Finite Group Databasebeta

?

← Prev (#10576072) Next (#10576074) →

C₂×#61062 #10576073

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

Aliases

Subgroups

10650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10483269);