The Hall resistance of a low density two-dimensional electron gas submitted to an intense magnetic field shows quantization at low temperatures. The Integer Quantum Hall effect (IQHE) is due to the arrangement of the electronic states into Landau levels, and in consequence the existence of gaps that cancel the longitudinal conductance. In the case of a quantum dot, mean field calculations like Hartree-Fock give a very good description of the experimentally measured phase transitions of the finite electronic system. At higher magnetic fields, and when the system is totally spin polarised, new gaps appear corresponding to the fractional occupation of one Landau level with a filling factor of 2/3,3/5,2/5 or 1/3, and this cannot be understood from the simple picture of the IQHE. We have obtained these FQHE phases for magnetic fields up to filling factor 1/2 in a ten electron quantum dot, using Configuration Interaction calculations.