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C₃×#919 #64042

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

133 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 690);