Let G be a group generated out of a set of $n$ distinct elements such that each of them has order $2$ and furthermore each element of the group has order $2$.
The group acts as follows. $a*b=a*b\neq b*a$ however $a*b*a*b$ is the identity since all elements have order 2.
When there are only $2$ elements $a,b$ this set has size $7: e,a,b,ab,ba,aba,bab$
How can I find the size for a given $n$?