Finite Group Databasebeta

?

← Prev (#6445841) Next (#6445843) →

C₂×#27026 #6445842

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

Aliases

Subgroups

2044 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6353038);