C₂₃×#1940 #15669559

order	2944
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#1940

Subgroups

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

248 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 136 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) = 2944

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

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7124, C₂₃×#8878, C₂₃×#8879, …
maximal normal subgroup of	C₂₃×#7124, C₂₃×#8878, C₂₃×#8879, …
maximal quotient of	C₂₃×#9597, C₂₃×#9598, C₂₃×#9599, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 672);