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C₂₃×#3555 #15671174

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

910 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 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)(24,25,29,32)(26,27,34,30)(28,36,37,31)(33,38,39,35)(40,41,44,47)(42,45,50,48)(43,51,52,46)(49,54,55,53);(24,26,29,34)(25,30,32,27)(28,33,37,39)(31,38,36,35)(40,41)(42,48)(43,46)(44,47)(45,50)(49,54)(51,52)(53,55);(24,27,29,30)(25,26,32,34)(28,35,37,38)(31,33,36,39);(24,26)(25,30)(27,32)(28,33)(29,34)(31,38)(35,36)(37,39)(40,42)(41,45)(43,49)(44,50)(46,53)(47,48)(51,54)(52,55);(24,28,29,37)(25,31,32,36)(26,33,34,39)(27,35,30,38)(40,43,44,52)(41,46,47,51)(42,49,50,55)(45,53,48,54)

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, 2287);