Finite Group Databasebeta

?

← Prev (#6440732) Next (#6440734) →

C₂×#27264 #6440733

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

Aliases

Subgroups

3936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6347929);