Finite Group Databasebeta

?

← Prev (#10576104) Next (#10576106) →

C₂×#61082 #10576105

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

Aliases

Subgroups

10850 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)(14,21)(15,22)(16,20)(17,19);(7,8)(9,14)(10,13)(11,20)(12,16)(15,17)(18,22)(19,21);(4,6)(7,9)(8,14)(10,19)(11,17)(12,18)(13,21)(15,20)(16,22);(7,9)(8,15)(10,17)(11,19)(12,18)(13,22)(14,20)(16,21);(7,10,12,11)(8,13,16,20)(9,17,18,19)(14,15,22,21)

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, 10483301);