Finite Group Databasebeta

?

← Prev (#8098877) Next (#8098879) →

C₂×#54921 #8098878

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

Aliases

Subgroups

7492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8006074);