C₃₁×#2551 #16842484

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₁×#2551

Subgroups

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

556 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 280 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) = 47
transitive degree	μ_t(G) = 3968

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

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#10348, C₃₁×#10349, C₃₁×#10350, …
maximal normal subgroup of	C₃₁×#10348, C₃₁×#10349, C₃₁×#10350, …
maximal quotient of	C₃₁×#13910, C₃₁×#14005, C₃₁×#14053, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1283);