C₃₁×#535 #14520716

order	1984
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₃₁×#535

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ G

334 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 162 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) = 496

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

Conjugacy classes & character table

682 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16846239, #16846244, #16846259, …
maximal subgroup of	C₃₁×#1910, C₃₁×#1911, C₃₁×#1914, …
maximal normal subgroup of	C₃₁×#1910, C₃₁×#1911, C₃₁×#1914, …
maximal quotient of	C₃₁×#2309, C₃₁×#2311, C₃₁×#2317, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 216);