C₃₁×#2847 #16842780

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₃₁×#2847

Subgroups

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

1224 conjugacy classes of subgroups; only the 288 normal subgroups are shown.

normal subgroups only

This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 288 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 992

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)(33,35)(37,39)(41,43);(40,41,42,43);(36,37)(38,39);(32,33)(34,35)(36,37)(38,39)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#9113, C₃₁×#9117, C₃₁×#9147, …
maximal normal subgroup of	C₃₁×#9113, C₃₁×#9117, C₃₁×#9147, …
maximal quotient of	C₃₁×#14680, C₃₁×#14694, C₃₁×#14696, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1579);