Finite Group Databasebeta

?

← Prev (#7636920) Next (#7636922) →

C₂×#39265 #7636921

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

Aliases

Subgroups

7154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7544117);