Object picking in cluttered scenes is a widely investigated field of robot manipulation, however, ambidextrous robot picking is still an important and challenging issue. We found the fusion of different prehensile actions (grasp and suction) can expand the range of objects that can be picked by robot, and the fusion of prehensile action and nonprehensile action (push) can expand the picking space of ambidextrous robot. In this paper, we propose a Push-Grasp-Suction (PGS) tri-mode grasping learning network for ambidextrous robot picking through the fusion of different prehensile actions and the fusion of prehensile action and nonprehensile aciton. The prehensile branch of PGS takes point clouds as input, and the 6-DoF picking configuration of grasp and suction in cluttered scenes are generated by multi-task point cloud learning. The nonprehensile branch with depth image input generates instance segmentation map and push configuration, cooperating with the prehensile actions to complete the picking of objects out of single-arm space. PGS generalizes well in real scene and achieves state-of-the-art picking performance.