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C₂×#52167 #7633499

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

Aliases

Subgroups

9926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540695);