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C₃×#14730 #10633337

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2578 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7718);