A very simple question. If you define the $D_4$ group to be defined by matrices generated by the matrices $$ \sigma = \begin{pmatrix} 1 &0 \\ 0 &-1 \end{pmatrix}, \ \ \epsilon = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$$ then you find that it has 5 irreps - 4 1D irreps and 1 2D irrep which just uses the same matrices as above.
Can we therefore say that the $D_4$ group 'is an irrep of itself'. Or is this a dangerous way of phrasing it. If so, why?