I'm looking down thru the specs page of obsolete US cartridges in 11th Ed of Barnes Cartridges of the World , but your measurements don't jibe with anything.
Does the case appear to be a straight-walled or slight bottleneck?
listed under military cartridges is the 11.4x50Rmm Brazillian Comblain M74(?). Chambered in Remington Rolling Blocks sold to Brazillian Civil Guardia.
Base dia. .588''
Rim dia .682''
Case length 2.02''
Neck dia .494''
Shoulder dia .530''