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C₂×#34149 #7625372

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

Aliases

Subgroups

8698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532568);