Finite Group Databasebeta

?

← Prev (#8092825) Next (#8092827) →

C₂×#53096 #8092826

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

Aliases

Subgroups

6870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8000022);