Finite Group Databasebeta

?

← Prev (#10577558) Next (#10577560) →

C₂×#62304 #10577559

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

Aliases

Subgroups

6982 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)(11,12)(13,17)(14,21)(15,24)(16,19)(18,22)(20,26)(23,25);(3,5)(4,7)(6,10)(8,9)(11,13,16,15)(12,17,19,24)(14,20,23,22)(18,21,26,25);(11,14,15,22,16,23,13,20)(12,18,17,21,19,26,24,25);(5,10)(7,9)(11,13,16,15)(12,17,19,24)(14,20,23,22)(18,21,26,25);(4,8)(7,9)(11,13,16,15)(12,17,19,24)(14,22,23,20)(18,25,26,21)

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, 10484755);