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C₂×#10953 #354121

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

Aliases

Subgroups

3314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 261317);