Finite Group Databasebeta

?

← Prev (#7637986) Next (#7637988) →

C₂×#40384 #7637987

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

Aliases

Subgroups

6134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(12,15)(16,18)(19,20)(21,22)(23,24)(25,26);(4,8)(6,9)(12,15)(13,17)(20,24)(21,25);(3,4)(5,9)(6,10)(7,8)(11,12)(13,16)(14,15)(17,18)(19,21,23,25)(20,22,24,26);(3,5,7,10)(4,9,8,6)(19,22)(20,25)(21,24)(23,26);(3,6,7,9)(4,10,8,5)(11,13)(12,16)(14,17)(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, 7545183);