Is there a presentation with two generator and two relators for the group $C_4 \cdot D_8$? This group is of order 32 and its IdSmallGroup in GAP is [32,15]. Also it has the following presentation with 2 generators and 3 relators:

$\langle x,y \;|\; y^x=y^3, (y^2)^x=y^{-2}, yx^{-1}y=x^3\rangle$