Finite Group Databasebeta

?

← Prev (#7629868) Next (#7629870) →

C₂×#36222 #7629869

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

Aliases

Subgroups

10398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537065);