We present the results of a search for galaxy clusters in the Subaru-XMM Deep Field (SXDF). We reach a depth for a total cluster flux in the 0.5-2 keV band of 2 × 10-15 erg cm-2 s-1 over one of the widest XMM-Newton contiguous raster surveys, covering an area of 1.3 deg2. Cluster candidates are identified through a wavelet detection of extended X-ray emission. The red-sequence technique allows us to identify 57 cluster candidates. We report on the progress with the cluster spectroscopic follow-up and derive their properties based on the X-ray luminosity and cluster scaling relations. In addition, three sources are identified as X-ray counterparts of radio lobes, and in three further sources, an X-ray counterpart of the radio lobes provides a significant fraction of the total flux of the source. In the area covered by near-infrared data, our identification success rate achieves 86 per cent. We detect a number of radio galaxies within our groups, and for a luminosity-limited sample of radio galaxies we compute halo occupation statistics using a marked cluster mass function. We compare the cluster detection statistics in the SXDF with that in the literature and provide the modelling using the concordance cosmology combined with current knowledge of the X-ray cluster properties. The joint cluster log(N) - log(S) is overpredicted by the model, and an agreement can be achieved through a reduction of the concordance σ8 value by 5 per cent. Having considered the dn/dz and the X-ray luminosity function of clusters, we conclude that to pin down the origin of disagreement a much wider (50 deg2) survey is needed.
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