The nearby elliptical galaxy Centaurus A (Cen A) is surrounded by a flattened system of dwarf satellite galaxies with coherent motions. Using a novel Bayesian approach, we measured the mean rotation velocity v rot and velocity dispersion σ int of the satellite system. We found v rot / σ int ≃ 0.7, indicating that the satellite system has non-negligible rotational support. Using Jeans’ equations, we measured a circular velocity of 258 km s −1 and a dynamical mass of 1.2 × 10 13 M ⊙ within 800 kpc. In a Λ cold dark matter cosmological context, we found that the Cen A group has a baryon fraction M b / M 200 ≃ 0.035 and is missing ∼77% of the cosmologically available baryons. Consequently, Cen A should have a hot intergalactic medium with a mass of ∼8 × 10 11 M ⊙ , which is more than ∼20 times larger than current X-ray estimates. Intriguingly, the whole Cen A group lies on the baryonic Tully-Fisher relation defined by individual rotationally supported galaxies, as expected in Milgromian dynamics (MOND) with no need of missing baryons.