C₂₃×#2062 #15669681

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2062

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator, Frattini, cosocle	C₂⁴	C₂³×C₂₃
prime radical	C₂⁴×C₂₃	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂⁴×C₂₃ ◁ G

314 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 736

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12226, C₂₃×#12227, C₂₃×#12228, …
maximal normal subgroup of	C₂₃×#12226, C₂₃×#12227, C₂₃×#12228, …
maximal quotient of	C₂₃×#10567, C₂₃×#10568, C₂₃×#10569, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 794);