Finite Group Databasebeta

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C₅×#875 #91678

• 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)(4,6,7,5)(9,13)(12,15)(16,17,18,19,20);(4,5,7,6)(8,10,11,14)(9,12,13,15);(2,3)(5,6)(8,9)(10,12)(11,13)(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, 754);