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C₂×#21788 #6374233

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

Aliases

Subgroups

6474 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)(9,13)(10,12)(11,14)(15,16,19,20,18,21,17,22);(7,9,10,14)(8,11,12,13)(15,17,18,19)(16,20,21,22);(4,6)(9,14)(11,13);(8,12)(11,13)(16,21)(20,22)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6281429);