Unfortunately, there is no version history stored for any of the organisational items (Folders, Structure Groups, Categories, Publications, etc), so you will not be able to get this, even if you use the Core Service.
I have seen an implementation in the past that used the Event System to store a copy of the Structure Group information every time it was saved (in a text file), but this has limited usefulness without being able to view / rollback to a previous version.
I try to get around this limitation (as far as possible) by using Components to store the configuration of these items. For example, storing Publication Settings in a separate Component, rather than in individual Publication Metadata fields. This also has the added benefit of being able to localise these Components (for other Publications), put these items through Workflow and controlling access to them through Security Permissions (rather than having to give
Publication Management Rights).