C₃₁×#387 #14520568

order	1984
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₃₁×#387

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₁	C₂³
commutator	C₂²	C₂²×C₄×C₃₁
Frattini, cosocle	C₂³	C₂³×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

154 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 90 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 — 3 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)(33,35)(36,37,39,38)(41,44)(42,46);(36,38,39,37)(40,41)(42,45)(43,44)(46,47);(32,33)(34,35)(40,42,43,46)(41,45,44,47)

Conjugacy classes & character table

868 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₃₁×#387, #16848149, #16848184, …
maximal subgroup of	C₂×C₃₁×#387, C₃₁×#2290, C₃₁×#2295, …
maximal normal subgroup of	C₂×C₃₁×#387, C₃₁×#2290, C₃₁×#2295, …
maximal quotient of	C₃₁×#1434, C₃₁×#1436, C₃₁×#1441, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 68);