Hexagonal YMnO3 is an intensively studied representative of materials exhibiting the coexistence of magnetic and electric order, called multiferroicity. Nevertheless, a controversy about its antiferromagnetic order remains. Initial reports suggested space-group symmetry P63c'm' with Mn3+ spins along the crystallographic y axis and antiparallel orientation of corresponding spins in adjacent xy planes. However, subsequent experiments increasingly supported P63́cm' symmetry with spins aligned along the crystallographic x axis and parallel orientation of corresponding spins in adjacent xy planes. Despite accumulating evidence for this structure, a neutron polarimetry study revealed an order according to space-group symmetry P63́, where the Mn3+ spins are rotated by 11◦ from the x toward the y axis. Here we report experiments by optical second harmonic generation that point to P63́cm' symmetry and no evidence for spin rotation within a noise-inflicted upper limit of ≲ 1◦. We suggest that the discrepancy could be resolved by an expansion of the configurations measured by neutron polarimetry and the use of samples with enlarged domains to prevent domain-wall-related contributions.