I believe 全く不愉快極まる is the predicate and the rest before the comma is the subject, but I don't understand how the two parts are connected by こと. Could you help me figure it out?
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You could imagine a similar sentence that has a は or が after the こと. こと is serving as the head of the relative clause which comes before it, and is basically a noun, which is why it can serve as the subject (and accordingly why it can be marked by subject/topic marking particles like が and は).
One way to analyze your sentence is that the lack of particle is due to one of は or が being dropped, since dropping of particles is possible in informal Japanese.
However, I think it’s best to think of it as a third way to mark subjects: with nothing, or rather, with a pause (which is why there is a comma).
I say this because it has a very slightly different nuance; in particular, it’s the most neutral way to put the sentence. Using が makes it feel like you’re either explicitly marking it as new information or trying to focus it, while は makes it feel like you’re trying to switch the topic to it, which may not be appropriate depending on how the sentence fits into the overall topic flow of the larger discourse — for example, a following sentence of これに関して、政府は(…) works better when your sentence doesn’t have a は in it and the whole point of bringing up the poor behavior thing was to talk about the government and its response. That is, the lack of topic in the first sentence prepares the listener for the real topic to come.