A giant flare from the Soft Gamma-ray Repeater SGR 1806-20 has been detected by several satellites on 2004 December 27. This tremendous outburst, the first one observed from this source, was a hundred times more powerful than the two previous giant flares from SGR 0525-66 and SGR 1900+14. We report the results obtained for this event with the Anticoincidence Shield of the SPI spectrometer on board the INTEGRAL satellite, which provides a high-statistics light curve at E>~80 keV. The flare started with a very strong pulse, which saturated the detector for ~0.7 s, and whose backscattered radiation from the Moon was detected 2.8 s later. This was followed by a ~400 s long tail modulated at the neutron star rotation period of 7.56 s. The tail fluence corresponds to an energy in photons above 3 keV of 1.6x10^44 (d/15 kpc)^2 erg. This is of the same order of the energy emitted in the pulsating tails of the two giant flares seen from other soft repeaters, despite the hundredfold larger overall emitted energy of the SGR 1806-20 giant flare. Long lasting (~1 hour) hard X-ray emission, decaying in time as t^-0.85, and likely associated to the SGR 1806-20 giant flare afterglow has also been detected.
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