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C₃×#33555 #10652162

• nilpotent
• supersolvable
• solvable
• monomial

Aliases

Subgroups

1146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 26543);