Finite Group Databasebeta

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C₃×#66264 #11756972

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

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 11167);