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C₂×#59317 #7666459

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

Aliases

Subgroups

7764 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573655);