Hi HomerJ,
There is a QCCR; QCCR1J21507 that is in deferred status asking for exactly that functionality. As it is currently the data is maintained between 2 tables: the ACTIONS table and the TABLES tables. Unfortunately these are identified by strings of binary and the groups ID number is converted to binary and then cross referenced within the other tables by the combination of the binary bits to determine which groups are affected and then the bits are once again turned on based upon binary cross references. As you can see this is a very tedious process for the average user to decipher and encode into a downloadable query. The database table cross reference shows the dependencies and how they are interconnected but as of current no way to generate a report of or export of group permissions exist.
I have found a reference to the following new tool that was recently released by Microfocus. It is recently released and recommended by a microfocus engineer and seems to be able to accomplish what you are desiring. I will mention that the groups and permissions are project dependent (unless you are managing them through a shared and distributed template for all your projects) and as such you would need to run the reports for each individual project or domain as they would differ amongst projects. The tool is here: https://marketplace.microfocus.com/appdelivery/content/qc-project-insight
Hope this helps,
Dan