Table 4:

Product irreducible representations in the special case of $𝒢\times {\mathbb{Z}}_M$, after plugging in the trivial irreducible representations

${\psi }_{k,m}((g,a))$	${\eta }_0(a)=1$	${\eta }_1(a)$	$\cdots$	${\eta }_{M-1}(a)$
${\rho }_0(g)=1$	$1$	${\eta }_1(a)$	$\cdots$	${\eta }_{M-1}(a)$
${\rho }_1(g)$	${\rho }_1(g)$	${\rho }_1(g){\eta }_1(a)$	$\cdots$	${\rho }_1(g){\eta }_{M-1}(a)$
${\rho }_2(g)$	${\rho }_2(g)$	${\rho }_2(g){\eta }_1(a)$	$\cdots$	${\rho }_2(g){\eta }_{M-1}(a)$
${\rho }_3(g)$	${\rho }_3(g)$	${\rho }_3(g){\eta }_1(a)$	$\cdots$	${\rho }_3(g){\eta }_{M-1}(a)$
$⋮$	$⋮$	$⋮$	$\ddots$	$⋮$