Well, this is particularly odd.
First of all, it isn't from 1951. It is a J frame Model 34-1 .22/32 Kit Gun from 1972 or 1973.
Second, it is extremely rare to find the serial number on the rear face of the cylinder on a revolver this late in the game. It just goes to show that you can "never say never" about S&W revolvers. An oddity shows up from time to time.
One weird fact here is the absence of the M on the cylinder. In this location they usually put the full serial number when they put one there at all.