Finite Group Databasebeta

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C₅×#5689 #11756074

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

412 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)(10,14)(12,15)(13,16)(17,19,20,24)(18,21,22,23);(10,13)(11,15)(17,18,20,22)(19,23,24,21);(9,10,12,13)(11,14,15,16);(7,8)(11,15)(14,16)

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, 10269);