Finite Group Databasebeta

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C₃×#947 #64070

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

171 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 18 points:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 718);