C₂₃×#2218 #15669837

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#2218

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

170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 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)(29,33)(30,34)(31,37)(35,39)(36,43)(38,42)(40,41);(28,29,34,41,31,36,38,39,32,35,42,43,37,40,30,33);(25,27)(29,35)(33,39)(36,40)(41,43)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7422, C₂₃×#7424, C₂₃×#13667, …
maximal normal subgroup of	C₂₃×#7422, C₂₃×#7424, C₂₃×#13667, …
maximal quotient of	C₂₃×#12433, C₂₃×#12442, C₂₃×#12454, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 950);