How can I find out what happened to my transaction? I have not received a 0.1777776 BTC transaction to my Coinbase wallet that was sent from Gladiacoin on 6/3/2017. Is there anyway I can find out where this payment went?
According to Bitcoin info part of the money was transferred from my coin base address to address another bit coin address and then immediately transferred to a third account.  I did not authorize any of this so do I have any recourse to get my money back
I'm assuming by asking where the payment went, you're asking how to find the transaction output address. If you have the transaction ID, you can search for it on a site like https://blockchain.info/. Then look for the output address. 

If you don't have the transaction ID, but you have your original Gladiacoin wallet address, you can look up the Gladiacoin wallet address on https://blockchain.info/ and see what transactions were made that way.