Finite Group Databasebeta

?

← Prev (#7629399) Next (#7629401) →

C₂×#35686 #7629400

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

Aliases

Subgroups

8790 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)(9,12)(10,13)(11,14);(3,4)(5,6)(7,9)(8,11)(10,14)(12,13)(15,16)(17,21)(18,22)(19,20);(7,9)(8,12)(10,14)(11,13)(15,17,19,18)(16,21,20,22);(7,8)(9,11)(10,13)(12,14)(15,18,19,17)(16,22,20,21)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536596);