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C₂×#10989 #357476

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

Aliases

Subgroups

5230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264672);