C₂₃×#1988 #15669607

order	2944
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₃×#1988

Subgroups

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

292 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 144 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)(25,27)(28,29)(30,34)(31,32)(33,35)(36,37,38,41,39,42,43,40);(24,25,26,27)(29,32)(33,34)(37,40)(38,43)(41,42);(28,30,31,35)(29,33,32,34)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8421, C₂₃×#8427, C₂₃×#8985, …
maximal normal subgroup of	C₂₃×#8421, C₂₃×#8427, C₂₃×#8985, …
maximal quotient of	C₂₃×#9865, C₂₃×#9869, C₂₃×#9898, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 720);