A phrase like "athletic department" can be used in two ways, either as a descriptive phrase using the words in their general uncapitalised sense, or as the proper name (or part thereof) of an organisation, in which case it would be capitalised. To check the exact form and usage of proper names it is usually best to check how the relevant organisation presents them. The FSU website is not totally consistent; probably in the majority of cases they do capitalise it, but sometimes they don't.
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