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C₂×#36419 #7630081

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

Aliases

Subgroups

9338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537277);