C₃₁×#2343 #16842276

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

Aliases

direct product

C₃₁×#2343

Subgroups

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

532 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 1984

A minimal faithful permutation representation — 4 generators on 51 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)(36,37)(38,41)(39,40)(42,43)(45,46)(49,50);(37,40)(41,43)(44,45,48,46)(47,50,51,49);(36,38,39,42)(37,41,40,43)(44,46,48,45)(47,50,51,49);(36,37)(38,41)(39,40)(42,43)(44,47)(45,49)(46,50)(48,51)

Conjugacy classes & character table

1550 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#17604, C₃₁×#17609, C₂×C₃₁×#2343, …
maximal normal subgroup of	C₃₁×#17604, C₃₁×#17609, C₂×C₃₁×#2343, …
maximal quotient of	C₃₁×#13799, C₃₁×#13805, C₃₁×#13806, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1075);

C31×#2343 #16842276