C₂₃×#2734 #15670353

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#2734

Subgroups

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

456 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 224 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 — 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)(29,30)(33,34)(36,37,40,42)(38,39,43,41);(25,27)(28,29,32,30)(31,34,35,33)(36,38,40,43)(37,41,42,39);(24,25)(26,27)(28,30,32,29)(31,34,35,33);(28,31)(29,33)(30,34)(32,35)(36,39,40,41)(37,38,42,43)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7741, C₂₃×#7757, C₂₃×#7766, …
maximal normal subgroup of	C₂₃×#7741, C₂₃×#7757, C₂₃×#7766, …
maximal quotient of	C₂₃×#14406, C₂₃×#14441, C₂₃×#14450, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1466);