Finite Group Databasebeta

?

← Prev (#7702862) Next (#7702864) →

C₂×#46260 #7702863

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

Aliases

Subgroups

6326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7610059);