C₂₃×#2313 #15669932

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₃×#2313

Subgroups

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

512 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 280 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)(24,25,26,27)(28,29,32,30)(31,34,35,33)(38,42)(40,43);(29,30)(33,34)(36,37,39,41)(38,40,42,43);(28,30,32,29)(31,34,35,33)(36,38)(37,40)(39,42)(41,43);(28,31)(29,33)(30,34)(32,35)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8737, C₂₃×#8755, C₂₃×#8758, …
maximal normal subgroup of	C₂₃×#8737, C₂₃×#8755, C₂₃×#8758, …
maximal quotient of	C₂₃×#13776, C₂₃×#13778, C₂₃×#13787, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1045);