Finite Group Databasebeta

?

← Prev (#7666271) Next (#7666273) →

C₂×#59980 #7666272

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

Aliases

Subgroups

6664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573468);