C₂₃×#1543 #15669162

order	2944
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#1543

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₄²	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×C₂²⋊C₄
prime radical	C₂₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

246 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 47
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 47 points:

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

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7488, C₂₃×#7490, C₂₃×#8241, …
maximal normal subgroup of	C₂₃×#7488, C₂₃×#7490, C₂₃×#8241, …
maximal quotient of	C₂₃×#7563, C₂₃×#7567, C₂₃×#7645, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 275);