The third and fourth greatest warriors in the Achaean army, among other possibilities
"Aeantes" is the Greek plural form of "Ajax", and is a word used most commonly to describe in plural the exploits of two powerful warriors who fought on the side of the Greeks in the Trojan War, as recounted in The Illiad of Homer.
The two Aeantes were unrelated to each other, and to distinguish them, the are known as "Ajax the Great" and "Ajax the Lesser", or else "Telemonian Ajax" and "Locrian Ajax", respectively.
A massive mountain of a man, Telemonian Ajax was the son of Telemon and a cousin of Achilles, and had trained together with Achilles under the tutelege of the centaur Chiron. Locrian Ajax, on the other hand, was the king of the Locrians.
Together they were the third and fourth most powerful warriors in Agamemnon's army, after only Achilles and Diomedes.
Presumably, the word "Aeantes" would also come in handy if you had to talk other things named "Ajax", such as different implementations of Asynchronous JavaScript and XML, different types of Ajax Household Cleaner, different units of the Ajax antiaircraft missile, or different models of the Ajax, which was Britain's first functioning flush toilet (invented 1596).