Class helps determine leadership in the novel. We learn little about the class backgrounds of the various boys, but we do learn about Ralph and Piggy's positions on the class ladder. Ralph tells Piggy that he is the son of naval commander, who he says will rescue them. We also learn he was sent away to boarding school. He is athletic and "mild" and represents the leadership class in England. We can imagine his values were formed on the playing fields of a good English school.
Piggy is lower than Ralph on the class ladder. His father is dead, and he lives with his aunt who owns a candy shop. He is fat because he can eat all the candy he wants, but his weight also indicates that he is the product of local day school, not a good boarding school. The fact that he is related to a shopkeeper would put him in the lower middle class. He doesn't speak with the fluency of Ralph or Jack, pronouncing, for instance, the word asthma as "ass-mar." The deficits that comes from his class background prevent him from being a leader despite his intelligence.
We learn nothing of Jack's background but that his is roughly the equivalent of Ralph's is suggested by the way he speaks with authority. Ralph thinks about Jack:
This was the voice of one who knew his own mind.
Jack is also leader of the choir boys, which includes Simon. The speech patterns of both boys suggest they come from the middle class as they use a very standard English.
Class is important, as well as age, to who assumes leadership. While on the surface nobody quite knows why they immediately elect Ralph as leader, it is clear that he looks and sounds like the kind of person they have been conditioned to look up to. Ralph embodies the values of the English leadership class: he is rational, thinks of the needs of the group as a whole, and is able to defer gratification. He is decent, athletic, and brave. It his class values, the very essence of Englishness, that come under attack when Jack challenges his leadership.