Finite Group Databasebeta

?

← Prev (#7630121) Next (#7630123) →

C₂×#36442 #7630122

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

Aliases

Subgroups

9478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537318);