Finite Group Databasebeta

?

← Prev (#7706284) Next (#7706286) →

C₂×#50808 #7706285

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

Aliases

Subgroups

6632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7613481);