Clearing Group Membership?

OK, having a ship being able to serve as a member of several numbered groups can be useful, but 2 questions:

How do you remove a ship from a specific numbered group?  The hotkey card says Ctrl+Shift+Number but it doesn't seem to work.  Is anyone having success with a hotkey combo?

How do you clear all group memberships from a specific ship to make it available for reassignment?

The workaround is to create a fresh group and Ctrl+Number to recreate it for each number you want to remove, but imposing a waste of time like that does not make sense for RTS gaming.

Thanks in advance for your help.