/*
Summary of M12 orbits (by conjugation) of Hamming words
that are close to the identity.
This file: Yellow, distance 7 from id.
*/

G:=PermutationGroup<12|(1,2,3,4,5,6,7,8,9,10,11),(3,4)(2,10)(6,7)(5,9),(11,12)(1,10)(2,5)(3,7)(4,8)(6,9)>;
M12:=G;

g:="Green";y:="Yellow";r:="Red";

procedure latex(u);
if u[1] eq 6 then printf "6H & ";elif u[1] eq -6 then printf "6N & ";else printf "%-2o & ",u[1];end if;
printf "%3o & %3o & %-6o & %o &%3o & ",u[2],u[3],u[4],u[5],u[6];
for i in [1..11] do printf "%o\\ ",u[7][i];end for;
printf "%o \\\\\n",u[7][12];
end procedure;

/*
Format of results is as follows.
<di,o1,o2,col,dm,nn,w>
where di = d(w,Id), except
di = -6 if w and Id differ on 6 points forming a non-hexad,
o1*o2 = #M12 conjugates of w,
o1 = #M12 images of supp(w),
o2 = #Conjugates of w under Stab_{M12}(supp(w)),
col = Colour of w (Green, Yellow or Red),
dm = d(w,M12),
nn = #Closest neighbours in M12 to w,
w = w, in list format [canonical element in M12-orbit].
*/

