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C₃×#33463 #10652070

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

652 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 26451);