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C₂×#23531 #6431941

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

Aliases

Subgroups

5142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339137);