₃₁×#12705, …
maximal normal subgroup of	C₃₁×#8453, C₃₁×#8534, C₃₁×#12705, …
maximal quotient of	C₃₁×#34171, C₃₁×#34198, C₃₁×#34200, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2216);

C31×#3484 #16843417