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C₂×#34283 #7625543

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

Aliases

Subgroups

9106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532739);