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C₃×#33541 #10652148

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 26529);