Finite Group Databasebeta

?

← Prev (#6630572) Next (#6630574) →

C₂×#33254 #6630573

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

Aliases

Subgroups

3458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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, 6537769);