Finite Group Databasebeta

?

← Prev (#7669049) Next (#7669051) →

C₂×#44527 #7669050

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

Aliases

Subgroups

5886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7576246);