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C₃×#875 #63998

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

167 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 646);