C₂₃×#2060 #15669679

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2060

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂³×C₂₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

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

normal subgroups only

This group has 246 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) = 39
transitive degree	μ_t(G) = 736

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7443, C₂₃×#12234, C₂₃×#12236, …
maximal normal subgroup of	C₂₃×#7443, C₂₃×#12234, C₂₃×#12236, …
maximal quotient of	C₂₃×#10567, C₂₃×#10570, C₂₃×#10572, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 792);