What contributed most to the growing gap between social classes during the Industrial Revolution?
The concentration of capital
During the Industrial Revolution, only the wealthy could invest and production means such as factories were in their hands. As time went by competition had the most competitive have the less competitive go bankrupt. This is what explains the emergence of Corporations that the 1890 Sherman Act tried to break up unsuccessfully.
Common people were unable to invest and as major sectors such as oil, steel or railways were more and more concentrated into fewer hands it was even harder to compete and the gap between the rich and the poor widened. The people who benefitted from such concentration, for instance Carnegie or Rockefeller were nicknamed the "Robber Barons"