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C₂×#22184 #6376148

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

Aliases

Subgroups

3214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6283344);