C₂₃×#2159 #15669778

order	2944
nilpotency class	4
isoclinism	isoclinic class of #509
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2159

Subgroups

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

156 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 104 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) = 1472

A minimal faithful permutation representation — 3 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)(29,33)(30,34)(31,37)(35,39)(36,43)(38,42)(40,41);(28,29,34,41,31,36,38,39,32,35,42,43,37,40,30,33);(29,35)(33,39)(36,40)(41,43)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12677, C₂₃×#12923, C₂₃×#12925, …
maximal normal subgroup of	C₂₃×#12677, C₂₃×#12923, C₂₃×#12925, …
maximal quotient of	C₂₃×#12009, C₂₃×#12025, C₂₃×#12035, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 891);