C₂₃×#2659 #15670278

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#2659

Subgroups

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

524 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 232 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)(30,32)(31,33)(34,35)(36,37,40,42)(38,39,43,41);(24,25,26,27)(28,29,31,33)(30,32,35,34)(36,38)(37,41)(39,42)(40,43);(24,25)(26,27)(28,29)(30,34)(31,33)(32,35)(36,39,40,41)(37,38,42,43);(28,30)(29,32)(31,35)(33,34)(36,38)(37,39)(40,43)(41,42)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9966, C₂₃×#9967, C₂₃×#9972, …
maximal normal subgroup of	C₂₃×#9966, C₂₃×#9967, C₂₃×#9972, …
maximal quotient of	C₂₃×#14275, C₂₃×#14281, C₂₃×#14327, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1391);