I want to export a list of our groups along with their key contact details. The group entry does not have an address/postcode/email etc linked to it - those details are linked to the key contact.
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I presume that your key contacts are linked to the group by a relationship?
If so, I would suggest that you use advanced search to find the related contacts. You can do this by selecting the appropriate Relationship Type in the Relationship section. This will be something like 'Key contact for' (depending on how you have named this relationship).
You can then export the search results by clicking on Actions > Export contacts.
Read more in the manual: Searching