There is no "assignment group" field on the task_sla table, nor is there a historic value for the field on the task_sla table.
Kingston Patch 4
The customer can create a custom field on the task_sla table, something like "u_assignment_group," and then create a Business Rule that runs on the incident table.
It will say something like...
When to run: when assignment group changes
The Business Rule script will say something like:
current.assignment_group = current.u_assignment_group;
This is only a suggestion. As this functionality is not provided OOB (Out of the Box, by default), it is a custom implementation.
If the customer has any questions with implementing something like this, or run into any issues as they try to implement - we can refer them to our Professional Services team (Note: there is a fee with this service).