C₃₁×#2253 #16842186

order	3968
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃₁×#2253

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ C₄×C₈×C₃₁ ◁ G

116 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 3968

A minimal faithful permutation representation — 3 generators on 71 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)(32,33,35,37)(34,38,39,36)(40,41,43,46)(42,50,52,64)(44,57,55,70)(45,58,56,49)(47,61,59,53)(48,63,60,51)(54,69,68,66)(62,67,65,71);(32,34,35,39)(33,36,37,38)(41,46)(47,59)(48,60)(49,58)(50,64)(57,70)(62,65)(66,69);(40,42,51,67,45,54,55,61,43,52,63,71,56,68,44,53)(41,47,57,66,49,62,60,64,46,59,70,69,58,65,48,50)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#7452, C₃₁×#7454, C₃₁×#12463, …
maximal normal subgroup of	C₃₁×#7452, C₃₁×#7454, C₃₁×#12463, …
maximal quotient of	C₃₁×#12907, C₃₁×#13165, C₃₁×#13166, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 985);

C31×#2253 #16842186