what parts in the story show us that jack is violent, brutal, cruel

There are many to pick from. From the outset Jack is determined to put on a show of violence, "he snatched his knife out of the sheath and stabbed it into a tree trunk". Jack carries on in much the same fashion. When punishment for rule infringement comes up Jack says, "We'll have rules! Lots of rules! Then when anyone breaks 'em pow....." Perhaps the most insidious line from Jack comes from a discussion over what they might hunt. Jack casually says, "'Use a littlun..." The boys laugh nervously but Jack is serious. As the norms of society quickly fade Jack becomes increasingly violent. In the end Jack is a little socio-path bent on destruction of the whole island.