let $K$ be the 27-dimensional complex vector space consisting of triples $m$ = ($m_1, m_2, m_3$) of complex 3 x 3-matrices $m_i$, $1 < i < 3$, where addition and scalar multiplication are defined coordinatewise. We define a cubic form( ) on $K$ by $(m)= det(m_1) + det(m_2) + det(m_3) - tr(m_1m_2m_3)$. Then $3E_6(C)$ is the subgroup of $GL(K)$ preserving the form ( ).
I am new to Magma. My question is if one could construct the exceptional group via Magma by defining the form first and then letting Magma find elements in $GL(K)$ that preserve the form?