Finite Group Databasebeta

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C₃×#20354 #10638961

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 23 points:

(1,2,3)(8,9)(10,16,18,13)(11,14)(12,15)(17,22,23,20)(19,21);(4,5,6,7)(8,10)(9,13)(11,17)(12,18)(14,20)(15,16)(19,23)(21,22);(8,11)(9,14)(10,17)(12,19)(13,20)(15,21)(16,22)(18,23);(11,19)(14,21)(17,23)(20,22)

Conjugacy classes & character table

246 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 13342);