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Aims. We study the behavior of the magnetic field and the line activity indicators of the single late-type giant β Ceti. Using spectropolarimetric data, we aim to reconstruct the magnetic field structure on the star's surface and to present the first magnetic maps for β Ceti. Methods. The data were obtained using two spectropolarimeters – Narval at the Bernard Lyot Télescope, Pic du Midi, France, and ESPaDOnS at CFHT, Hawaii. Thirty-eight circularly-polarized spectra have been collected in the period June 2010–January 2012. The least square deconvolution method was applied for extracting high signal-to-noise ratio line profiles, from which we measured the surface-averaged longitudinal magnetic field Bl. Chromospheric activity indicators CaII K, Hα, CaII IR (854.2 nm), and radial velocity were simultaneously measured, and their variability was analyzed along with the behavior of Bl. The Zeeman Doppler imaging (ZDI) inversion technique was employed for reconstructing the large-scale magnetic field and two magnetic maps of β Ceti are presented for two periods (June 2010–December 2010 and June 2011–January 2012). Results. The Bl stays with a same positive polarity for the whole observational period and shows significant variations in the interval 0.1–8.2 G. The behavior of the line activity indicators is in good agreement with the Bl variations. Searching for periodic signals in the Stokes V time series, we found a possible rotation period of 215 days. The two ZDI maps show a mainly axisymmetric and poloidal magnetic topology and a simple surface magnetic field configuration dominated by a dipole. Little evolution is observed between the two maps, in spite of a 1 yr interval between both subsets. We also use state-of-the-art stellar evolution models to constrain the evolutionary status of β Ceti. We derive a mass of 3.5 M⊚ and propose that this star is already in the central helium-burning phase. Conclusions. Considering all our results and the evolutionary status of the star, we suggest that dynamo action alone may not be efficient enough to account for the high magnetic activity of β Ceti. As an alternate option, we propose that it is a descendant of an Ap star presently undergoing central helium-burning and still exhibiting a remnant of the Ap star magnetic field. [ABSTRACT FROM AUTHOR]