C₂₃×#1801 #15669420

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1801

Subgroups

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

272 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 124 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 — 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)(28,29,31,35,32,34,40,42)(30,36,37,43,38,33,39,41);(24,25,26,27);(28,30,32,38)(29,33,34,36)(31,39,40,37)(35,43,42,41)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7238, C₂₃×#7323, C₂₃×#8354, …
maximal normal subgroup of	C₂₃×#7238, C₂₃×#7323, C₂₃×#8354, …
maximal quotient of	C₂₃×#8558, C₂₃×#8560, C₂₃×#8562, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 533);