Finite Group Databasebeta

?

← Prev (#7635290) Next (#7635292) →

C₂×#37840 #7635291

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

Aliases

Subgroups

10932 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542487);