Interpreting the Integer Sequences from Group Theory Perspective. Looking for a list of different types in Group Theory led to The On-line Encyclopedia of Integer Sequences and the index. It looks like there are millions of integer sequences. A quick search returns results that look almost like a formal standards document like those from the w3c. As a newcomer I am left wondering what I can do with this. Looking at the FAQ:

Q: What is the purpose of the OEIS? A: The main purpose is to allow mathematicians or other scientists to find out if some sequence that turns up in their research has ever been seen before.
If it has, they may find that the problem they're working on has already been solved, or partially solved, by someone else. Or they may find that the sequence showed up in some other situation, which may show them an unexpected relationship between their problem and something else.

So that makes sense. If you come across a sequence, you can look it up and potentially benefit from previous work on it.
Wikipedia provides a starters interface in their named OEIS sequences page. It is still a little bit complicated though.
Wikipedia also has a list of small groups page which has some images which is helpful. Yay, this looks like a good starting point. I am looking to learn about some interesting and different groups, in order to expand my understanding of groups. What I would like to know is what the values in the table below mean. Specifically:


*

*The column headers 0-15.

*The row headers 0-128.

*The block values.

*What an example of a group is to demonstrate the different numbers meanings.

*If there is a preferred alternative resource that may be simpler for learning about a large number of groups.


Thank you for your help.

A: The table has 144 boxes, which represent the orders of group. Each cell tells you how many nonisomorphic groups exist of such order. For example, in the first row, below the number 4 it says "2", meaning that there are two non-isomorphic groups of order 2, namely $\mathbb Z_4$ and $\mathbb Z_2\times \mathbb Z_2$. 
The number on the left indicate the order of the first box in the row: so the first row goes from orders 0 to 15, the second from 16 to 31, etc. The last entry of the last row tells you that there is a single group of order $128+15=143$. If you move one place to the left, there are two groups of order $128+14=142$. On the other hand, the last number in the column labelled $0$ tells you that there are $2328$ nonisomorphic groups of order $128$. 
