If we break down the word, "Fraternity," it comes from the Latin word, "Frater," meaning "brother." In the world of Of Mice and Men, fraternity and friendship are conspicuously missing, apart from Lennie and George. This is actually what sets them apart from everyone else in the novella. Slim makes this observation in a conversation he has with George. The text says:
Slim looked through George and beyond him. “Ain’t many guys travel around together,” he mused. “I don’t know why. Maybe ever’body in the whole damn world is scared of each other.”
Slim is accurate in his words. There is no friendship or fraternity in the book. Everyone is scared, and alienation reigns supreme. For example, in all the years that Crooks has been on the farm, he has never had a visitor. Candy, the older swamper, has no friends, and he feels useless on account of his old age. Curley's wife is not even given a name.
In light of these examples, the only friendship is the friendship between George and Curley. The irony of all of this is that it is George's loyalty to Lennie that makes him shot Lennie at the end of the story. This shows that the world of migrant workers is a severely broken one.