We present a catalogue of 179 hyperluminous infrared galaxies (HLIRGs) from the Imperial IRAS-FSS Redshift (IIFSCz) Catalogue. Of the 92 with detections in at least two far infrared bands, 62 are dominated by an M82-like starburst, 22 by an Arp220-like starburst and 8 by an AGN dust torus. On the basis of previous gravitational lensing studies and an examination of HST archive images for a further 5 objects, we estimate the fraction of HLIRGs that are significantly lensed to be 10-30%. We show simple infrared template fits to the SEDs of 23 HLIRGs with spectroscopic redshifts and at least 5 photometric bands. Most can be fitted with a combination of two simple templates: an AGN dust torus and an M82-like starburst. In the optical, 17 of the objects are fitted with QSO templates, 6 are fitted with galaxy templates. 20 of the 23 objects (87%) show evidence of an AGN either from the optical continuum or from the signature of an AGN dust torus, but the starburst component is the dominant contribution to bolometric luminosity in 14 out of 23 objects (61%). The implied star-formation rates, even after correcting for lensing magnification, are in excess of 1000 Mo /yr. We use infrared template-fitting models to predict fluxes for all HLIRGs at submillimetre wavelengths, and show predictions at 350 and 850 mu. Most would have 850 mu fluxes brighter than 5 mJy so should be easily detectable with current submillimetre telescopes. At least 15% should be detectable in the Planck all-sky survey at 350 mu and all Planck all-sky survey sources with z < 0.9 should be IIFSCz sources. From the luminosity-volume test we find that HLIRGs show strong evolution. A simple exponential luminosity evolution applied to all HLIRGs would be consistent with the luminosity functions found in redshift bins 0.3-0.5, 0.5-1 and 1-2.
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