C₃₁×#2285 #16842218

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

Aliases

direct product

C₃₁×#2285

Subgroups

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

656 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)(36,37,38,39)(40,41)(42,45)(43,44)(46,47);(41,44)(45,47);(32,33,34,35);(40,42,43,46)(41,45,44,47)

Conjugacy classes & character table

1736 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#7893, C₃₁×#7896, C₃₁×#7897, …
maximal normal subgroup of	C₃₁×#7893, C₃₁×#7896, C₃₁×#7897, …
maximal quotient of	C₃₁×#13755, C₃₁×#13756, C₄×C₃₁×#380, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1017);

C31×#2285 #16842218