= Character table from a cyclic quotient and two elementary-abelian orbits
{title2=$C_3^2\rtimes C_4$}
A group of order thirty-six with a normal $C_3^2$ and a cyclic quotient of order four acting freely on its eight nonzero elements has six <conjugacy classes> of sizes $1,4,4,9,9,9$. Its four <linear characters> are lifted from the cyclic quotient. The remaining irreducible degrees are four and four, by the sum of squared degrees. <Column orthogonality> forces the last three values of both degree-four rows to vanish. The square of the order-four action is inversion on $C_3^2$, making the first two nontrivial class values real. Orthogonality then gives sum minus one and product minus two, so the rows are $(4,1,-2,0,0,0)$ and $(4,-2,1,0,0,0)$. This illustrates why reality must be justified when reconstructing a <character table> from orthogonality.
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