Context. Asteroseismology of massive pulsating stars of β Cep and SPB types can help us to uncover the internal structure of massive stars and understand certain physical phenomena that are taking place in their interiors. We study β Centauri (Agena), a triple system with two massive fast-rotating early B-type components which show p-and g-mode pulsations; the system's secondary is also known to have a measurable magnetic field. Aims. This paper aims to precisely determine the masses and detect pulsation modes in the two massive components of β Cen with BRITE-Constellation photometry. In addition, seismic models for the components are considered and the effects of fast rotation are discussed. This is done to test the limitations of seismic modeling for this very difficult case. Methods. A simultaneous fit of visual and spectroscopic orbits is used to self-consistently derive the orbital parameters, and subsequently the masses, of the components. Time-series analysis of BRITE-Constellation data is used to detect pulsation modes and derive their frequencies, amplitudes, phases, and rates of frequency change. Theoretically-predicted frequencies are calculated for the appropriate evolutionary models and their stability is checked. The effects of rotational splitting and coupling are also presented. Results. The derived masses of the two massive components are equal to 12.02 ± 0.13 and 10.58 ± 0.18 M . The parameters of the wider, A-B system, presently approaching periastron passage, are constrained. Analysis of the combined blue-and red-filter BRITEConstellation photometric data of the system revealed the presence of 19 periodic terms, of which eight are likely g modes, nine are p modes, and the remaining two are combination terms. It cannot be excluded that one or two low-frequency terms are rotational frequencies. It is possible that both components of β Cen are β Cep/SPB hybrids. An attempt to use the apparent changes of frequency to distinguish which modes originate in which component did not succeed, but there is potential for using this method when more BRITE data become available. Conclusions. Agena seems to be one of very few rapidly rotating massive objects with rich p-and g-mode spectra, and precisely known masses. It can therefore be used to gain a better understanding of the excitation of pulsations in relatively rapidly rotating stars and their seismic modeling. Lacking proper mode identification, the pulsation frequencies found in β Cen cannot yet be used to constrain the internal structure of the components, but it may be possible to achieve this in the future with the use of spectroscopy and spectropolarimetry. In particular, these kinds of data can be used for mode identification since they provide new radial velocities. In consequence, they may help to improve the orbital solution, derive more precise masses, magnetic field strength and geometry, inclination angles, and reveal rotation periods. They may also help to assign pulsation frequencies to components. Finally, the case studied here ...