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