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C₂×#59168 #7666116

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

Aliases

Subgroups

9174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573312);