Finite Group Databasebeta

?

← Prev (#7666450) Next (#7666452) →

C₂×#59178 #7666451

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

Aliases

Subgroups

7824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573647);