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C₂×#22435 #6379107

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

Aliases

Subgroups

5024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6286303);