Finite Group Databasebeta

?

← Prev (#7634964) Next (#7634966) →

C₂×#37829 #7634965

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

Aliases

Subgroups

8082 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542161);