It appears to be a .357 Magnum revolver with a 3.5" barrel. I am assuming that there is a letter "S" in front of the serial number on the butt; the S is part of the serial number. The numbers on the frame and yoke that you see when the cylinder swings out are irrelevant for identification purposes.
Your gun probably dates from the mid-1950s. Collectors sometimes call this model the Pre-27 because in the 1957-58 timeframe S&W began assigning model numbers to their guns, and the large frame .357 Magnum became known as the Model 27.