This infiltrating ductal carcinoma of the breast is definitely infiltrating the surrounding breast. The central white area is very hard and gritty, because the neoplasm is producing a desmoplastic reaction with lots of collagen. This is often called a "scirrhous" appearance. There may also be focal dystrophic calcification giving the cut surface a gritty texture.
Production of connective tissue stroma by a neoplasm is often what makes it appear firm on palpation. With invasion, this stroma may attach the cancer to surrounding structures so that it does not move freely with palpation.