C₂₃×#1580 #15669199

order	2944
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1580

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂×D₄
commutator	C₄	C₂²×C₈×C₂₃
Frattini, cosocle	C₄²	C₂³×C₂₃
socle	C₂²×C₂₃	C₄×D₄
prime radical	C₂×D₈×C₂₃	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

192 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 39
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,27,29)(26,28,31,30)(32,33,35,38,36,34,37,39);(25,28)(26,31)(29,30);(25,29)(28,30)(32,34,35,39,36,33,37,38)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12065, C₂₃×#12067, C₂₃×#12077, …
maximal normal subgroup of	C₂₃×#12065, C₂₃×#12067, C₂₃×#12077, …
maximal quotient of	C₂₃×#8200, C₂₃×#8284, C₂₃×#8845, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 312);