The Fred Gretsch Mfg Co was formed by Friedrich Gretsch at the age of 27 when he left his job of working for the drum and banjo makers Albert Houdlet & Son, of Brooklyn, NY.
With a few workmen he opened a small shop at 128 Middleton Street, Brooklyn and manufactured drums, banjos and tambourines. Fred Gretsch died on 1895 when his firm had but a dozen employees, and was housed in a wooden building in South 4th Street, Brooklyn.
Within 5 years, his son Fred (the eldest of Fred Sr's 7 children) had impressively altered the firms operations to include the making of mandolins, (then popular in the States) and, in addition, the importation of most musical instruments and their various accessories.
They also had acquired impressive factory premises at 104 Middle Street which were vacated in 1916 for the mammoth 10 story office and factory building at 60 Broadway, Brooklyn, which is still (1972) the home of The Fred Gretsch Mfg. Co.
They were making and advertising  banjos from about 1870 and in 1902introduced 'Daynor" banjos, each of which had a hole in the vellum.
After World War 1 they made a range of banjos which the trade name "Rex"
and these were being  advertised well into the 1920s. By 1928 their range of banjos had been extended, for the company was by then advertising their "Gretsch", "Clarophone" and Orchestrekka" models in addition the still popular "Rex" range.
In addition to this, they were making banjos for sale under many other brand names, notably Wurlitzer and Bruno.
In March 1940, the company acquired the Bacon Banjo Company of Croton, Conn., and the post-war "B&D" range of banjos has been made in their factory and sold by them.
This Banjo Ukulele is of sound construction and has a lovely tone.

My grateful thanks to John Clough, Vensac, France for the above information