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C₂×#23731 #6432407

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

Aliases

Subgroups

4302 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339603);