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C₃×#27694 #10646301

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

626 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 20682);