C₃₁×#2326 #16842259

order	3968
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₁ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₃₁×#2326

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator	C₂²	C₂³×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

612 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)(33,35)(36,37,39,38)(40,41)(42,44)(43,46)(45,47);(36,38,39,37)(41,42)(45,46);(32,33,34,35)(40,42,44,41)(43,46,47,45);(40,43,44,47)(41,45,42,46)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#9099, C₃₁×#9102, C₃₁×#9103, …
maximal normal subgroup of	C₃₁×#9099, C₃₁×#9102, C₃₁×#9103, …
maximal quotient of	C₃₁×#13779, C₃₁×#13785, C₃₁×#13786, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1058);

C31×#2326 #16842259