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C₂×#9546 #202333

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

Aliases

Subgroups

1136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 109529);