Exercise 7. This software determines the order of $$Aut(Z_p \oplus Z_p \oplus Z_p)$$, where $$p$$ is a prime less than 101. Run the software for $$p = 3, 5,$$ and $$7$$. What is the highest power of $$p$$ that divides the order? What is the highest power of $$p-1$$ that divides the order? What is the highest power of $$p+1$$ that divides the order? Make a conjecture about the order of $$Aut(Z_p \oplus Z_p \oplus Z_p)$$ for all primes $$p$$.

Please enter $$p$$.