Finite Group Databasebeta

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C₅×#5706 #11756091

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

468 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)(13,16)(17,19)(18,21)(20,23)(22,24);(9,11,12,15)(10,13,14,16)(19,23)(21,24);(9,10)(11,13)(12,14)(15,16)(17,18,20,22)(19,24,23,21);(7,8)(19,23)(21,24)

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10286);