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C₂×#52164 #7633494

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

Aliases

Subgroups

9948 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540690);