Flipped $SU\left(6\right)$ unification of the sequential $SU(3{)}_c\times SU(3{)}_L\times U(1{)}_X$ model

We propose to partially unify the sequential $SU(3{)}_c\times SU(3{)}_L\times U(1{)}_X$ model (with $\beta =1/\sqrt{3}$) into the flipped $SU\left(6\right)$ model with the gauge group $SU\left(6\right)\times U(1{)}_K$. Gauge anomaly cancellation can easily be satisfied. We discuss the relevant Higgs sector, the low energy 331 model spectrum, and the unification of $SU(3{)}_c$ and $SU(3{)}_L$ gauge couplings. Neutrino mass generation and successful gauge coupling unification can set lower/upper bounds on the 331 breaking scale. The partial proton decay lifetime of various channels, for example, the $p\to e^{+}{\pi }^0$ channel, in flipped $SU\left(6\right)$ GUT are discussed. We find that certain parameter region with $M_{331}\sim {10}^{15}\mathrm{GeV}$ of case II (for case with $M_{331}$ scale ${\tilde{H}}_{3,8}$ Higgs field) can predict a partial proton lifetime of order ${10}^{34}\mathrm{years}$ for $p\to e^{+}{\pi }^0$ mode, which can be tested soon by future DUNE and Hyper-Kamiokande experiments.