Finite Group Databasebeta

?

← Prev (#10585906) Next (#10585908) →

C₂³×#544 #10585907

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

Aliases

Subgroups

37026 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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

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, 10493103);