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C₃×#14025 #10632632

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 19 points:

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

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 7013);