I'm having trouble understanding how to find the length of a group presentation. By a presentation of a group $G$, I mean a representation of $G$ by generators and relations. In "On the complexity of matrix group problems, I" (1984) Babai and Szemerédi define the length of a presentation to be "the total number of characters required to write down all relations. (Although it does not matter, we may agree that exponents are written in binary.)"
So, for example, if I have the following presentation $G$ for the alternating group of degree $5$ due to Carmichael $${G} = \langle x,y,z\mid {x^3} = {y^3} = {z^3} = {(xy)^2} = {(xz)^2} = {(yz)^2} = 1\rangle$$ would its length be: $3 + 3(3) + 4(3) = 24$? And how does one write this length in binary?