Let $M$ be a manifold. The total Stiefel-Whitney class of $M$ is defined to be the Stiefel-Whitney class of the tangent bundle $TM$ $$ w(M)=1+w_1(TM)+w_2(TM)+\cdots $$ I want to find references for $$ w(SO(n)/SO(k)),(i.e. w(V_{n-k}(\mathbb{R}^n))), \\ w(U(n)/U(k)),(i.e. w(V_{n-k}(\mathbb{C}^n))), \\ w(Sp(n)/Sp(k)),(i.e. w(V_{n-k}(\mathbb{H}^n))),\\ w(SO(n)/(SO(k)\times SO(n-k))),(i.e. w(G_{n-k}(\mathbb{R}^n))), \\ w(U(n)/(U(k)\times U(n-k))),(i.e. w(G_{n-k}(\mathbb{C}^n))), \\ w(Sp(n)/(Sp(k)\times Sp(n-k))),(i.e. w(G_{n-k}(\mathbb{H}^n))). $$ Which ones of the above are known? Where could I find these formulas?