Error
It is possible to set a Group attribute value by using the Run SQL action, and there are probably other ways ...
it would be obvious for newbies, like me, how to do this if there was an action type 'Attribute Set From Group' like there is 'Attribute Set From Person'. Allow the specification of Group Type, then Group, and put the resulting (GUID?) into the specified group attribute. (I guess there is some reason why it's not there yet, but it took me a long time to work out an alternative way to do this, and the documentation isn't clear how to do it.)
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