Finite Group Databasebeta

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C₃×#66102 #11755779

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

524 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)(10,15)(12,21)(13,17)(14,18)(16,23)(19,20)(22,24);(10,14)(11,19)(12,20)(15,23)(17,21)(18,24);(9,10)(11,18)(12,16)(13,14)(15,17)(19,23)(20,22)(21,24);(5,6)(7,8)(11,17)(15,18)(19,21)(23,24)

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, 9974);