Finite Group Databasebeta

?

← Prev (#7629739) Next (#7629741) →

C₂×#36116 #7629740

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

Aliases

Subgroups

8278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(8,9)(13,14)(16,20)(21,22);(4,6)(7,8,12,9)(10,13,11,14)(15,16)(17,21)(18,22)(19,20);(3,4)(5,6)(7,9,12,8)(10,14,11,13)(15,17,19,18)(16,21,20,22);(4,6)(7,10,12,11)(8,13,9,14)(15,17,19,18)(16,21,20,22);(3,4)(5,6)(7,11,12,10)(8,14,9,13)(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, 7536936);