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C₂×#52165 #7633496

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

Aliases

Subgroups

10290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540692);