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C₃×#36260 #10654867

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

4154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 19 points:

(1,2,3)(5,7)(9,10)(12,13)(14,17)(15,16)(18,19);(8,9,11,10)(13,16)(17,18);(4,5,6,7)(8,10,11,9)(12,13)(14,18)(15,16)(17,19);(12,14)(13,17)(15,19)(16,18);(12,13)(14,18)(15,16)(17,19)

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 29248);