  Due to the orbifold singularities, the intersection numbers on the moduli
space of curves $\bar{\sM}_{g,n}$ are in general rational numbers rather than
integers. We study the properties of the denominators of these intersection
numbers and their relationship with the orders of automorphism groups of stable
curves. In particular, we prove a conjecture of Itzykson and Zuber. We also
present a conjectural multinomial type numerical property for Hodge integrals.
