C₂₃×#2186 #15669805

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2186

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ C₂²×C₈×C₂₃ ◁ G

230 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 1472

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

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2186, C₂₃×#33516, C₂₃×#33519, …
maximal normal subgroup of	C₂×C₂₃×#2186, C₂₃×#33516, C₂₃×#33519, …
maximal quotient of	C₂₃×#12104, C₂₃×#12160, C₂₃×#12280, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 918);