Finite Group Databasebeta

?

← Prev (#8102217) Next (#8102219) →

C₂×#53432 #8102218

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

Aliases

Subgroups

7186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8009414);