Finite Group Databasebeta

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C₃×#66079 #11755756

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

516 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)(9,11,12,18,13,17,19,23)(10,15,16,22,14,20,21,24);(10,14)(15,20)(16,21)(22,24);(11,17)(15,20)(18,23)(22,24);(5,6)(7,8)(9,10)(11,15)(12,16)(13,14)(17,20)(18,22)(19,21)(23,24)

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9951);