Finite Group Databasebeta

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C₅×#5620 #11756005

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

504 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)(18,22)(20,24)(21,23);(11,15)(13,16)(18,21)(19,24);(9,11)(10,13)(12,15)(14,16)(19,24)(22,23);(7,8)(9,10)(11,13)(12,14)(15,16)(17,18)(19,23)(20,21)(22,24)

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, 10200);