One of the twelve ships in the Zion military fleet, Ajax became its captain during the Sixth Matrix Resistance.
The crew of the Icarus, along with those of the rest of the fleet, attended the Crisis Meeting to hear Niobe's news of the impending attack on Zion by an army of Sentinels and Diggers. On entering the Matrix, they took a hovercraft through the sewers to get to the rendezvous.
The Icarus was one of five hovercraft sent by Commander Jason Lock on a pre-emptive ambush against the Sentinels at the tunnel bottlenecks leading to Zion. It was one of the two first to be positioned for the EMP counterattack, and the first to give confirmation to Zion command that they were in place.
Soon after however, contact was lost, along with Novalis and the Caduceus, when Bane, possessed by Smith in the Real World, triggered the EMP of the Caduceus, leaving the ships unprotected, and allowing the Sentinels to massacre the crews of all the ships. Only the Mjolnir, which was too far away to be affected, escaped destruction, and went to check for survivors; only Bane was still alive.
The ship's last captain before its destruction was Ajax (who was not joined around the table at the Crisis Meeting by any of his crew) but it had at least one female crew member (presumably Zion born) whose mother petitioned Neo to protect her daughter on the Icarus on his return from the Crisis Meeting.