Finite Group Databasebeta

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C₅×#70147 #14313306

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,4,5)(6,7,8)(9,12,14,25)(10,16,18,32)(11,20,22,23)(13,24,27,40)(15,28,29,30)(17,31,26,39)(19,33,34,37)(21,35,36,38);(7,8)(9,11,14,22)(10,15,18,29)(12,23,25,20)(13,21,27,36)(16,30,32,28)(17,19,26,34)(24,38,40,35)(31,37,39,33);(7,8)(9,10)(11,19)(12,16)(13,26,27,17)(14,18)(15,21,29,36)(20,33)(22,34)(23,37)(24,39,40,31)(25,32)(28,35,30,38)

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 39004);