Finite Group Databasebeta

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C₅×#5825 #11756210

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 28 points:

(1,2,3,4,5)(6,7,8)(10,12)(15,22)(18,26)(21,28)(25,27);(13,16,17,24)(14,19,20,23)(15,21,22,28)(18,25,26,27);(13,15)(14,18)(16,21)(17,22)(19,25)(20,26)(23,27)(24,28);(7,8)(9,10)(11,12)(13,14,17,20)(15,18,22,26)(16,23,24,19)(21,27,28,25)

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10405);