Finite Group Databasebeta

?

← Prev (#6346862) Next (#6346864) →

C₂×#18317 #6346863

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

Aliases

Subgroups

4974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6254059);