C₂₃×#1535 #15669154

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#1535

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₄²	C₂³×C₂₃
prime radical	C₂₃×#121	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

200 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 55
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,28,33,29,32,27,31)(26,34,35,39,36,30,37,38)(40,41)(42,48,50,55)(43,47)(44,46)(45,49,53,51)(52,54);(24,26)(25,30)(27,35)(28,37)(29,36)(31,38)(32,34)(33,39)(40,42)(41,45)(43,51)(44,50)(46,53)(47,55)(48,54)(49,52);(24,27,29,28)(25,31,32,33)(26,35,36,37)(30,38,34,39)(41,46)(45,53)(47,54)(48,55)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8489, C₂₃×#8490, C₂₃×#8500, …
maximal normal subgroup of	C₂₃×#8489, C₂₃×#8490, C₂₃×#8500, …
maximal quotient of	C₂₃×#7594, C₂₃×#7596, C₂₃×#7599, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 267);