The AutoKron can't determine the cohomology of $\text{Gr}_3(\mathbb{R}^{7,2})$.

There are 2 possibilities.
Here are their Poincaré polynomials: $$x^{12} y^{5} + x^{11} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{4} + 3 x^{8} y^{4} + x^{8} y^{3} + x^{7} y^{4} + 3 x^{7} y^{3} + 4 x^{6} y^{3} + x^{6} y^{2} + 2 x^{5} y^{3} + 2 x^{5} y^{2} + 4 x^{4} y^{2} + 3 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{12} y^{5} + x^{11} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{4} + 3 x^{8} y^{4} + x^{8} y^{3} + 4 x^{7} y^{3} + 5 x^{6} y^{3} + 2 x^{5} y^{3} + 2 x^{5} y^{2} + 4 x^{4} y^{2} + 3 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 2 possibilities:
1 1 2 2 3 3 3 3 3 3 1 1 3 3 3 4 4 4 4 1 2 2 2 2 4 4 4 4 3 3 3 1 1 1 1
1 1 2 2 3 3 3 3 3 3 1 4 4 4 4 5 5 5 5 5 2 2 2 2 4 4 4 4 3 3 3 1 1 1 1