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C₃×#33531 #10652138

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 26519);