Finite Group Databasebeta

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C₃×#90344 #13060999

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

692 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)(12,14)(15,17,18,21)(16,20,19,22);(11,12)(13,14)(16,19)(20,22);(15,16)(17,20)(18,19)(21,22);(5,6)(7,8)(9,10)(17,21)(20,22)

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 10288);