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C₂×#36226 #7629873

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

Aliases

Subgroups

9746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537069);