It looks like either a slip joint nut, or something else serving as a slip joint nut. I understand it does not look like a normal slip joint nut. There would also be a slip joint washer.
I am thinking either of these could replace this if the OD on your thread is 1.66 inch.
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Make tubular drain applications a breeze with the 1-1/4 in. Slip Joint Zinc Nut with Washer. The nut features die-cast zinc construction with chrome plating for a long life. The included washer is durability
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The thing that connects between there and your lavatory tailpiece would be a 1-1/4 slip joint trap. Available in plastic or chrome-plated brass.
If the OD on your thread is 1.9 inch, then similar widely-available choices exist.
You would unscrew the existing nut by turning the hex CCW.