The chemical reaction is as follows:
$$C_5H_8 + 2KMnO_4 + H_2SO_4 → C_5H_6O_2 + 2MnO_2 + K_2SO_4 + H_2O$$
The products of the reaction are adipic acid, manganese dioxide, potassium sulfate, and water. In this reaction, the potassium permanganate acts as an oxidizing agent, while the sulfuric acid provides the acidic environment necessary for the reaction to take place.