The Church of course is charismatic, and it is also missionary, evangelistic, and many other qualities. Obviously, the Church, when formulating the Niceno-Constantinopolitan Creed, had to find those most essential qualities that best encompass her identity. And the Church Fathers decided upon one, holy, catholic and apostolic.
The Church is one since Jesus founded only one Church, who is the Bride of the the only one God. The Church is one also because there is only one true faith. And she is one also because we are called to be one people, one family.
The Church is holy because God is holy, and the Church in essence is His Bride. The Church is holy also because she is sustained by the Holy Spirit, and thus through her has the power to cleanse us from sins and bestow the power to make us into God‘s children. While her children are sinners, she has the power to teach, sanctify and govern us towards holiness.
The Church is catholic, meaning the Church is universal. Universal because the Church is for all people; all are welcome to join us regardless of race, language or background. She is universal also because she is called to evangelize the whole world.
The Church is lastly apostolic, since she was founded by the apostles, and she was sent out by Jesus to make disciples of the whole world.
I suppose from the above, charismatic would be under holy and apostolic. But since the Holy Spirit also draws all people together into one, charismatic is also under one and catholic. Well, there you have it.