You have a post war .38/44 Heavy Duty manufactured between 1946 & 1950. These were built on the large .44 sized N Frame (hence .38/44) and were intended to shoot the .38 High Speed, a hot loaded .38 special round which was superceded by the .357 magnum.
Yours is considered a transitional gun as it has the pre war long action and the post war internal hammer block safety. By 1950 the long action was replaced with the current short action, so the transitional variant had a short run, with around 2500 manufactured between 1946 & 1950 in the serial range S62496 & S75206.
In 2006 the Standard catalog of S&W gave the following values: ANIB $1500, Excellent condition $850, very Good $550, Good $385, Fair $250, Poor $125.
keyboard commando is thinking of the smaller K framed .38 Military & Police which also had an S prefix, but all of the K frame S prefix guns had a six digit serial number.