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C₂×#52147 #7633475

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

Aliases

Subgroups

7920 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540671);