Even though symmetry-breaking orders only really form in the thermodynamic limit, we can detect and study them using simulations of finite lattices, either through the emergence of Bragg peaks in their correlation functions, or through their low-energy excited states, whose symmetry quantum numbers (the so-called tower of states) serve as a fingerprint of the order. In this talk, I will demonstrate how these notions generalise to molecular magnets through the example of large fullerene molecules, such as the famous C60 buckminsterfullerene. Using neural-network quantum states, I obtain the low-energy spectrum of the molecules resolved by symmetry quantum numbers. Ground-state correlation functions show signs of an incipient Néel order on the hexagonal faces of the fullerene, which is, however, frustrated by the pentagonal faces, leading to a noncoplanar magnetic structure. The same structure is reflected as a tower of states in the low-energy spectrum. For several molecules, the incipient ordering is chiral, with potentially interesting consequences for their superconducting behaviour.