Finite Group Databasebeta

?

← Prev (#7669492) Next (#7669494) →

C₂×#44878 #7669493

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

Aliases

Subgroups

8790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7576689);