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C₂×#10993 #357533

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

Aliases

Subgroups

5114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

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, 264729);