Finite Group Databasebeta

?

← Prev (#7667159) Next (#7667161) →

C₂×#43059 #7667160

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

Aliases

Subgroups

6240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574356);