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C₂×#52168 #7633497

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

Aliases

Subgroups

8402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(7,8)(9,11)(10,14)(12,13)(15,16)(17,20)(18,19)(21,22);(3,4)(5,6)(7,9)(8,10)(11,13)(12,14)(16,19)(17,21);(4,6)(16,19)(20,22);(7,10,12,11)(8,9,13,14)(15,17,18,21)(16,20,19,22);(7,11,12,10)(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, 7540693);