Finite Group Databasebeta

?

← Prev (#7703007) Next (#7703009) →

C₂×#46335 #7703008

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

Aliases

Subgroups

7722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4,7,8)(5,6,9,10)(13,17)(16,18)(19,20,23,22)(21,25,26,24);(4,8)(5,9)(12,14)(13,17)(20,22)(24,25);(11,12,15,14)(13,16,17,18)(19,21)(20,24)(22,25)(23,26);(3,5)(4,6)(7,9)(8,10)(11,13,15,17)(12,16,14,18)(19,22,23,20)(21,25,26,24);(3,6)(4,5)(7,10)(8,9)(11,14,15,12)(13,18,17,16)(19,21)(20,24)(22,25)(23,26)

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, 7610204);