Finite Group Databasebeta

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C₃×#4058 #91629

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,4,5,3)(7,12)(8,15)(9,18)(11,19)(14,21)(16,17)(22,23,24);(6,8)(7,11)(9,15)(10,17)(12,14)(13,21)(16,18)(19,20);(2,3)(4,5)(6,7)(8,14)(9,13)(10,12)(11,17)(15,19)(16,21)(18,20)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 705);