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We present fully general relativistic 3D numerical simulations of accretion-induced collapse (AIC) of white dwarfs (WDs). We evolve three different WD models (non-rotating, rotating at 80 per cent and 99 per cent of the Keplerian mass shedding limit) that collapse due to electron capture. For each of these models, we provide a detailed analysis of their gravitational waves (GWs), neutrinos, and electromagnetic counterpart and discuss their detectability. Our results suggest that fast rotating AICs could be detectable up to a distance of 8 Mpc with third-generation GW observatories, and up to 1 Mpc with LIGO. AIC progenitors are expected to have large angular momentum due to their accretion history, which is a determining factor for their stronger GW emission compared to core-collapse supernovae (CCSNe). Regarding neutrino emission, we found no significant difference between AICs and CCSNe. In the electromagnetic spectrum, we find that AICs are two orders of magnitude fainter than type Ia supernovae. Our work places AICs as realistic targets for future multimessenger searches with third generation ground-based GW detectors.