How do you find out if my deceased dad had service Group life insurance?

If by service Group life insurance you mean life insurance relating to the armed services, check with the Veterans Administration. Check the bank records to see if any insurance premiums have been paid, and to which insurance companies. Check any documents left behind by your dad. There should be some record of any insurance that he may have had. Most people keep all their legal documents in a file, somewhere. Sometimes it's in a safety deposit box.