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C₂×#23969 #6451796

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

Aliases

Subgroups

5038 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6358992);