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C₂×#27767 #6457640

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

Aliases

Subgroups

3062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6364836);