Finite Group Databasebeta

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C₃×#12667 #10631274

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

296 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 5655);