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C₂×#51780 #7707722

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

Aliases

Subgroups

10478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7614918);