Finite Group Databasebeta

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C₅×#5724 #11756109

• 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)(9,10,11,12)(14,20)(18,26)(19,28)(25,27);(10,12)(13,16,17,24)(14,19,20,28)(15,21,22,23)(18,25,26,27);(13,15,17,22)(14,18,20,26)(16,23,24,21)(19,27,28,25);(7,8)(13,14)(15,18)(16,19)(17,20)(21,25)(22,26)(23,27)(24,28)

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, 10304);