There are numerous points in the book where Jack behaves with what one could term savagery, and these savage behaviors become more intense as the novel progresses. One of his first savage acts is when he plows into Piggy's stomach and breaks his glasses. Although he is actually mad at himself, to some extent, for letting the signal fire go out just as the ship was passing the island, and he is mad at Ralph for being in the right and for having reprimanded him, he takes out his anger on Piggy—someone who is less respected by the group and weaker. By violently targeting a weaker person, he is behaving with savagery.
Later, when he has separated from Ralph's group and needs fire for his own tribe, he raids Ralph's camp during the night, and he and his boys beat up Ralph's group and steal Piggy's glasses. This was unnecessary because Ralph would have shared fire with Jack's group, but Jack chooses violence as his way to get what he wants.
During Jack's frenzied feast, Jack and all the other boys murder Simon in a savage mob attack.
When Jack sets up his camp on Castle Rock, he has the boys keep Wilfred tied up all day, and then he beats him, which is another act of savagery—this time against his own followers.
Finally, after Piggy's death, Jack plans to hunt Ralph and kill him. He sets fire to the island to smoke Ralph out of his hiding place. He is ready to commit bold premeditated murder—his greatest act of savagery.