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C₂×#37448 #7633661

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

Aliases

Subgroups

11326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540857);