There is a lot to say.
The best place to go to examine the dynamics of Jack’s tribe are chapters nine and ten. In chapter nine, Jack hosts a feast, as they cooked the pig. Even though Ralph tries to dissuade those under his control not to go, they all wind up going. When Ralph arrives, Jack is akin to a savage king. His face is painted and he has complete authority. It is clear that he is in charge. The boys sing and dance and are caught in what seems like a bacchic frenzy. They even accidently kill Simon.
In Jack’s camp, there is no question who is in charge. Jack issues orders at will, and the boys listen and obey. Jack even punishes the boys. For example, Wilfred, one of the boys, is beaten.
Jack is not content with this power though, as he wants to kill the beast and even take over Ralph’s camp. In chapter ten, he makes a raid and attacks Ralph and those with him. He wanted Piggy's glasses to have the power of fire.
Based on this point, Jack is a tyrant that is ruled by his passions. He introduces a reign of terror.