Classify the group G Consider $G$,  all $3\times 3$ matrices where all elements are in $\mathbb Z_2 .\;$ $G$ is a non-abelian group. 
What steps do I go about to classify this group? 
This means I have to find another group that it is isomorphic to,  correct?
$$G =\begin{pmatrix} 1&a&b\\0&1&c\\0&0&1\end{pmatrix}$$

A good first step is to count the elements in $G$. As the entries are in $\mathbb{F}_2$, it follows that $|G|=2\cdot2\cdot2$ where we have a binary choice for each $a,b,c$. 
So the group has $8$ elements, which leaves us with only $5$ choices for what $G$ could be isomorphic to. But you know $G$ is not abelian, so what would be a good guess?
