Finite Group Databasebeta

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C₃×#6510 #10621258

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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(672, 840);