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C₃×#33359 #10651966

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 19 points:

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

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 26347);