Finite Group Databasebeta

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C₅×#5696 #11756081

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

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, 10276);