Finite Group Databasebeta

?

← Prev (#611525) Next (#611527) →

C₂×#16787 #611526

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

Aliases

Subgroups

4378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 518722);