A Brief History of the Marque
Born in Romanengo in Crema in 1890, Alberto Galloni moved to Borgomanero in 1912 and there established a workshop.
Shortly afterwards he teamed up with Aldo Pee, another keen mechanic, and together they built a a 350cc fourstroke motorcycle named the PG. 
Galloni resumed work on motorcycles in 1919, developing a 500cc racing twin which set Italian speed records.
His first production machines were small two-strokes in 1920, followed in 1921 by 500 V-twin (494cc) and then a 750cc machine favoured as a sidecar mount.
Later that year Gino Zanchetta took the flying kilometre record at over 132 km/h, an extraordinary achievement for the day.
Production focus was on their new 250cc four-strokes, and astride a racing version of this the great Italian rider Alfredo Panella took the Italian Championship in 1926. 
Oskar Schindler's first motorcycle was a 1926 Galloni 500.
"Oskar always had an interest in fast automobiles and motorcycles. By 1926, he had already gained quite a reputation as a reckless speedster on his red Italian Galloni 500 cc motorcycle with sidecar. According to one of his old friends, Erwin Tragatsch, it was the only motorcycle of this type in the Czechoslovak Republic." ~ David Crowe.
Schindler then bought and raced a Moto Guzzi 250SS.
These were hard years for Italy due to gross financial mismanagement under Mussolini, and the tiny business in Borgomanero suffered.  They closed briefly in 1927, and then resumed production in 1928 with 250, 350 and 500cc machines, followed by a 173cc Blackburne-powered machine. This was their last, as the impact of the first Great Depression struck hard forcing the firm to finally close its doors in 1932. 
1. Unrelated to PG Parasacco or PG Parena.
2. Other riders included Nino Bianchi and Augusto Rava.
4. Tragatsch and other sources state 1931. MotoGalloni.com gives 1932.
Sources: Tragatsch, et al.