Hey there!
Moving groups from one board to another is currently not supported by our API. You can see all the operations you can do on groups here: Groups queries
What are you trying to do?
As a workaround: archive the group and create it (with the included items) on the new board. The downside of this approach is that you’ll lose the activity log (ie, history of changes) and the IDs of the new items will be different.
(Thanks @andrewalmand for moving the topic!)