Finite Group Databasebeta

?

← Prev (#8098906) Next (#8098908) →

C₂×#56292 #8098907

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

Aliases

Subgroups

6732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,8)(6,9)(12,15)(16,18);(3,4)(5,9)(6,10)(7,8)(13,17)(16,18)(19,20)(21,25)(22,24)(23,26);(4,8)(5,10)(11,12,14,15)(13,16,17,18)(19,20,22,24)(21,23,26,25);(3,5)(4,6)(7,10)(8,9)(11,12)(13,16)(14,15)(17,18)(19,20)(21,23)(22,24)(25,26);(3,6)(4,5)(7,9)(8,10)(11,13)(12,16)(14,17)(15,18)(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, 8006103);