Finite Group Databasebeta

?

← Prev (#7635922) Next (#7635924) →

C₂×#38468 #7635923

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

Aliases

Subgroups

6636 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7543119);