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C₃×#33572 #10652179

• nilpotent
• supersolvable
• solvable
• monomial

Aliases

Subgroups

1108 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)(7,15)(8,14)(9,24)(10,26)(11,16)(12,18)(13,22)(19,27)(20,34)(21,32)(23,31)(25,30)(28,33)(29,35);(4,6)(5,12)(7,18)(8,20)(9,25)(10,19)(11,21)(13,27)(14,29)(15,32)(16,30)(17,24)(22,35)(23,33)(26,28)(31,34);(4,7,11,9)(5,13,16,31)(6,18,21,25)(8,22,10,23)(12,27,30,34)(14,24,26,15)(17,28,32,29)(19,33,20,35);(4,8,11,10)(5,14,16,26)(6,19,21,20)(7,22,9,23)(12,28,30,29)(13,24,31,15)(17,27,32,34)(18,33,25,35)

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 26560);