What is a 30M1 carbine with serial number 4770017 with QUAU H.M.C stand for?

The QUAU H.M.C. on the gun stands for Quality Hardware Manufacturing Company which was one of the companies producing M1 carbines. Quality Hardware made about 360,000 carbines for the US Army during World War 2 times. The serial number of the gun would date its production to a period of time between September 1943 and May 1944. This info was taken from J.C. Harrison's "Collecting The M1 Carbine III" which has a list of carbine manufacturers and serial numbers by date.