C₃₁×#2540 #16842473

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₃₁×#2540

Subgroups

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

760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1984

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)(32,33,34,35)(40,41)(42,46)(43,45)(44,47);(36,37,38,39)(40,41,43,45)(42,44,47,46);(32,33)(34,35)(36,37)(38,39)(40,41)(42,44)(43,45)(46,47);(40,42,43,47)(41,44,45,46)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#10004, C₃₁×#10008, C₃₁×#18272, …
maximal normal subgroup of	C₃₁×#10004, C₃₁×#10008, C₃₁×#18272, …
maximal quotient of	C₃₁×#13905, C₃₁×#13954, C₃₁×#13997, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1272);

C31×#2540 #16842473