Finite Group Databasebeta

?

← Prev (#7630203) Next (#7630205) →

C₂×#36516 #7630204

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

Aliases

Subgroups

9246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537400);