Finite Group Databasebeta

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C₅×#5578 #11755963

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

444 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)(10,14)(13,16)(17,19,20,24)(18,21,22,23);(9,11,12,15)(10,13,14,16);(17,18,20,22)(19,23,24,21);(7,8)(9,10)(11,13)(12,14)(15,16)

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10158);