Finite Group Databasebeta

?

← Prev (#7707946) Next (#7707948) →

C₂×#51965 #7707947

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

Aliases

Subgroups

6776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7615143);