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C₃×#60426 #10679033

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 23 points:

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

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, 53414);