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C₃×#66113 #11755790

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

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9985);