C₂₃×#2090 #15669709

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₃×#2090

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂³×C₂₃	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

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

normal subgroups only

This group has 176 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) = 47
transitive degree	μ_t(G) = 1472

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)(26,31)(27,29)(28,30)(32,33,36,39,37,41,35,40)(34,38,42,47,44,45,43,46);(24,26,28,27)(25,29,30,31)(32,34)(33,38)(35,43)(36,42)(37,44)(39,47)(40,46)(41,45);(24,27,28,26)(25,29,30,31)(33,39)(34,42)(35,36)(38,45)(40,41)(43,44)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2090, C₂₃×#23674, C₂₃×#23675, …
maximal normal subgroup of	C₂×C₂₃×#2090, C₂₃×#23674, C₂₃×#23675, …
maximal quotient of	C₂₃×#10653, C₂₃×#10654, C₂₃×#10655, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 822);