Finite Group Databasebeta

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C₃×#13269 #10631876

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

308 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 6257);