Finite Group Databasebeta

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C₃×#912 #64035

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

135 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 22 points:

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

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 683);