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C₂×#23495 #6431878

• 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)(10,15)(11,14)(12,16)(17,20)(18,22)(19,21);(3,4)(5,6)(7,9)(8,13)(10,17)(11,19)(12,18)(14,21)(15,20)(16,22);(3,5,6,4)(8,14)(10,11)(13,20)(15,16)(17,19)(21,22);(7,10,12,11)(8,15,16,14)(9,17,18,19)(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, 6339074);