Finite Group Databasebeta

?

← Prev (#7705508) Next (#7705510) →

C₂×#49559 #7705509

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

Aliases

Subgroups

10040 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8,11,9)(10,13,14,12);(8,9)(12,13)(16,19)(17,21);(3,4)(5,6)(15,16,18,19)(17,20,21,22);(7,9,11,8)(10,13,14,12)(15,16)(17,20)(18,19)(21,22);(7,10,11,14)(8,12,9,13)(15,17)(16,20)(18,21)(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, 7612705);