I am given that f = (1 2 3 4 5 6) and g = (1 2). I am told to compute $f^2gf^4$. I know that $f^2 = (1 3 5)(2 4 6)$ and $f^4 = (1 5 3)(2 6 4)$. But I am having trouble computing the product of all three together. So far I have: $$ f^2gf^4 = (1 3 5)(2 4 6)*(1 2)*(1 5 3)(2 6 4) $$ $$f^2g = (1 4 6 2)(3 5)$$ then I computed that, $$f^2gf^4 = (13)$$
Did i do something wrong?