The birational automorphism group of a general 15-nodal quartic surface is generated by 264 explicit symmetries (192 involutions and 120 infinite-order automorphisms), with defining relations determined by 19 orbits of chamber faces.
15-nodal quartic surfaces
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15-nodal quartic surfaces. Part II: The automorphism group
The birational automorphism group of a general 15-nodal quartic surface is generated by 264 explicit symmetries (192 involutions and 120 infinite-order automorphisms), with defining relations determined by 19 orbits of chamber faces.