Finite Group Databasebeta

?

← Prev (#7630205) Next (#7630207) →

C₂×#36518 #7630206

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

Aliases

Subgroups

8756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537402);