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C₂×#26842 #6443878

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

Aliases

Subgroups

2580 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6351074);