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C₃×#20956 #10639563

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 13944);