C₂₃×#2101 #15669720

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2101

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

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

normal subgroups only

This group has 198 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) = 2944

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

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2101, C₂₃×#23744, C₂₃×#23746, …
maximal normal subgroup of	C₂×C₂₃×#2101, C₂₃×#23744, C₂₃×#23746, …
maximal quotient of	C₂₃×#10689, C₂₃×#11208, C₂₃×#11268, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 833);