C₃₁×#3585 #16843518

order	3968
nilpotency class	3
isoclinism	isoclinic class of #3585
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₃₁×#3585

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₃₁
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₁ ◁ C₂×#41×C₃₁ ◁ G

1464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 496

A minimal faithful permutation representation — 5 generators on 47 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)(34,38)(35,37)(36,39)(40,43)(41,45)(42,44)(46,47);(33,37)(35,43)(38,44)(39,40)(42,47)(45,46);(32,34)(33,38)(35,42)(36,41)(37,44)(39,45)(40,46)(43,47);(34,41)(38,45)(42,47)(44,46);(33,39)(37,40)(38,45)(44,46)

Conjugacy classes & character table

1271 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#23872, C₃₁×#23874, C₃₁×#23882, …
maximal normal subgroup of	C₃₁×#23872, C₃₁×#23874, C₃₁×#23882, …
maximal quotient of	C₃₁×#60087, C₃₁×#60089, C₃₁×#60109, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2317);

C31×#3585 #16843518