Finite Group Databasebeta

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C₅×#5770 #11756155

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

516 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)(9,11,13,19)(10,15,14,17)(12,21,20,18)(16,23,22,24);(10,14)(11,18)(12,20)(15,23)(17,24)(19,21);(9,10)(11,17)(12,16)(13,14)(15,19)(18,23)(20,22)(21,24);(7,8)(10,14)(15,17)(16,22)(23,24)

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, 10350);