Finite Group Databasebeta

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C₃×#66044 #11755721

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

432 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)(17,20,21,22)(18,19,23,24);(9,11,12,15)(10,13,14,16)(17,19)(18,22)(20,23)(21,24);(9,10)(11,13)(12,14)(15,16)(17,18,21,23)(19,20,24,22);(5,6)(7,8)(11,15)(13,16)(19,24)(20,22)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9916);