 British General Bernard Montgomery ( commanding the ground forces in Normandy ) now wanted an attack on the eastern flank of the front to capture Falaise , intending that such a move would precipitate a general German collapse . The First Canadian Army , commanded by Lieutenant General Harry Crerar , held this part of the Allied front . It consisted of the British I Corps , responsible for the extreme eastern flank of the Allied lines , and II Canadian Corps south of Caen . Canadian II Corps , which was to launch Operation Totalize , was commanded by Lieutenant General Guy Simonds and consisted of the 2nd Canadian Infantry Division , 3rd Canadian Infantry Division , 49th ( West Riding ) Infantry Division , 51st ( Highland ) Infantry Division , 4th Canadian ( Armoured ) Division , 1st Polish Armoured Division , 2nd Canadian Armoured Brigade and the British 33rd Armoured Brigade . 
