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C₂×#27934 #6457315

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

Aliases

Subgroups

3010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6364511);