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C₅×#5766 #11756151

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 40 points:

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

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, 10346);