That's a "Tri-5" rear end, 55-57 passenger car. The bolt-in center carrier assembly was used through 1964, with the 58-64 housing using coil spring suspension. Those rear ends managed to survive behind torquey 348 and 409 engines, so ignore the "They're too weak" comments. They did have a tendency to turn axle shafts into corkscrews during full throttle "Kamikaze" shifts on the drag strip with cheater slicks on the Super Stock cars. There should still be a good selection of aftermarket gears for those rear ends and limited slip carriers available from places like JEGS or Summit racing.
Jerry


"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!