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C₂×#59835 #7666790

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

Aliases

Subgroups

7738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573986);