C₃₁×#2883 #16842816

order	3968
nilpotency class	3
isoclinism	isoclinic class of #2883
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₁ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₃₁×#2883

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₁	C₂²×C₂²⋊C₄
commutator	C₂²	C₂³×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁴×C₃₁
prime radical	C₂×C₃₁×H(5,𝔽₂)	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₁ ◁ C₂²×D₄×C₃₁ ◁ G

800 conjugacy classes of subgroups; only the 340 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 340 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) = 496

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

Conjugacy classes & character table

1271 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#13100, C₃₁×#13102, C₃₁×#21776, …
maximal normal subgroup of	C₃₁×#13100, C₃₁×#13102, C₃₁×#21776, …
maximal quotient of	C₃₁×#17350, C₃₁×#17351, C₃₁×#17367, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1615);