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C₃×#926 #64049

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

179 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 697);