Finite Group Databasebeta

?

← Prev (#10576508) Next (#10576510) →

C₂×#61347 #10576509

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

Aliases

Subgroups

6732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483705);