I don't know where you went wrong since you didn't post your work but the characteristic polynomial Maxima gave you is correct:

http://www.wolframalpha.com/input/?i=Det[{{2-x%2C0%2C0%2C1%2C0%2C1}%2C{0%2C2-x%2C0%2C0%2C1%2C0}%2C{0%2C0%2C2-x%2C0%2C0%2C0}%2C{-1%2C0%2C0%2C3-x%2C1%2C1}%2C{1%2C0%2C0%2C0%2C1-x%2C-1}%2C{-1%2C0%2C0%2C1%2C1%2C4-x}}]