C₃₁×#2361 #16842294

order	3968
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₁ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₃₁×#2361

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator	C₂²	C₂³×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1984

A minimal faithful permutation representation — 4 generators on 43 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)(32,33,35,34)(37,39)(40,41,43,42);(33,34)(40,42,43,41);(36,37)(38,39);(32,34,35,33)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#22855, C₃₁×#22858, C₃₁×#22863, …
maximal normal subgroup of	C₃₁×#22855, C₃₁×#22858, C₃₁×#22863, …
maximal quotient of	C₂²⋊C₄×C₄⋊C₄×C₃₁, C₃₁×#13813, C₃₁×#13820, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1093);

C31×#2361 #16842294