Finite Group Databasebeta

?

← Prev (#8101289) Next (#8101291) →

C₂×#53534 #8101290

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

Aliases

Subgroups

6412 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8008486);