Finite Group Databasebeta

?

← Prev (#7707051) Next (#7707053) →

C₂×#51068 #7707052

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

Aliases

Subgroups

11392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7614248);