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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
just for completeness, I added this statement:
The integral cohomology ring of the classifying space is
where
is the first Pontryagin class
is the Euler class,
is the integral Stiefel-Whitney class.
Notice that the cup product of the Euler class with itself is the second Pontryagin class
which therefore, while present, does not appear as a separate generator.
I hope I got this right that does not appear.
Yes, it seems to me that you only have out of the integral SW classes, based on one of those sources I sent you.
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