It states that the gauge group is either

${\displaystyle SU(3)_{C}\times SU(3)_{L}\times SU(3)_{R}}$ 

or

${\displaystyle [SU(3)_{C}\times SU(3)_{L}\times SU(3)_{R}]/\mathbb {Z} _{3}}$ ;

and that the fermions form three families, each consisting of the representations: ${\displaystyle \mathbf {Q} =(3,{\bar {3}},1)}$ , ${\displaystyle \mathbf {Q} ^{c}=({\bar {3}},1,3)}$ , and ${\displaystyle \mathbf {L} =(1,3,{\bar {3}})}$ . The L includes a hypothetical right-handed neutrino, which may account for observed neutrino masses (see neutrino oscillations), and a similar sterile "flavon."

There is also a ${\displaystyle (1,3,{\bar {3}})}$  and maybe also a ${\displaystyle (1,{\bar {3}},3)}$  scalar field called the Higgs field which acquires a vacuum expectation value. This results in a spontaneous symmetry breaking from

${\displaystyle SU(3)_{L}\times SU(3)_{R}}$  to ${\displaystyle [SU(2)\times U(1)]/\mathbb {Z} _{2}}$ .

The fermions branch (see restricted representation) as

${\displaystyle (3,{\bar {3}},1)\rightarrow (3,2)_{\frac {1}{6}}\oplus (3,1)_{-{\frac {1}{3}}}}$ ,

${\displaystyle ({\bar {3}},1,3)\rightarrow 2\,({\bar {3}},1)_{\frac {1}{3}}\oplus ({\bar {3}},1)_{-{\frac {2}{3}}}}$ ,

${\displaystyle (1,3,{\bar {3}})\rightarrow 2\,(1,2)_{-{\frac {1}{2}}}\oplus (1,2)_{\frac {1}{2}}\oplus 2\,(1,1)_{0}\oplus (1,1)_{1}}$ ,

and the gauge bosons as

${\displaystyle (8,1,1)\rightarrow (8,1)_{0}}$ ,

${\displaystyle (1,8,1)\rightarrow (1,3)_{0}\oplus (1,2)_{\frac {1}{2}}\oplus (1,2)_{-{\frac {1}{2}}}\oplus (1,1)_{0}}$ ,

${\displaystyle (1,1,8)\rightarrow 4\,(1,1)_{0}\oplus 2\,(1,1)_{1}\oplus 2\,(1,1)_{-1}}$ .

Note that there are two Majorana neutrinos per generation (which is consistent with neutrino oscillations). Also, each generation has a pair of triplets ${\displaystyle (3,1)_{-{\frac {1}{3}}}}$  and ${\displaystyle ({\bar {3}},1)_{\frac {1}{3}}}$ , and doublets ${\displaystyle (1,2)_{\frac {1}{2}}}$  and ${\displaystyle (1,2)_{-{\frac {1}{2}}}}$ , which decouple at the GUT breaking scale due to the couplings

${\displaystyle (1,3,{\bar {3}})_{H}(3,{\bar {3}},1)({\bar {3}},1,3)}$ 

and

${\displaystyle (1,3,{\bar {3}})_{H}(1,3,{\bar {3}})(1,3,{\bar {3}})}$ .

Note that calling representations things like ${\displaystyle (3,{\bar {3}},1)}$  and (8,1,1) is purely a physicist's convention, not a mathematician's, where representations are either labelled by Young tableaux or Dynkin diagrams with numbers on their vertices, but it is standard among GUT theorists.

Since the homotopy group

${\displaystyle \pi _{2}\left({\frac {SU(3)\times SU(3)}{[SU(2)\times U(1)]/\mathbb {Z} _{2}}}\right)=\mathbb {Z} }$ ,

this model predicts 't Hooft–Polyakov magnetic monopoles.

Trinification is a maximal subalgebra of E₆, whose matter representation 27 has exactly the same representation and unifies the ${\displaystyle (3,3,1)\oplus ({\bar {3}},{\bar {3}},1)\oplus (1,{\bar {3}},3)}$  fields. E₆ adds 54 gauge bosons, 30 it shares with SO(10), the other 24 to complete its ${\displaystyle \mathbf {16} \oplus \mathbf {\overline {16}} }$ .