Finite Group Databasebeta

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C₃×#66067 #11755744

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

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, 9939);