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C₂×#11165 #357925

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

Aliases

Subgroups

2646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265121);