Finite Group Databasebeta

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C₃×#20584 #10639191

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

4006 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)(10,16,18,13)(11,14)(12,15)(17,22,23,20)(19,21);(8,10)(9,13)(11,17)(12,18)(14,20)(15,16)(19,23)(21,22);(5,7);(8,11,12,19)(9,14,15,21)(10,17,18,23)(13,20,16,22)

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, 13572);