C₂₃×#1666 #15669285

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1665
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₃×#1666

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃
prime radical	C₂₃×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ G

172 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 72 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)(33,36)(34,38)(37,39);(24,25,26,28,27,29,30,31);(32,33,35,37)(34,39,38,36)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#1666, C₂₃×#19114, C₂₃×#19124, …
maximal normal subgroup of	C₂×C₂₃×#1666, C₂₃×#19114, C₂₃×#19124, …
maximal quotient of	C₂₃×#8643, C₂₃×#9220, C₂₃×#9222, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 398);