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C₃×#20788 #10639395

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 13776);