Finite Group Databasebeta

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C₅×#5757 #11756142

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10337);