Finite Group Databasebeta

?

← Prev (#64012) Next (#64014) →

C₃×#890 #64013

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

125 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 22 points:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 661);