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C₃×#21009 #10639616

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1708 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 13997);