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C₂×#46826 #7700645

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

Aliases

Subgroups

8356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7607841);