Finite Group Databasebeta

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C₃×#64941 #11749549

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

308 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3)(4,5,7,8,6)(9,11,12,10)(14,16)(18,22)(21,24);(13,14)(15,16)(17,19,20,23)(18,21,22,24);(5,6)(7,8)(9,10,12,11)(17,18)(19,21)(20,22)(23,24)

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 3744);