Nick repeatedly described Tom in terms of Tom's physical bearing, suggesting that Tom is a "brute" on numerous occasions.
In Tom's first appearance in the story, Nick describes Tom as having "[t]wo shining arrogant eyes" which "established dominance over his face and gave him the appearance of always leaning aggressively forward". Tom's physicality is seen, by Nick, as brutal and cruel, as we see here. These physical characteristics match Tom's behavior as well.
Nick remarks on Tom's infidelities and tells the story of a time when he sees Tom strike Myrtle. This violent bearing is not, however, limited to personality alone but is also linked to Tom's wealth, which insulates him from blame and, it would seem, from moral considerations of any kind. He does not feel any need to be nice to people, as we see in his treatment of his wife and his mistress. He also views his business with Myrtle's husband as a sort of joke, underscoring his lack of empathy and apparent immunity from guilty feelings. (He promises to sell Wilson a car as a pretense for stopping in and making a date with Myrtle. He even brings Nick along to watch.)
While the link is not entirely direct, Nick's description of Tom's wealth is significantly tied to Tom's overbearing and aggressive stature; his "paternal contempt...even toward people he liked". Coming from an "enormously wealthy" family, Tom is not vulnerable to potential failure as most people are just as he is physically sturdy and built as if from brick.
There is, in all this, a decidedly obtuse aspect to Tom. He is not entirely stupid but he is also largely ignorant (and indifferent) regarding the feelings and lives of others around him. Tom's brutishness is, partly, the result of a lack of caring and the lack of a need to care. It is also partly the result of a lack of intelligence (emotional intelligence at least).
"Completely without taste, culture, or sensitivity" (eNotes), Tom stands as a nearly opposite figure to Gatsby, who remains vulnerable despite his wealth. Both men lack taste and culture, but Gatsby seeks approval where Tom is described as being beyond the need for approval. His family's wealth entitles him to the most unenlightened opinions, which still do not threaten his social position.