C₂₃×#2230 #15669849

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2230
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₃×#2230

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	#476
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
prime radical	C₂₃×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

126 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 60 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)(25,28)(26,34,36,31)(27,29)(32,33)(35,37,38,39);(24,25,27,28,30,33,29,32)(26,31,35,37,36,34,38,39);(24,26)(25,31)(27,35)(28,37)(29,38)(30,36)(32,39)(33,34)

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12364, C₂₃×#12365, C₂₃×#12366, …
maximal normal subgroup of	C₂₃×#12364, C₂₃×#12365, C₂₃×#12366, …
maximal quotient of	C₂₃×#12823, C₂₃×#12950, C₂₃×#13116, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 962);