Finite Group Databasebeta

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C₅×#877 #91680

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 20 points:

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 756);