Finite Group Databasebeta

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C₅×#5526 #11755911

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

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, 10106);