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C₂×#22453 #6379172

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

Aliases

Subgroups

4692 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6286368);