Finite Group Databasebeta

?

← Prev (#608940) Next (#608942) →

C₂×#15406 #608941

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

Aliases

Subgroups

5450 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 516137);