C₂₃×#2031 #15669650

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

Aliases

direct product

C₂₃×#2031

Subgroups

	subgroup	G/H
center	C₄×C₂₃	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂×C₂₃	#393
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

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

normal subgroups only

This group has 244 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)(26,33,35,39)(27,31)(28,37)(29,32)(30,36,38,34);(26,34,35,36)(30,33,38,39);(24,26)(25,30)(27,34)(28,36)(29,35)(31,39)(32,38)(33,37)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2031, C₂₃×#23472, C₂₃×#23833, …
maximal normal subgroup of	C₂×C₂₃×#2031, C₂₃×#23472, C₂₃×#23833, …
maximal quotient of	C₂₃×#10362, C₂₃×#10363, C₂₃×#10364, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 763);