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C₂×#10742 #353421

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

Aliases

Subgroups

4198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260617);