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C₂×#22260 #6376394

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

Aliases

Subgroups

3354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6283590);