C₂₃×#2004 #15669623

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#2004

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂₃×#535	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

394 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 92 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)(24,25)(26,27)(28,29)(30,36)(31,39)(32,35)(33,37)(34,41)(38,43)(40,42);(28,30,32,38)(29,33,35,42)(31,40,41,37)(34,43,39,36);(25,27)(31,41)(33,42)(34,39)(37,40)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2004, C₂₃×#23399, C₂₃×#23401, …
maximal normal subgroup of	C₂×C₂₃×#2004, C₂₃×#23399, C₂₃×#23401, …
maximal quotient of	C₂₃×#9916, C₂₃×#9918, C₂₃×#9924, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 736);