Finite Group Databasebeta

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C₅×#5651 #11756036

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

392 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)(10,14)(13,16)(19,26)(22,31)(25,28)(30,32);(11,15)(13,16)(17,20,21,29)(18,23,24,27)(19,25,26,28)(22,30,31,32);(9,11)(10,13)(12,15)(14,16)(17,19)(18,22)(20,28)(21,26)(23,32)(24,31)(25,29)(27,30);(7,8)(9,10)(11,13)(12,14)(15,16)(17,18,21,24)(19,22,26,31)(20,27,29,23)(25,32,28,30)

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10231);