No, IATA tickets numbers go up in sequential order at the issuing office and so bear no relation to what's been booked, which is a good thing given the potential security nightmare it could be if you could somehow figure out from a confirmation/reservation number what was booked. A website like www.virtuallythere.com is operated by Sabre, which IIRC, is who Orbitz uses and so you can just enter your Sabre booking number and it will pull up more info including classes of service. Might be worth a try.

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