The chemical versatility of carbon imparts manifold properties to organic compounds, where magnetism remains one of the most desirable but elusive. Polycyclic aromatic hydrocarbons, also referred to as nanographenes, show a critical dependence of electronic structure on the topologies of the edges and the π-electron network, which makes them model systems with which to engineer unconventional properties including magnetism. In 1972, Erich Clar envisioned a bow-tie-shaped nanographene, C₃₈H₁₈ (refs.), where topological frustration in the π-electron network renders it impossible to assign a classical Kekulé structure without leaving unpaired electrons, driving the system into a magnetically non-trivial ground state. Here, we report the experimental realization and in-depth characterization of this emblematic nanographene, known as Clar's goblet. Scanning tunnelling microscopy and spin excitation spectroscopy of individual molecules on a gold surface reveal a robust antiferromagnetic order with an exchange-coupling strength of 23 meV, exceeding the Landauer limit of minimum energy dissipation at room temperature. Through atomic manipulation, we realize switching of magnetic ground states in molecules with quenched spins. Our results provide direct evidence of carbon magnetism in a hitherto unrealized class of nanographenes, and prove a long-predicted paradigm where topological frustration entails unconventional magnetism, with implications for room-temperature carbon-based spintronics.