Greater Ajax, often referred to as Ajax the Great, was son of Telemon (hence his other name, Telemonian Ajax) and the king of Salamis. He a massive and powerful man, called a 'bulwark' (6.5), and second only among the Achaean troops to Achilles. Throughout the book he is characterized by his prowess and fighting abilities.
Lesser Ajax was the second swiftest of the Achaean forces, second only to Achilles. Inside of the Iliad he is characterized by such, cutting quickly through enemy Trojan ranks. Outside of the Iliad, he is most well known for his tragic raping of Cassandra, daughter of King Priam and brother of Hector, after the fall of Troy. In Athena's temple he advanced on her, and accordingly Athena threatened to destroy the Achaean fleet if he was not immediately stoned.