C₂₃×#1503 #15669122

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×#1503

Subgroups

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

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

normal subgroups only

This group has 240 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) = 39
transitive degree	μ_t(G) = 736

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)(33,37,38,39);(24,25,27,29)(26,31,30,28)(32,33)(34,37)(35,39)(36,38);(32,34,36,35)(33,37,38,39)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8252, C₂₃×#8254, C₂₃×#8256, …
maximal normal subgroup of	C₂₃×#8252, C₂₃×#8254, C₂₃×#8256, …
maximal quotient of	C₂₃×#7562, C₂₃×#7570, C₂₃×#7571, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 235);