C₂₃×#1985 #15669604

order	2944
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1985

Subgroups

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

280 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 136 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)(36,37,41,42,40,43,39,38);(24,25,26,27)(29,32)(33,34)(36,38,39,43,40,42,41,37);(28,30,31,35)(29,33,32,34)(36,39,40,41)(37,42,43,38)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7061, C₂₃×#7133, C₂₃×#7284, …
maximal normal subgroup of	C₂₃×#7061, C₂₃×#7133, C₂₃×#7284, …
maximal quotient of	C₂₃×#9867, C₂₃×#9868, C₂₃×#9869, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 717);