I’m trying to identify a book by a rather vague plot line that I’ve been given... Society is split into three classes. The lower, middle and untouchables. Teenagers are trained to be SAS type killers.
Could be Uglies by Scott Westerfeld. The book and its sequels "Pretties" and "Specials" takes place in a dystopian future where children are born as "Uglies". The three factions your friend might be thinking of correspond to each of the titles in the series.
From the wikipedia article (which sums up the societal factions):
Everyone on their sixteenth birthday receives the “pretty” operation which transforms them into the society's standard of beautiful. After the operation, new Pretties cross the river that divides the city and lead a new life with no responsibilities or obligations. There are two other operations available, one to transform Pretties into “Middle-Pretties” (adults with a job), and another to transform Middle-Pretties into "Crumblies".
Without giving too much away, the "Pretty" procedure turns them into model citizens in every way. Inevitably, there are some dissenters who do not undergo the standard procedures, they're known as "Smokies", and on top of that, there are special operatives: the "Specials". The Specials act as a sort of law enforcement agency to make sure everyone gets their proper procedures. They have enhanced physicality/senses (from the "Special" procedure) and could be viewed as "SAS type killers".
A quick search shows that you can find the Audiobooks on YouTube.