We investigate the symmetry structure of the WDVV equations. We obtain an r-parameter group of symmetries, where r= 1/2 (n 2+7n+4)+n/2. Moreover, it is proved that for n=3 and n=4 these comprise all symmetries. We determine a subgroup, which defines an SL2-action on the space of solutions. For the special case n=3 this action is compared to the SL2-symmetry of the Chazy equation. We construct similar solutions in the cases n=4 and n=5.