Finite Group Databasebeta

?

← Prev (#10586314) Next (#10586316) →

C₂×#62970 #10586315

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

32484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 34 points:

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493511);