Finite Group Databasebeta

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C₅×#5701 #11756086

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 32 points:

(1,2,3,4,5)(6,7,8)(11,16)(14,15)(17,20,21,29)(18,23,24,27)(19,26,25,28)(22,31,30,32);(9,12,13,10)(11,15,16,14)(19,25)(22,30)(26,28)(31,32);(9,11)(10,14)(12,15)(13,16)(17,19,21,25)(18,22,24,30)(20,28,29,26)(23,32,27,31);(7,8)(9,10,13,12)(11,14,16,15)(17,18,21,24)(19,22,25,30)(20,27,29,23)(26,32,28,31)

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, 10281);