Finite Group Databasebeta

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C₃×#65864 #11755541

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

476 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,3)(4,5,7,8,6)(10,14)(13,16)(17,19,20,23)(18,22,21,24);(9,11,12,15)(10,13,14,16)(18,21)(22,24);(17,18,20,21)(19,22,23,24);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(19,23)(22,24)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9736);