Finite Group Databasebeta

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C₃×#66096 #11755773

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

516 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)(9,11,13,18)(10,15,14,21)(12,20,19,17)(16,24,22,23);(11,17)(12,19)(15,23)(16,22)(18,20)(21,24);(10,14)(15,21)(16,22)(23,24);(5,6)(7,8)(9,10)(11,15)(12,16)(13,14)(17,23)(18,21)(19,22)(20,24)

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, 9968);