Finite Group Databasebeta

?

← Prev (#7630210) Next (#7630212) →

C₂×#36523 #7630211

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

Aliases

Subgroups

5832 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537407);