C₂₃×#2050 #15669669

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2050

Subgroups

	subgroup	G/H
center	C₄×C₂₃	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂×C₂₃	#394
prime radical	C₂₃×#575	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

266 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 368

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7414, C₂₃×#7415, C₂₃×#12173, …
maximal normal subgroup of	C₂₃×#7414, C₂₃×#7415, C₂₃×#12173, …
maximal quotient of	C₂₃×#10456, C₂₃×#10457, C₂₃×#10458, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 782);