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C₂₃×#1711 #15669330

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 55 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)(26,32)(27,36)(28,30)(29,34)(31,33)(35,38)(37,39)(40,41)(42,48)(43,45)(44,52)(46,50)(47,51)(49,54)(53,55);(24,26,33,39,28,35,27,34)(25,29,36,38,30,37,31,32)(41,45)(46,53)(47,52)(48,54);(25,30)(29,37)(31,36)(32,38)(40,42,44,50,43,49,51,55)(41,46,47,48,45,53,52,54)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 443);