Finite Group Databasebeta

?

← Prev (#201600) Next (#201602) →

C₂×#9492 #201601

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

Aliases

Subgroups

1706 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 108797);