Finite Group Databasebeta

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C₃×#4016 #91587

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 663);