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C₂×#22817 #6380644

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

Aliases

Subgroups

2576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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, 6287840);