Finite Group Databasebeta

?

← Prev (#7701677) Next (#7701679) →

C₂×#47683 #7701678

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

Aliases

Subgroups

9666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 7608874);