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C₂×#12696 #493366

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

Aliases

Subgroups

4262 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)(9,15,16,22)(10,18,20,13)(11,14)(12,17)(19,21);(7,9)(8,12)(10,19)(11,16)(13,22)(14,21)(15,18)(17,20);(4,6)(9,16)(12,21)(15,22)(17,19)

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400562);