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C₃×#60444 #10679051

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53432);