C₂₃×#2007 #15669626

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

Aliases

direct product

C₂₃×#2007

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

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

normal subgroups only

This group has 370 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)(28,29,33,37)(30,38,40,43)(31,36,32,35)(34,41,42,39);(24,25)(26,27)(28,30)(29,34)(31,41)(32,39)(33,40)(35,43)(36,38)(37,42);(25,27)(28,30)(29,34)(31,39)(32,41)(33,40)(35,38)(36,43)(37,42)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7409, C₂₃×#12098, C₂₃×#12100, …
maximal normal subgroup of	C₂₃×#7409, C₂₃×#12098, C₂₃×#12100, …
maximal quotient of	C₂₃×#9934, C₂₃×#9935, C₂₃×#9936, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 739);