We present high spatial resolution integral-field spectroscopy of 28 elliptical (E) and lenticular (S0) galaxies from the SAURON representative survey obtained with the OASIS spectrograph during its operation at the CFHT. These seeing-limited observations explore the central 8x10 (typically one kiloparsec diameter) regions of these galaxies using a spatial sampling four times higher than SAURON (0.27 vs. 0.94 spatial elements), resulting in almost a factor of two improvement in the median PSF. These data allow accurate study of the central regions to complement the large-scale view provided by SAURON. Here we present the stellar and gas kinematics, stellar absorption-line strengths and nebular emission-line strengths for this sample. We also characterise the stellar velocity maps using the kinemetry technique, and derive maps of the luminosity-weighted stellar age, metallicity and abundance ratio via stellar population models. We give a brief review of the structures found in our maps, linking also to larger-scale structures measured with SAURON. We present two previously unreported kinematically-decoupled components (KDCs) in the centres of NGC3032 and NGC4382. We compare the intrinsic size and luminosity-weighted stellar age of all the visible KDCs in the full SAURON sample, and find two types of components: kiloparsec-scale KDCs, which are older than 8 Gyr, and are found in galaxies with little net rotation; and compact KDCs, which have intrinsic diameters of less than a few hundred parsec, show a range of stellar ages from 0.5 - 15 Gyr (with 5/6 younger than 5 Gyr), are found exclusively in fast-rotating galaxies, and are close to counter-rotating around the same axis as their host. (abridged)
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