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C₂×#59011 #7665806

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

Aliases

Subgroups

10682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573002);