Sort

Consider the following HUGE numbers:

• $$a=googol!$$
• $$b=\text{Skewes’ number}=e^{e^{e^{79}}}$$
• $$c=2^{3^{4^{5^6}}}$$
• $$d=6^{5^{4^{3^2}}}$$
• $$e=4!!!!$$
• $$f=p_{googol}\mathrm{\#}(p_n\mathrm{\#}\text{is the primorial function})$$

Sort these numbers in ascending order.

Answer format: Comma separated list.
Example: f,e,d,c,b,a

For the record, the primorial function $p_n\mathrm{\#}$ is the product of the first n prime numbers.
$$p_5\mathrm{\#}=2\times 3\times 5\times 7\times 11=2310$$