Finite Group Databasebeta

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C₅×#5631 #11756016

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

584 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 20 points:

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

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10211);