Finite Group Databasebeta

?

← Prev (#7636452) Next (#7636454) →

C₂×#39044 #7636453

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

Aliases

Subgroups

6410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7543649);