Finite Group Databasebeta

?

← Prev (#7635367) Next (#7635369) →

C₂×#38064 #7635368

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

Aliases

Subgroups

7100 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)(11,12,15,17)(13,14,18,16);(4,7)(8,9)(11,13,15,18)(12,16,17,14)(20,23)(21,25);(11,14)(12,13)(15,16)(17,18)(19,20,22,23)(21,24,25,26);(3,5)(4,8)(6,10)(7,9)(11,14)(12,13)(15,16)(17,18);(3,4)(5,8)(6,7)(9,10)(11,13)(12,14)(15,18)(16,17)(19,21)(20,24)(22,25)(23,26)

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, 7542564);