C₂₃×#1483 #15669102

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

Aliases

direct product

C₂₃×#1483

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₄²	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×C₂²⋊C₄
prime radical	C₂₃×#121	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

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

normal subgroups only

This group has 234 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) = 39
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8401, C₂₃×#8402, C₂₃×#8510, …
maximal normal subgroup of	C₂₃×#8401, C₂₃×#8402, C₂₃×#8510, …
maximal quotient of	C₂₃×#7676, C₂₃×#7677, C₂₃×#7678, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 215);