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C₂×#21467 #6372686

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

Aliases

Subgroups

4624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6279882);