  In this work the extreme nonlinear optical response of a giant fullerene
molecule C$_{240}$ in strong laser field is studied. The investigation of
high-order harmonic generation in such quantum nanostructure is presented
modeling the C$_{240}$ molecule and its interaction with the laser field in the
scope of the tight-binding mean-field approach. Electron-electron interaction
is modeled by the parametrized Ohno potentail, which takes into account
long-range Coulomb interaction. The essential role of many body Coulomb
interaction in determining of harmonics intensities is demonstrated. We also
consider vacancy-deffected molecule C$_{240}$. The presence of a single vacancy
breaks the icosahedral symmetry leading to the emergence of intense even-order
harmonics. We examine the dependence of moderate harmonics on laser frequency
that shows the multiphoton resonant nature of high harmonics generation. The
dependence of cutoff harmonics on both laser intensity and frequency are
examined too.
