Copied from http://planetmath.org/encyclopedia/ExamplesOfNonMatrixLieGroup.html

While most well-known Lie groups are matrix groups, there do in fact exist Lie groups which are not matrix groups. That is, they have no faithful finite dimensional representations.

For example, let $H$ be the real Heisenberg group

$$H=\{\begin{pmatrix} 1 & a & b\newline 0&1&c\newline 0 &0 &1\end{pmatrix}\mid a,b,c\in\mathbb{R} \},$$

and $\Gamma$ the discrete subgroup

$$\Gamma=\{\begin{pmatrix} 1 & 0 & n\newline0&1&0\newline 0 &0 &1\end{pmatrix}\mid n\in\mathbb{Z}\}.$$

The subgroup $\Gamma$ is central, and thus normal. The Lie group $H/\Gamma$ has no faithful finite dimensional representations over $\mathbb{R}$ or $\mathbb{C}$.

Copied from PlanetMath.

While most well-known Lie groups are matrix groups, there do in fact exist Lie groups which are not matrix groups. That is, they have no faithful finite dimensional representations.

For example, let $H$ be the real Heisenberg group

$$H=\{\begin{pmatrix} 1 & a & b\newline 0&1&c\newline 0 &0 &1\end{pmatrix}\mid a,b,c\in\mathbb{R} \},$$

and $\Gamma$ the discrete subgroup

$$\Gamma=\{\begin{pmatrix} 1 & 0 & n\newline0&1&0\newline 0 &0 &1\end{pmatrix}\mid n\in\mathbb{Z}\}.$$

The subgroup $\Gamma$ is central, and thus normal. The Lie group $H/\Gamma$ has no faithful finite dimensional representations over $\mathbb{R}$ or $\mathbb{C}$.