show that the relations $a^4=1$, $b^2=a^2$, $b^{-1}ab=a^{-1}$ define a group of order 8.
This is a homework problem I got. I don't understand what they mean by 'a group of order 8', because I think it only makes sense to talk about the order of an element in a group. For example, the element 2 has order 2 in the group $Z_4$.
Should I try to show that it can be generated by an element of order 8? I don't think this is right though, because $a^4=1$, so the least order should be 4.