Is this a gerund phrase after hate?

"I hate not being able to control my temper."

From my understanding, hate is one of those verbs that is followed by a gerund OR an infinitive. In this situation, is "being" a gerund?

From EF.com https://www.ef.com/ca/english-resources/english-grammar/using-hate-love/ the verbs "to hate", "to like", and "to love" The verbs hate, love, like, & prefer are usually followed by a gerund when the meaning is general, and by the infinitive when they refer to a particular time or situation. You must always use the infinitive with the expressions would love to, would hate to, etc. These verbs can also be followed by a that-clause or by a noun.

Solution 1:

being in this case heads a gerund-participial clause. It has the internal structure of a complex-intransitive clause with adjunct not.

(my/me) [understood subject]

not [adjunct - negation]

being [verb at the head of the clause]

able to control my temper [subjective predicative complement]

These are also known as -ing clauses or present participle clauses depending on who you ask. The Oxford Dictionary of English Grammar p217

-ing clause A non-finite clause whose verb phrase contains a verb ending in -ing as its head. Also called present participle clause, -ing participle clause, and gerund-participial clause. Examples:

The boss hates him always complaining about everything

I love working late

Notice that the first example contains its own subject, whereas the second example does not.