SU(6) (physics)
SU(6) is a grand unified theory which includes the Georgi-Glashow SU(5) gauge group.
The fermionic matter content of this model comes in three generations (copies) of
$$15\oplus \bar{6}\oplus \bar{6}$$
as SU(6) representations.
This gauge group is broken down to the Georgi-Glashow model by a pair of 6H/$\bar{6}_H$ Higgs fields.
$$SU(6)\begin{matrix}6_H/\bar{6}_H\\ \longrightarrow \end{matrix} SU(5)\times U(1)$$
The fermions decompose as
15 → 10 ⊕ 5
$$\bar{6}\rightarrow \bar{5}\oplus 1$$
The Yukawa coupling $<\bar{6}_H>\bar{6} 15$ causes 5 and a $\bar{5}$ SU(5)-rep of fermions to pair up and acquire GUT scale masses for each generation.
An adjoint Higgs 35H breaks the model down further to the standard model.