TITLE: Reference requests: Integral cohomology of $G_2$-homogeneous spaces
QUESTION [11 upvotes]: Do  you  know  a  place  where  the integral cohomology of $G_2$-homogeneous spaces  is  computed?
Great  computational  efforts  using  representation  theory  in order  to  determine  the  characteristic  classes  of   homogeneous spaces  were  done  by  Borel and Hirzebruch  in  a  series  of  papers: 

Characteristic classes and homogeneous spaces. I.
Amer. J. Math. 80 1958, 491–504.
Characteristic classes and homogeneous spaces. II.
Amer. J. Math. 81 1959 315–382.
Characteristic classes and homogeneous spaces. III.
Amer. J. Math. 82 1960 458–538. 

I  was unable  to  find  there a  systematic  answer to  the  question.

REPLY [4 votes]: I don't know how "systematic" the answer you are looking has to be, but for the quotients of the form $G_2/T$ and $G_2/P$ (P: Parabolic subgroup) you can find the results in Schubert presentation of the integral cohomology ring of the flag manifolds G/T, by Haibao Duan and Xuezhi Zhao