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C₃×#47846 #10666453

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 23 points:

(1,2,3)(4,5,6,7)(8,9)(10,14)(11,12)(13,15)(16,17,20,22)(18,19,23,21);(9,12)(13,14)(16,18)(17,21)(19,22)(20,23);(4,5)(6,7)(17,22)(18,23);(8,9)(10,13)(11,12)(14,15)(16,18)(17,19)(20,23)(21,22);(8,10)(9,13)(11,15)(12,14)(16,19)(17,18)(20,21)(22,23)

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 40834);