You'll need to verify the S prefix on the butt, but the serial number is repeated on the rear face of the cylinder. S146777 places it in the 1955-1956 range for post war N frame revolvers (Models 21-29 and 57-58).
S&W switched to the 4 screw side plate in the first 6 months of 1957, so yours should have 5 screws in the frame and side plate - one will be hidden under the grip, and one will be in the front of the frame.
As indicated above S&W switched to model and dash numbers in 1957, stamping them on the frame under the crane.
It's possibly a 1950 .45 Target Model.[/b]
These were introduced in Feb 1950 in .45 ACP (standard) and later in .45 Colt (scarce). They had a 6 1/2" ribbed, tapered and pinned barrel. In .45 Colt the six shot fluted cylinder should be 1.67" long (.45 ACP has a 1.55" long cylinder). The .265" wide trigger was standard, but a .500" target trigger was optional, and they came with a .400" wide semi-target hammer. The barrel should be marked ".45 CAL MODEL 1950", but some of the earliest production revolvers lacked the caliber marking on the barrel.
A total of 200 were chambered in .45 Colt from 1953 to 1957 out of a total of 2,768 produced from 1950 to 1961 and they all fall in the serial number range of S76212 to S211000.
The .45 ACP version became the Model 26, and a pre-26 in 99% condition is probably a $1500 revolver. In excellent condition, it's an $1800-$1900 revolver.
The same revolver in .45 Colt will bring between two and four times those amounts, and in that case you're probably looking at a $4000-$5000 revolver.
There were a few made with experimental 6 1/2" heavy barrels and there have been some reported with 4" and 5" barrels, and those are extremely rare.
Consequently, if you've got a .45 Colt Model of 1950 with a 4" or 5" barrel, in excellent condition you've got a very spendy revolver. Condition is hard to tell in your pictures, but even if it is not in 99%-100% condition, it's still worth a lot of money as it would be a very rare example of a scarce caliber with a rare barrel length.
I'd definitely write S&W and get a factory letter for it.