= Minimal anomaly-free chiral family in SU(6)
{title2=$\mathbf{15}\oplus2\overline{\mathbf6}$}
The <SU(6)> <representations> $\mathbf{15}=\Lambda^2\mathbf6$ and $\overline{\mathbf6}$ branch under <SU(5)> as $\mathbf{10}\oplus\mathbf5$ and $\overline{\mathbf5}\oplus\mathbf1$. Their cubic <gauge anomaly> coefficients are $2$ and $-1$ in fundamental normalization. Thus $\mathbf{15}\oplus2\overline{\mathbf6}$ is anomaly-free and gives one <Standard Model> family $\mathbf{10}\oplus\overline{\mathbf5}$, a <vectorlike gauge spectrum> $\mathbf5\oplus\overline{\mathbf5}$, and two singlets. With these <representations> and their conjugates, precisely one net chiral family requires $m_{15}-m_{\overline{15}}=1$ and $m_{\bar6}-m_6=2$, so this is the smallest such choice.
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