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C₂×#59641 #7666194

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

Aliases

Subgroups

8734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573390);