Not part of a musical group, but he does appear to be a musician:
Chris Austin Hadfield (born August 29, 1959) is a Canadian retired astronaut, engineer, fighter pilot, musician, and writer.
During his free time on Expedition 35, Hadfield recorded music for an album, using the Larrivée Parlor guitar previously brought to the ISS.
His collaboration with Ed Robertson of Barenaked Ladies and the Wexford Gleeks, Is Somebody Singing?—sometimes shortened I.S.S.—was aired on the CBC Radio program Q and released by CBC Music online on February 8, 2013.
Hadfield has been credited musically on his brother Dave Hadfield’s albums.
Which major musical group is he a part of?
Not part of a musical group, but he does appear to be a musician:
Chris Hadfield Wikipedia
Oh, thank you! I knew he did a cover of Space Oddity, but hadn’t heard of his professional musical endeavors