Finite Group Databasebeta

?

← Prev (#10679685) Next (#10679687) →

C₃×#61079 #10679686

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2826 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)(10,16)(11,20)(12,14)(13,18)(15,21)(17,23)(19,22);(8,10)(9,13)(11,17)(12,19)(14,23)(15,22)(16,20)(18,21);(5,7)(8,9)(10,13)(11,15)(12,14)(16,18)(17,22)(19,23)(20,21);(10,17)(11,21)(13,22)(15,20)(16,23)(18,19);(9,14)(13,23)(15,20)(16,22)

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 54067);