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Aims:This paper is the third in a series implementing a classification systemfor Gaia observations of unresolved galaxies. The system makes use of templategalaxy spectra in order to determine spectral classes and estimate intrinsicastrophysical parameters. In previous work we used synthetic galaxy spectraproduced by PEGASE.2 code to simulate Gaia observations and to test theperformance of Support Vector Machine (SVM) classifiers and parametrizers. Herewe produce a semi-empirical library of galaxy spectra by fitting SDSS spectrawith the previously produced synthetic libraries. We present (1) thesemi-empirical library of galaxy spectra, (2) a comparison between the observedand synthetic spectra, and (3) first results of claassification andparametrization experiments with simulated Gaia spectrophotometry of thislibrary. Methods: We use chi2-fitting to fit SDSS galaxy spectra with thesynthetic library in order to construct a semi-empirical library of galaxyspectra in which (1) the real spectra are extended by the synthetic ones inorder to cover the full wavelength range of Gaia, and (2) astrophysicalparameters are assigned to the SDSS spectra by the best fitting syntheticspectrum. The SVM models were trained with and applied to semi-empiricalspectra. Tests were performed for the classification of spectral types and theestimation of the most significant galaxy parameters (in particular redshift,mass to light ratio and star formation history). Results: We produce asemi-empirical library of 33670 galaxy spectra covering the wavelength range250 to 1050 nm at a sampling of 1 nm or less. Using the results of the fittingof the SDSS spectra with our synthetic library, we investigate the range of theinput model parameters that produces spectra which are in good agreement withobservations. (abridged)

A semi-empirical library of galaxy spectra for Gaia classification based on SDSS data and PEGASE models