I thought it would be about a girl who decides to make a club (which helps people), or she is a president of school. Good leader, always listens to other people's problmes and tries to help them. Like a superhero. Very smart and talented in lots of subject. Something like Misa-chan from 'Kaichou wa Maid-sama'.
How it really is:
[Warning: SPOILERS (around episodes 1-8)]
The only thing I guessed was that she makes a club (but it was Kyon who gived her idea, I think in episode 2). She forces people to join the club and doesn't really care about their say or ideas. She loves supernatural things like aliens, esper or time traveler. Anything unusual!
People that are one of them (but she don't know about it) says that the world spins areound her. If she wants she can destroy the world and make a new one