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C₂×#41410 #7639762

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

Aliases

Subgroups

9628 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8)(9,14)(10,13)(11,12)(15,16,19,17)(18,21,22,20);(8,12)(10,14)(16,17)(20,21);(3,4,5,6)(8,12)(9,13)(15,17,19,16)(18,21,22,20);(7,9,11,13)(8,10,12,14)(15,18,19,22)(16,20,17,21);(7,10)(8,13)(9,12)(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, 7546958);