Finite Group Databasebeta

?

← Prev (#7640736) Next (#7640738) →

C₂×#42364 #7640737

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

Aliases

Subgroups

6250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7547933);