C₂₃×#2085 #15669704

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

Aliases

direct product

C₂₃×#2085

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

214 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 100 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)(41,43);(28,30,32,31)(29,33,34,35)(37,41)(39,42)(40,43);(25,27)(28,31,32,30)(29,33,34,35)(36,37)(38,40)(39,43)(41,42)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2085, C₂₃×#23656, C₂₃×#23657, …
maximal normal subgroup of	C₂×C₂₃×#2085, C₂₃×#23656, C₂₃×#23657, …
maximal quotient of	C₂₃×#10655, C₂₃×#10656, C₂₃×#10657, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 817);