Number of abelian groups Vs Number of non-abelian groups I would like to see a table that shows the number of non-abelian group for every order n. It is a preferable if the table contains the number of abelian groups of order n (this is not necessary though). If anyone could provide me with such a table , I would be grateful.
Note: I already checked wikipedia. They have a table similar to the one I want but its small.
Here is a simliar table to the one I want:
http://oeis.org/wiki/Number_of_groups_of_order_n#Table_of_number_of_distinct_groups_of_order_n
Thank you
 A: Here are the GAP functions which will allow you to get these numbers:
NumberSmallGroups(n) : gives you the number of groups of order $n$
IdsOfAllSmallGroups : Gives you a list consisting of the ID of each of the groups satisfying the criteria given (type ?IdsOfAllSmallGroups to get a description of the syntax). Note that this will not work for certain orders, as there are just too many such groups. In those cases, you can compute the number of abelian groups by hand, since these just involve the number of partitions of some not too large numbers.
To get the number of the groups, use the function Size() which returns the number of elements in a list.
The above function can also be used to get groups with suitable other properties, such as solvable, nilpotent, M-groups and any other property you might want.
A: As it's a reference-request and the amounts given there seem sufficient:
The number of goups of order $n$ is listed at OEIS as A00001. On its description page is a link to a table of $n$, $a_n$ for $n=1,\ldots, 2047$. For abelian groups, A000688 lsts the counts up to $n=10000$ as these are quite easily calculated.
Intriguingly, A060689 (non-abelian groups) gives only a list up to $n=2015$, sou you can earn merit by computing the differences from the tables and submit a bigger table. 
