Finite Group Databasebeta

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C₃×#33557 #10652164

• nilpotent
• supersolvable
• solvable
• monomial

Aliases

Subgroups

1258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 26545);