Finite Group Databasebeta

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C₅×#5708 #11756093

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

428 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)(9,11,12,16)(10,14,13,15)(17,19)(18,21)(20,23)(22,24);(10,13)(14,15)(17,18,20,22)(19,21,23,24);(9,10,12,13)(11,15,16,14)(19,23)(21,24);(7,8)(19,23)(21,24)

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, 10288);