How do I decompose this representation of $S_4$ in $\Bbb Z_2^3$?

Question

The matrices $$\begin{pmatrix} 1 & 1 & 1\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{pmatrix}, \begin{pmatrix} 0 & 1 & 0\\ 1 & 0 & 0\\ 0 & 0 & 1 \end{pmatrix}, \begin{pmatrix} 1 & 1 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{pmatrix} $$ with entries in $\Bbb Z_2$ generate the symmetric group $S_4$. Is this representation irreducible, and if not how does it decompose? I tried to use charactertables $\mod{p}$ but this fails when the order of the group is a multiple of $p$.