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C₂×#34963 #7628136

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

Aliases

Subgroups

12386 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535332);