Finite Group Databasebeta

?

← Prev (#7706670) Next (#7706672) →

C₂×#50861 #7706671

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

Aliases

Subgroups

9270 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)(10,12)(11,14)(15,16,20,22)(17,21,18,19);(7,8,10,12)(9,11,14,13)(15,17)(16,21)(18,20)(19,22);(3,4)(5,6)(16,22)(17,18);(7,8)(9,11)(10,12)(13,14)(15,18,20,17)(16,19,22,21);(7,9,10,14)(8,11,12,13)(15,19)(16,17)(18,22)(20,21)

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, 7613867);