Finite Group Databasebeta

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C₃×#10716 #10629323

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 23 points:

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

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 3704);