What classification is Tylenol?

"Class" is a bit ambiguous.

"Tylenol 2" refers to a specific brand and formulation of acetaminophen (paracetamol) and codeine. Acetaminophen is an analgesic (pain reliever) and antipyretic (fever reducer). Codeine is a narcotic (it also has other properties, such as being an antitussive (cough suppressant)).

Codeine itself is a Schedule II drug, but when mixed with acetaminophen, it is usually classified as Schedule III (mixing it with acetaminophen reduces the abuse potential, because acetaminophen is toxic to the liver in doses much above the recommended therapeutic dose; this keeps people from just taking many Tylenol 2 pills to obtain a large dose of codeine).