C₃₁×#577 #14520758

order	1984
nilpotency class	3
isoclinism	isoclinic class of #576
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₁×#577

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₄	C₂⁴×C₃₁
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₁ ◁ #41×C₃₁ ◁ G

258 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 158 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)(32,33,36,40)(34,38,41,45)(35,37,43,39)(42,44,47,46);(33,37)(35,43)(38,44)(39,40)(42,47)(45,46);(32,34)(33,38)(35,42)(36,41)(37,44)(39,46)(40,45)(43,47);(34,41)(38,45)(42,47)(44,46)

Conjugacy classes & character table

682 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16857473, #16857484, #16857491, …
maximal subgroup of	C₃₁×#3288, C₃₁×#3289, C₃₁×#3290, …
maximal normal subgroup of	C₃₁×#3288, C₃₁×#3289, C₃₁×#3290, …
maximal quotient of	C₃₁×#2897, C₃₁×#2898, C₃₁×#2912, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 258);