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C₂×#10973 #357444

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

Aliases

Subgroups

5094 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 264640);