Let $G$ and $H$ be finite groups.
Denote the ordinary character table of $G$ by ctG and the ordinary character table of $H$ by ctH.
Then, it is well-known how to get the ordinary character table of $G\times H$.
Is it possible to get the ordinary character table of $G\times H$ in MAGMA in such a way that the ordering of the ordinary irreducible characters is
$\chi_1 \times \psi_1,\ \chi_2 \times \psi_1,\ \chi_3 \times \psi_1,\ \chi_4 \times \psi_1,\ \dots ,\ \chi_2 \times \psi_1,\ \chi_2 \times \psi_2,\ \chi_2 \times \psi_3,\ \dots$ (where the $\chi_i$ are the ordinary characters in ctG and the $\psi_j$ are those in ctH)?
Thanks for the help.
EDIT:
I mean an easier way than computing $G\times H$, restricting each ordinary irred. char. of Irr($G\times H$) to $G$ and $H$, respectively, and then changing the ordering.