75497472 is the largest amount of symmetries of any grid in Sudoku Topology. This gets more interesting when you notice it's a tie between two grids (Sphere32 and the nested cuboctahedron grid). Its prime factorization is 2²³×3².
Thanks for the number suggestion!
While playing Sudoku Topology, one can calculate that for Sphere32, there are 2¹⁶ choices for swapping around pairs of cells that are in the exact same pair of regions, 4!² choices for permuting rows and columns, and 2 choices for switching the rows with the columns. that multiplies out to 2²³×3².
For the nested cuboctahedron grid, there are 48 ways of applying symmetries, 2¹⁸ choices for swapping pairs of cells that are in the exact same set of regions, and 3! ways of permuting the layers. This also multiplies out to 2²³×3². However, I think you need to divide by 2 because the first two lists of symmetries both include central inversion. This thus makes the number of symmetries equal to 2²²×3².
Overall, I think numbers of this form are interesting since the number of symmetries for certain objects grows much faster than people anticipate.
