Finite Group Databasebeta

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C₅×#5647 #11756032

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

440 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)(10,14)(11,15)(18,22)(21,24);(10,14)(13,16)(17,19,20,23)(18,21,22,24);(9,11)(10,13)(12,15)(14,16)(17,18,20,22)(19,24,23,21);(7,8)(9,10)(11,13)(12,14)(15,16)(19,23)(21,24)

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10227);