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C₃×#21559 #10640166

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

868 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 35 points:

(1,2,3)(4,5,9,15,11,16,10,14)(6,17,8,12,20,27,19,28)(7,21,23,13,24,29,25,30)(18,32,22,31,33,26,34,35);(4,6,9,8,11,20,10,19)(5,12,14,17,16,28,15,27)(7,18,23,22,24,33,25,34)(13,26,21,31,30,32,29,35);(4,7)(5,13)(6,18)(8,22)(9,23)(10,25)(11,24)(12,26)(14,21)(15,29)(16,30)(17,31)(19,34)(20,33)(27,35)(28,32);(4,8,9,20,11,19,10,6)(5,12,15,27,16,28,14,17)(7,22,23,33,24,34,25,18)(13,26,29,35,30,32,21,31)

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 14547);