We would like to thank the referee for his or her valuable suggestions.
We have edited the paper according to these recommendations.

Minor corrections:
-we replaced the term "class of permutations" with "family of permutations" everywhere.
-we added a more exact definition of $\zeta_n$. 
-we added to Definition 5.6 that a semiprimitive or primitive partition must be reduced. Special thanks for catching this one!
-added reference to sequence A297179 in OEIS at the end of the paper.
-added a phrase to Theorem 4.2 and 4.4 clarifying that this statements holds only for families of permutations that 
do not contain the empty permutation. 

Major changes:
-we rewrote the introduction in an effort to better explain the historic context and the importance of 
the notion of genus, adding the suggested statements regarding future research at the end.
-inserted a remark after Theorem 4.2, highlighting the importance of the result beyond the present topic. 
-amended the Acknowledgement section, thanking our referee.   