Finite Group Databasebeta

?

← Prev (#10575543) Next (#10575545) →

C₂×#60834 #10575544

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

Aliases

Subgroups

7804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482740);