Finite Group Databasebeta

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C₃×#13200 #10631807

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 6188);