C₂₃×#2040 #15669659

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2040

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂₃×#537	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

290 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 736

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)(25,26)(28,29)(30,38)(31,36)(32,35)(33,37)(34,40)(39,43)(41,42);(24,25)(26,27)(28,30)(29,34)(31,40)(32,41)(33,39)(35,43)(36,38)(37,42);(24,26,27,25)(29,35)(30,39)(32,33)(36,37)(40,41)(42,43)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7416, C₂₃×#12141, C₂₃×#12143, …
maximal normal subgroup of	C₂₃×#7416, C₂₃×#12141, C₂₃×#12143, …
maximal quotient of	C₂₃×#10403, C₂₃×#10404, C₂₃×#10407, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 772);