FFT of input length 1536
Note that $1536 = 3\cdot 512$. You can use a decimation in time method. See http://www.altera.com/literature/an/an480.pdf

I'll add some extra information here in response to your comment to sansuiso's answer (even though this comment actually referred to the pdf file I mentioned above in this answer). As explained in the above document, you need to compute 3 FFTs of length 512. You do this by taking time samples 0,3,6,9, ... and compute their FFT, then you take the samples 1,4,7,10,... and compute another FFT. Finally you compute the FFT of samples 2,5,8,11,... Then you combine the 3 FFTs using the appropriate twiddle factors to obtain the desired 1536-point FFT. This last step is the radix-3 stage. Have a look at Equation (2) on page 3 of the document (also Fig. 1 on page 4).

Also check out this blog post. It also includes a little Matlab program.