Finite Group Databasebeta

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C₅×#5669 #11756054

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

432 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)(9,12,13,11)(10,14,15,16)(18,22)(21,24);(9,11,13,12)(10,14,15,16)(17,19,20,23)(18,21,22,24);(11,12)(14,16)(17,18)(19,21)(20,22)(23,24);(7,8)(9,10,13,15)(11,14,12,16)

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, 10249);