Finite Group Databasebeta

?

← Prev (#7640946) Next (#7640948) →

C₂×#42504 #7640947

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

Aliases

Subgroups

6714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548143);