C₂₃×#2733 #15670352

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₂₃×#2733

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

592 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 192 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 — 4 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)(28,29,32,30)(31,34,35,33)(37,38)(41,42);(25,27)(29,30)(31,35)(36,37,40,38)(39,42,43,41);(24,25)(26,27)(28,30,32,29)(31,34,35,33)(36,38,40,37)(39,42,43,41);(28,31,32,35)(29,33,30,34)(36,39)(37,41)(38,42)(40,43)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7742, C₂₃×#7758, C₂₃×#7781, …
maximal normal subgroup of	C₂₃×#7742, C₂₃×#7758, C₂₃×#7781, …
maximal quotient of	C₂₃×#14399, C₂₃×#14445, C₂₃×#14467, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1465);