Jack is a very powerful character. From the beginning, he had leadership qualities. He is the choir leader and voices that from day one. Not only is he very dominating with his personality, but he is a tall kid as well. When he makes decisions, the littluns would rather go along with him and make him happy (so they don't get punished). He also offers fun to them. There they are, trapped on a deserted island with no adults. What better way to spend your time--painting faces, hunting for pigs--playing "fort" or whatever it is that they do at Castle Rock. When Ralph wants to work and act like grown-ups, Jack offers them a chance to "play." They would much rather have fun and play than work. So his power comes from the fact that he stands up to and challenges their chief. He offers these things that Ralph (as a true leader who wants to get rescued) can't offer.
Many things make Jack powerful. First is that he is hungry for power. Second in that he is physically big. But ultimately Jack is powerful because he is prepared to use the wild power of the uncivilised tyrant.
Jack is Saddam Hussein gassing the Kurdish villages that may contain rebels. He is Stalin starving millions of Ukrainians as a warning to others. He is Pol Pot killing the middle class Cambodians because they are a threat to his rule.
Jack is powerful because he doesn't care about 'the rules' of society and is determined to be absolute ruler, at any cost.