Is the extraversion the most important to be a leader of a group? The best leader must be extrovert?

1. Once we were assigned to accomplish a project with several teams together,
and from those teams we had to choose a leader to each team and a manager for
being responsible all teams. Thus, we decided to elect the manager with
anonymous vote. After counting the votes, there are several candidates with very
close numbers of voting. But in the end the manager was the one who wasn’t
really extrovert. Other people, who were normally acting extrovert, were the
supporting roles to the manager.
Interesting situation happened, when we started to discuss several issues,
the supporting roles were starting to talk and taking over the manager’s voice.
The whole environment was wired. The manager was totally silence. In contrast,
the supporting roles kept showing their own opinions and trying to make the
decision for all. With this situation, we can easily find out Extraversion is
partially important of leadership. If you are not extrovert enough, people take
over your speech and power. On the other hand, with too much extraversion,
people tend to be less receptive. In this case, even lack of respect to the manager.
Since we were in a group that members were likely proactive. In the end
shows even we elected an ambivert leader, making our project not only turning
out on time, but also being perfect. Due to our leader was open to experiences
and agreeable. Therefore it enhanced our overall performance.
Furthermore, since the leader was flexible to talk and listening. It gained
organizational commitments easily. People obeyed the rules and did tasks
efficiently. People felt obligate to the project, and gave the best working
performance.
During the leadership classes I learned being extrovert is not the only either
the most important element to be a leader. It actually depends what kind of the
group where you belong. But having certain extraversion is a path to avoid
people stepping over you and also it helps you to inspire followers. Like the
classes mentioned, being less extrovert person it doesn’t mean you could not be a
leader. Charisma can be developed. The important is not fitting the exact profile
of a leader to be a leader. The goal is to develop the style of leadership that fits
your personality. Last but not least, being a good leader, is not just about you,
sometimes organization culture also determines what is the better way to be a
better leader.