I have 3 matrices and I want to generate the group associated does anyone know how to do this without doing it manually?

thanks

M 

I want to produce the matrix representation for the symmetric group.

I have the 3 generator matrices for

(12),(13),(14) but I am having trouble producing the complete set of 24 matrices with no repeats.

I would like some kind of algorithmic process as I would like to produce the S5 and A4 groups later.

many thank for any help

M