Finite Group Databasebeta

?

← Prev (#7707699) Next (#7707701) →

C₂×#51756 #7707700

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

Aliases

Subgroups

7134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7614896);