C₂₃×#2057 #15669676

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

Aliases

direct product

C₂₃×#2057

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

282 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 116 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) = 2944

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)(28,29,32,34)(30,35,31,33)(36,37)(38,40)(39,42)(41,43);(24,25)(26,27)(28,30,32,31)(29,33,34,35);(25,27)(28,31,32,30)(29,33,34,35)(37,40)(38,43)(41,42)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7751, C₂₃×#7752, C₂₃×#7756, …
maximal normal subgroup of	C₂₃×#7751, C₂₃×#7752, C₂₃×#7756, …
maximal quotient of	C₂₃×#10567, C₂₃×#10569, C₂₃×#10573, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 789);