Finite Group Databasebeta

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C₃×#90368 #13061010

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

580 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

201 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 10299);