# Homology of SL(2,R) with finite coefficients

Consider the third homology group of a real special linear group $$H_3 (SL(2,\mathbb{R}),\mathbb{F}_p)$$. It is known$$[1]$$ that for $$p=2$$ the third homology group of $$SL(2,\mathbb{R})$$ vanishes.

Question: is it true that there exists a prime number $$p>2$$ such that $$H_3 (SL(2,\mathbb{R}),\mathbb{F}_p) \neq 0$$?

$$[1]$$ Walter Parry, Chih-Han Sah, Third homology of $$SL(2,\mathbb{R})$$ made discrete.