What are some examples of indirect characterization of Tom Buchanan in The Great Gatsby?

Indirect characterization involves the author demonstrating what a character is like by that character's words, actions, and appearance. This is as opposed to direct characterization, where the narrator simply tells the reader what a character is like. Check out some examples of how the two look different in the link below. 

In The Great Gatsby, Tom is characterized as a powerful and wealthy man, whose power and wealth gives him an extreme arrogance about his position above those around him. Another aspect of his character is his obsession with the societal fear that "lesser" races will overcome his white, Nordic race. This racist language creeps into his fears and complaints about many other things:

"'Self-control!' repeated Tom incredulously. 'I suppose the latest thing is to sit back and let Mr. Nobody from Nowhere make love to your wife. Well, if that's the idea you can count me out […] Nowadays people begin by sneering at family life and family institutions, and next they'll throw everything overboard and have intermarriage between black and white.'

Flushed with his impassioned gibberish, he saw himself standing alone on the last barrier of civilization." (Chapter 7)

Here, we get indirect characterization of Tom from his own words, as well as Nick's direct characterization in filtering them through to us. Tom's view of himself is as the last remaining vestige of civilized behavior and common sense in the face of an absurd modern world. 

Though Nick describes Tom's "cruel body" in an instance of direct characterization when we first meet him, readers see Tom's cruel words throughout that story. One such instance is after Gatsby fails to get Daisy to run away with him and claim that she never loved Tom. When his position has been confirmed by Daisy's inability to do what Gatsby wants, Tom says,

"Go on. He won't annoy you. I think he realizes that his presumptuous little flirtation is over" (Chapter 7).

He isn't only cruel to Gatsby's feelings, but also Daisy's. He does nothing to hide his infidelity from her, nor does he apologize for his behavior:

"'And what's more, I love Daisy too. Once in a while I go off on a spree and make a fool of myself, but I always come back, and in my heart I love her all the time.'

'You're revolting,' said Daisy. She turned to me, and her voice, dropping an octave lower, filled the room with thrilling scorn: 'Do you know why we left Chicago? I'm surprised that they didn't treat you to the story of that little spree.'" (Chapter 7)

This conversation shows Tom's carelessness for others' feelings and his easy confidence that Daisy will always be his, no matter how he acts.