June 2 (Reuters) - Federal Reserve Chair Jerome Powell held a phone call with the head of UBS Group AG in the days before the bank was propelled by Swiss authorities to buy smaller rival Credit Suisse, just one of the dozens of calls and meetings Powell held from mid-March onward as a banking crisis unfolded. Powell's monthly meeting logs, released by the Fed on May 5, showed the U.S. central bank chief spoke with Ralph Hamers, then the UBS chief executive, for 30 minutes on March 14. That was five days before UBS agreed to buy Credit Suisse in a deal engineered by Swiss authorities to avoid more market-shaking turmoil in global banking. (Reporting By Dan Burns; Editing by Chizu Nomiyama)