Finite Group Databasebeta

?

← Prev (#8099029) Next (#8099031) →

C₂×#56362 #8099030

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

Aliases

Subgroups

6444 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8006226);