when was this group established?
September 1934
Universal Music Group
The company's origins go back to the formation of the American branch of Decca Records in September 1934. 
when was taylor swift's first album released October 24, 2006 which label released it? Big Machine Records who owns this label? Universal Music Group
wiki:19539211
Universal Music Group [SEP] Early history
The company's origins go back to the formation of the American branch of Decca Records in September 1934. The Decca Record Co. Ltd. of England spun American Decca off in 1939. MCA Inc. merged with American Decca in 1962. In November 1990, Japanese multinational conglomerate Matsushita Electric agreed to acquire MCA for $6.59 billion. In 1995, Seagram acquired 80 percent of MCA from Matsushita. On December 9, 1996, the company was renamed Universal Studios, Inc., and its music division was renamed Universal Music Group; MCA Records continued as a label within the Universal Music Group. In May 1998, Seagram purchased PolyGram and merged it with Universal Music Group in early 1999.