C₂₃×#2076 #15669695

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

Aliases

direct product

C₂₃×#2076

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂⁴×C₂₃	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

256 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 96 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)(28,29)(30,33)(31,32)(34,35)(36,37,39,42,38,40,43,41);(24,25)(26,27)(29,32)(33,35)(37,40)(41,42);(25,27)(28,30,31,34)(29,33,32,35)(37,41)(39,43)(40,42)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7077, C₂₃×#7085, C₂₃×#12281, …
maximal normal subgroup of	C₂₃×#7077, C₂₃×#7085, C₂₃×#12281, …
maximal quotient of	C₂₃×#10616, C₂₃×#10618, C₂₃×#10622, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 808);