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C₃×#33539 #10652146

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 26527);