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C₂×#23500 #6431887

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

Aliases

Subgroups

4878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339083);