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C₂×#13822 #513492

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

Aliases

Subgroups

6234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420688);