C₂₃×#1540 #15669159

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

Aliases

direct product

C₂₃×#1540

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

256 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 108 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)(24,25,27,29,28,31,26,30)(32,33,36,41,37,40,35,39)(34,42,43,47,44,38,45,46);(25,29)(26,27)(30,31)(32,34)(33,38)(35,43)(36,45)(37,44)(39,46)(40,42)(41,47);(32,35,37,36)(33,39,40,41)(34,43,44,45)(38,46,42,47)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8251, C₂₃×#8253, C₂₃×#8255, …
maximal normal subgroup of	C₂₃×#8251, C₂₃×#8253, C₂₃×#8255, …
maximal quotient of	C₂₃×#7560, C₂₃×#7565, C₂₃×#7642, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 272);