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C₃×#34290 #10652897

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3960 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

264 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 27278);