The former head of the Federal Communications Commission is starting a new job at the secretive private equity firm the Carlyle Group. Nicknamed “the Ex-President’s Club,” Carlyle’s roster has included a long list of powerful figures, including both Bush presidents. Carlyle owns a majority stake in Booz Allen Hamilton, the military contractor that employed Edward Snowden. Julius Genachowski, who led the FCC for four years under President Obama, will serve as a managing director and partner, specializing in telecommunications.