Finite Group Databasebeta

?

← Prev (#10576334) Next (#10576336) →

C₂×#61163 #10576335

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

Aliases

Subgroups

7906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4,6,8)(5,9,10,7)(11,12)(13,17)(14,22)(15,19)(16,20)(18,21)(23,25)(24,26);(3,5)(4,7)(6,10)(8,9)(11,13,16,15)(12,17,20,19)(14,21,23,24)(18,25,26,22);(11,14)(12,18)(13,21)(15,24)(16,23)(17,25)(19,22)(20,26);(5,10)(7,9);(11,13,16,15)(12,19,20,17)(14,21,23,24)(18,22,26,25)

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483531);