C₂₃×#2084 #15669703

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

Aliases

direct product

C₂₃×#2084

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

230 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 108 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) = 2944

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

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7791, C₂₃×#7793, C₂₃×#7798, …
maximal normal subgroup of	C₂₃×#7791, C₂₃×#7793, C₂₃×#7798, …
maximal quotient of	C₂₃×#10651, C₂₃×#10652, C₂₃×#10654, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 816);