Finite Group Databasebeta

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C₃×#60372 #10678979

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

5126 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)(11,13)(12,16)(15,19)(17,21)(18,20)(22,23);(9,13)(11,19)(14,20)(15,16)(18,23)(21,22);(5,7);(8,10)(9,14)(11,18)(12,17)(13,20)(15,22)(16,21)(19,23);(10,17)(14,21)(18,23)(20,22)

Conjugacy classes & character table

183 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 53360);