Finite Group Databasebeta

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C₃×#20605 #10639212

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 23 points:

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

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, 13593);