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C₂×#59651 #7665961

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

Aliases

Subgroups

8676 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573157);