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C₂×#36441 #7630121

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

Aliases

Subgroups

11242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537317);