Finite Group Databasebeta

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C₃×#61059 #10679666

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2878 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)(10,16)(11,20)(12,14)(13,19)(15,21)(17,23)(18,22);(8,10,12,17)(9,13,14,22)(11,18,21,19)(15,23,20,16);(5,7)(10,17)(13,22)(16,23)(18,19);(10,18)(11,21)(13,23)(15,20)(16,22)(17,19);(9,14)(13,22)(15,20)(16,23)

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, 54047);