You weren't given a Model # because the gun predates model numbers which started in 1957. It has the Model name of 38/44 Heavy Duty. It became the Model 20 in 1957 so you can look for parts for that Model #.

The Mod 28 cylinder is a 357 Magnum cylinder but also is correct to shoot 38 Specials. But do not shoot 357s in it even though they chamber because the frame was not designed for 357 mag.

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Jim
S&WCA #819