BEST IC RIM CYLINDER HOUSING STANDARD SPINDLE in the  605 bright brass Finish.
Housing in the listing sold less cylinder

Standard rim cylinder applications require the use of BEST's 1E rim cylinder series. BEST rim cylinders are interchangeable with other manufacturers' rim cylinders. BEST rim cylinders are machined from solid bar stock and are available in a variety of finishes. The item in the listing includes cylinder housing  with RP1 ring package part number  1E-72 includes dimension of  1-11/32"   and door thickness 1-1/4" to 3"
tailpiece, clamp plate and clamp plate screws. BEST original instructions included.

Cylinder diameter — 1-5/32"