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C₂×#21761 #6374147

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

Aliases

Subgroups

6710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

(1,2);(3,4,5,6)(7,8)(9,13)(10,12)(11,14)(15,16)(17,22)(18,21)(19,20);(7,9)(8,11)(10,14)(12,13)(15,17,18,19)(16,20,21,22);(9,14)(11,13)(16,20)(17,19)(21,22);(8,12)(11,13)(16,21)(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, 6281343);