Finite Group Databasebeta

?

← Prev (#610827) Next (#610829) →

C₂×#16343 #610828

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

Aliases

Subgroups

4798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518024);