C₂₃×#2061 #15669680

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

Aliases

direct product

C₂₃×#2061

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

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

normal subgroups only

This group has 230 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) = 47
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 3 generators on 47 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)(32,33,35,39)(34,41,42,37)(36,38,44,40)(43,47,45,46);(24,26,28,27)(25,29,30,31)(32,34,35,42)(33,37,39,41)(36,45,44,43)(38,47,40,46);(24,27,28,26)(25,29,30,31)(33,38)(36,44)(37,46)(39,40)(41,47)(43,45)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7442, C₂₃×#12235, C₂₃×#12237, …
maximal normal subgroup of	C₂₃×#7442, C₂₃×#12235, C₂₃×#12237, …
maximal quotient of	C₂₃×#10568, C₂₃×#10569, C₂₃×#10571, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 793);