Is it "admiration for" or "admiration of"?
For instance, does the sentence "He had a great admiration of Washington Irving." make sense?
Possibly there's a US/UK divide here. I don't much like OP's example usage.
It's not obvious why the adjective "great" should affect the acceptable preposition either, but I must say "He had an admiration of Washington Irving" sounds awful to me. I'd always use for, and drop the article...
EDIT: As @Armen Ծիրունյան's answer points out, admiration of still occurs fairly often, but it tends to be used with "adjectival" constructions involving [to be] in admiration of - where admiration has a more overt "noun" sense, we use [to have] [an] admiration for.
Note that in both those NGram links, the alternative preposition doesn't occur often enough to show on the chart. Since OP's example is the second of the above constructions, it's clear the overwhelmingly majority of writers use for in that context.
Both admiration of and admiration for are correct, and have the same meaning. Google NGrams Viewer shows that although admiration of used to be prevalent before 1920, neither has a decisive upper hand now.