Finite Group Databasebeta

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C₅×#5685 #11756070

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

400 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)(9,12,13,16)(10,14,11,15)(17,20)(18,22)(19,23)(21,24);(9,11,13,10)(12,14,16,15)(17,19)(18,20)(21,22)(23,24);(17,19,21,22)(18,20,23,24);(7,8)(9,10,13,11)(12,15,16,14)(17,18,21,23)(19,20,22,24)

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, 10265);