Finite Group Databasebeta

?

← Prev (#7630084) Next (#7630086) →

C₂×#36422 #7630085

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

Aliases

Subgroups

9762 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537281);