Finite Group Databasebeta

?

← Prev (#7629207) Next (#7629209) →

C₂×#35889 #7629208

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

Aliases

Subgroups

5908 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536404);