Finite Group Databasebeta

?

← Prev (#7706262) Next (#7706264) →

C₂×#50634 #7706263

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

Aliases

Subgroups

10206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7613459);