C₃₁×#2858 #16842791

order	3968
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

direct product

C₃₁×#2858

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#127	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

752 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 264 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) = 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)(33,34)(37,38)(42,45)(43,47);(32,33,35,34)(36,37,39,38)(40,41,44,46)(42,43,45,47);(36,37,39,38)(40,42,44,45)(41,43,46,47);(32,34,35,33)(36,38,39,37)(40,43)(41,45)(42,46)(44,47)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#7659, C₃₁×#7679, C₃₁×#7699, …
maximal normal subgroup of	C₃₁×#7659, C₃₁×#7679, C₃₁×#7699, …
maximal quotient of	C₃₁×#14687, C₃₁×#14700, C₃₁×#14708, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1590);