# Homology of wedge sum of projective plane and dunce cap

I am to construct a space $X$, whose fundamental group is $\Bbb(Z/2Z)\times(Z/3Z)$, and compute its homology. I know that $X$ is (or could be) a wedge sum of the projective plane $\Bbb RP^2$ and the dunce cap. I know how to commpute the homology of both, but have problems with computing the homology group of their wedge sum.

• The homology of a wedge sum is a direct product of homologies: math.stackexchange.com/questions/1555224/… – freakish May 4 '17 at 23:23
• (For spaces which behave nicely enough near the basepoint.) – Alex Provost May 4 '17 at 23:37
• @freakish, thank you for pointing me in the right direction. – Halinka May 5 '17 at 21:15