C₃₁×#2404 #16842337

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₃₁×#2404

Subgroups

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

1056 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 992

A minimal faithful permutation representation — 4 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)(37,39)(41,44)(42,46);(33,35)(37,39)(40,41,43,44)(42,45,46,47);(32,33)(34,35)(36,37)(38,39)(40,41)(42,45)(43,44)(46,47);(40,42)(41,45)(43,46)(44,47)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#9475, C₃₁×#9479, C₃₁×#9511, …
maximal normal subgroup of	C₃₁×#9475, C₃₁×#9479, C₃₁×#9511, …
maximal quotient of	C₃₁×#13868, C₃₁×#13956, C₃₁×#13967, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1136);

C31×#2404 #16842337