Finite Group Databasebeta

?

← Prev (#10574197) Next (#10574199) →

C₂×#60144 #10574198

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

Aliases

Subgroups

10750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481394);