Would have to at least know the frame size.
You must call S&W
it was made around the 1960's
If its a 5 shot its most likely a J frame. If its a 6 shot its most likely a K frame.
It is a J frame.
Open the cylinder and look at the frame that is usually hidden by the crane. The serial number is stamped on the frame.
Your early J frame model 36 Smith and Wesson was made in the year 1955 with the serial number that you have provided.
Call Smith and Wesson and they will tell you. You will be in the early 80's time frame.