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C₂×#35714 #7629165

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

Aliases

Subgroups

11222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536361);