Finite Group Databasebeta

?

← Prev (#8100385) Next (#8100387) →

C₂×#55419 #8100386

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

Aliases

Subgroups

7310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,7)(6,8)(9,10)(20,23)(24,25);(6,10)(8,9)(11,12,15,16)(13,14,17,18)(19,20,22,23)(21,25,26,24);(4,5)(8,9)(12,16)(13,17)(19,21,22,26)(20,24,23,25);(3,5,7,4)(6,9,10,8)(11,13)(12,14)(15,17)(16,18)(19,21)(20,24)(22,26)(23,25);(3,6,7,10)(4,8,5,9)(11,14)(12,13)(15,18)(16,17)(19,20)(21,24)(22,23)(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, 8007582);