Finite Group Databasebeta

?

← Prev (#7629158) Next (#7629160) →

C₂×#35713 #7629159

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

Aliases

Subgroups

11746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536355);