C₃₁×#2359 #16842292

order	3968
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₁×#2359

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

652 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)(42,46)(43,44)(45,47);(36,38,39,37)(41,44)(45,46);(32,33)(34,35)(40,42,43,47)(41,45,44,46);(40,41)(42,45)(43,44)(46,47)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₁×#2359, C₃₁×#34136, C₃₁×#34149, …
maximal normal subgroup of	C₂×C₃₁×#2359, C₃₁×#34136, C₃₁×#34149, …
maximal quotient of	C₃₁×#13799, C₃₁×#13813, C₃₁×#13814, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1091);

C31×#2359 #16842292