Finite Group Databasebeta

?

← Prev (#7666038) Next (#7666040) →

C₂×#60031 #7666039

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

Aliases

Subgroups

7594 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)(13,17)(14,18)(15,16);(4,7)(8,9)(12,16)(13,18)(21,25)(24,26);(11,13)(12,14)(15,18)(16,17)(19,20,23,22)(21,24,25,26);(3,4)(5,8)(6,7)(9,10)(11,13)(12,14)(15,18)(16,17)(19,21)(20,24)(22,26)(23,25);(3,5)(4,8)(6,10)(7,9)(11,14)(12,13)(15,17)(16,18)(19,22,23,20)(21,26,25,24)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573235);