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C₂×#10776 #353360

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

Aliases

Subgroups

4890 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260556);