Finite Group Databasebeta

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C₃×#66064 #11755741

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

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, 9936);