Finite Group Databasebeta

?

← Prev (#10576089) Next (#10576091) →

C₂×#61092 #10576090

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

Aliases

Subgroups

10710 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)(9,15)(10,19)(11,13)(12,18)(14,20)(16,22)(17,21);(7,9)(8,12)(10,16)(11,17)(13,22)(14,21)(15,19)(18,20);(4,6)(7,8)(9,12)(10,14)(11,13)(15,18)(16,21)(17,22)(19,20);(9,16)(10,20)(12,21)(14,19)(15,22)(17,18);(8,13)(9,17)(14,19)(16,18)

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483286);