Finite Group Databasebeta

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C₃×#65874 #11755551

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

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, 9746);