Group G3
Let i run through all times from 0 to p(n) and j run through all tape squares from -p(n) through p(n)+1. (There are p(n)*2(p(n)+1) combinations.
For each (i,j) add {S[i,j,s0],S[i,j,s1], … ,S[i,j,sk]}, where s0,s1, … ,sk run through all tape symbols in T.