C₂₃×#1997 #15669616

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#1997

Subgroups

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

260 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 120 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)(24,25)(26,30)(27,28)(29,31)(32,33,35,38,36,37,39,34);(25,28)(29,30)(32,34,35,37,36,38,39,33);(24,26,27,31)(25,29,28,30)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8470, C₂₃×#8471, C₂₃×#8473, …
maximal normal subgroup of	C₂₃×#8470, C₂₃×#8471, C₂₃×#8473, …
maximal quotient of	C₂₃×#9878, C₂₃×#9879, C₂₃×#9882, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 729);