Finite Group Databasebeta

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C₃×#65970 #11755647

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

456 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)(10,14)(12,15)(13,16)(17,20,21,19)(18,23,22,24);(11,15)(14,16)(17,19,21,20)(18,23,22,24);(10,13)(11,15)(17,18)(19,23)(20,24)(21,22);(5,6)(7,8)(9,10)(11,14)(12,13)(15,16)(18,22)(23,24)

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9842);