res7y:=[
<7,792,6,y,7,96,[2,6,2,2,2,2,2,8,9,10,11,12]>,
<7,792,30,y,7,72,[2,8,2,2,8,8,2,8,9,10,11,12]>,
<7,792,60,y,7,96,[2,8,8,5,8,8,8,8,9,10,11,12]>,
<7,792,120,y,7,72,[2,8,8,9,9,8,9,8,9,10,11,12]>,
<7,792,120,y,7,72,[2,8,8,10,8,10,10,8,9,10,11,12]>,
<7,792,30,y,7,96,[2,9,9,9,9,1,9,8,9,10,11,12]>,
<7,792,5,y,7,56,[6,6,6,6,6,8,6,8,9,10,11,12]>,
<7,792,15,y,7,72,[6,6,6,6,11,11,11,8,9,10,11,12]>,
<7,792,40,y,7,160,[6,6,6,9,12,10,11,8,9,10,11,12]>,
<7,792,60,y,7,160,[6,6,8,8,12,11,10,8,9,10,11,12]>,
<7,792,60,y,7,160,[6,6,8,9,9,10,11,8,9,10,11,12]>,
<7,792,120,y,7,160,[6,6,8,9,12,10,10,8,9,10,11,12]>,
<7,792,120,y,7,192,[6,6,8,9,12,10,11,8,9,10,11,12]>,
<7,792,15,y,7,56,[6,6,9,9,9,9,9,8,9,10,11,12]>,
<7,792,120,y,7,56,[6,8,8,8,8,8,9,8,9,10,11,12]>,
<7,792,120,y,7,72,[6,8,8,8,12,12,12,8,9,10,11,12]>,
<7,792,120,y,7,160,[6,8,8,9,12,10,11,8,9,10,11,12]>,
<7,792,5,y,7,8,[8,8,8,8,8,8,8,8,9,10,11,12]>,
<7,792,120,y,7,14,[8,8,8,8,8,8,9,8,9,10,11,12]>,
<7,792,20,y,7,14,[8,8,8,8,8,9,8,8,9,10,11,12]>,
<7,792,120,y,7,18,[8,8,8,8,8,9,9,8,9,10,11,12]>,
<7,792,120,y,7,24,[8,8,8,8,8,9,10,8,9,10,11,12]>,
<7,792,120,y,7,24,[8,8,8,8,8,9,11,8,9,10,11,12]>,
<7,792,120,y,7,24,[8,8,8,8,8,9,12,8,9,10,11,12]>,
<7,792,60,y,7,18,[8,8,8,8,9,8,9,8,9,10,11,12]>,
<7,792,120,y,7,24,[8,8,8,8,9,8,10,8,9,10,11,12]>,
<7,792,120,y,7,24,[8,8,8,8,9,8,11,8,9,10,11,12]>,
<7,792,120,y,7,24,[8,8,8,8,9,8,12,8,9,10,11,12]>,
<7,792,60,y,7,20,[8,8,8,8,9,9,9,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,9,9,10,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,9,9,11,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,9,9,12,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,9,10,9,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,9,10,10,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,8,9,10,11,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,8,9,10,12,8,9,10,11,12]>,
<7,792,60,y,7,30,[8,8,8,8,9,11,9,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,8,9,11,10,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,9,11,11,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,8,9,11,12,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,8,9,12,10,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,8,9,12,11,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,9,12,12,8,9,10,11,12]>,
<7,792,120,y,7,18,[8,8,8,8,10,8,10,8,9,10,11,12]>,
<7,792,120,y,7,24,[8,8,8,8,10,8,11,8,9,10,11,12]>,
<7,792,60,y,7,24,[8,8,8,8,10,8,12,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,10,9,10,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,8,10,9,11,8,9,10,11,12]>,
<7,792,60,y,7,40,[8,8,8,8,10,9,12,8,9,10,11,12]>,
<7,792,120,y,7,20,[8,8,8,8,10,10,10,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,10,10,11,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,10,10,12,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,10,11,10,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,10,11,11,8,9,10,11,12]>,
<7,792,60,y,7,40,[8,8,8,8,10,11,12,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,10,12,10,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,8,10,12,11,8,9,10,11,12]>,
<7,792,120,y,7,24,[8,8,8,8,11,8,10,8,9,10,11,12]>,
<7,792,60,y,7,18,[8,8,8,8,11,8,11,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,8,11,9,10,8,9,10,11,12]>,
<7,792,60,y,7,30,[8,8,8,8,11,9,11,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,11,10,10,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,11,10,11,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,11,11,10,8,9,10,11,12]>,
<7,792,60,y,7,20,[8,8,8,8,11,11,11,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,8,11,12,10,8,9,10,11,12]>,
<7,792,60,y,7,24,[8,8,8,8,12,8,10,8,9,10,11,12]>,
<7,792,60,y,7,40,[8,8,8,8,12,9,10,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,8,12,10,10,8,9,10,11,12]>,
<7,792,60,y,7,40,[8,8,8,8,12,11,10,8,9,10,11,12]>,
<7,792,120,y,7,20,[8,8,8,9,9,8,9,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,9,9,8,10,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,9,9,8,11,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,9,9,8,12,8,9,10,11,12]>,
<7,792,120,y,7,20,[8,8,8,9,9,9,9,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,9,9,9,10,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,9,9,9,11,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,9,9,9,12,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,9,9,10,9,8,9,10,11,12]>,
<7,792,120,y,7,36,[8,8,8,9,9,10,10,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,9,10,11,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,9,10,12,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,9,9,11,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,9,11,10,8,9,10,11,12]>,
<7,792,120,y,7,36,[8,8,8,9,9,11,11,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,9,11,12,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,9,9,12,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,9,12,10,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,9,12,11,8,9,10,11,12]>,
<7,792,120,y,7,36,[8,8,8,9,9,12,12,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,9,10,8,9,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,9,10,8,10,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,9,10,8,11,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,9,10,8,12,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,9,10,9,9,8,9,10,11,12]>,
<7,792,120,y,7,36,[8,8,8,9,10,9,10,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,10,9,11,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,10,9,12,8,9,10,11,12]>,
<7,792,120,y,7,36,[8,8,8,9,10,10,9,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,9,10,10,10,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,10,10,11,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,10,10,12,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,10,11,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,10,11,10,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,10,11,11,8,9,10,11,12]>,
<7,792,120,y,7,64,[8,8,8,9,10,11,12,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,10,12,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,10,12,10,8,9,10,11,12]>,
<7,792,120,y,7,64,[8,8,8,9,10,12,11,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,10,12,12,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,9,11,8,9,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,9,11,8,10,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,9,11,8,11,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,9,11,8,12,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,9,11,9,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,11,9,10,8,9,10,11,12]>,
<7,792,120,y,7,36,[8,8,8,9,11,9,11,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,11,9,12,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,11,10,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,11,10,10,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,11,10,11,8,9,10,11,12]>,
<7,792,120,y,7,64,[8,8,8,9,11,10,12,8,9,10,11,12]>,
<7,792,120,y,7,36,[8,8,8,9,11,11,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,11,11,10,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,9,11,11,11,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,11,11,12,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,11,12,9,8,9,10,11,12]>,
<7,792,120,y,7,64,[8,8,8,9,11,12,10,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,11,12,11,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,11,12,12,8,9,10,11,12]>,
<7,792,40,y,7,40,[8,8,8,9,12,8,11,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,9,12,9,11,8,9,10,11,12]>,
<7,792,40,y,7,64,[8,8,8,9,12,10,11,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,10,9,8,9,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,10,9,8,10,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,10,9,8,12,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,10,9,9,9,8,9,10,11,12]>,
<7,792,120,y,7,36,[8,8,8,10,9,9,10,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,9,9,12,8,9,10,11,12]>,
<7,792,120,y,7,36,[8,8,8,10,9,10,9,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,10,9,10,10,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,9,10,12,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,9,11,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,9,11,10,8,9,10,11,12]>,
<7,792,120,y,7,64,[8,8,8,10,9,11,12,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,9,12,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,9,12,10,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,9,12,12,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,10,10,8,9,8,9,10,11,12]>,
<7,792,40,y,7,20,[8,8,8,10,10,8,10,8,9,10,11,12]>,
<7,792,120,y,7,36,[8,8,8,10,10,9,9,8,9,10,11,12]>,
<7,792,60,y,7,32,[8,8,8,10,10,9,10,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,10,10,10,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,10,11,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,10,12,9,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,10,11,8,9,8,9,10,11,12]>,
<7,792,120,y,7,40,[8,8,8,10,11,8,12,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,11,9,9,8,9,10,11,12]>,
<7,792,120,y,7,64,[8,8,8,10,11,9,12,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,11,10,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,11,10,12,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,11,11,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,11,11,12,8,9,10,11,12]>,
<7,792,120,y,7,64,[8,8,8,10,11,12,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,10,11,12,12,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,11,9,8,9,8,9,10,11,12]>,
<7,792,40,y,7,40,[8,8,8,11,9,8,12,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,11,9,9,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,11,9,9,12,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,11,9,10,9,8,9,10,11,12]>,
<7,792,40,y,7,64,[8,8,8,11,9,10,12,8,9,10,11,12]>,
<7,792,120,y,7,36,[8,8,8,11,9,11,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,11,9,12,9,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,8,11,11,8,9,8,9,10,11,12]>,
<7,792,120,y,7,36,[8,8,8,11,11,9,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,11,11,10,9,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,8,11,11,11,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,11,11,12,9,8,9,10,11,12]>,
<7,792,40,y,7,40,[8,8,8,12,11,8,9,8,9,10,11,12]>,
<7,792,120,y,7,48,[8,8,8,12,11,9,9,8,9,10,11,12]>,
<7,792,40,y,7,64,[8,8,8,12,11,10,9,8,9,10,11,12]>,
<7,792,60,y,7,18,[8,8,9,9,8,8,8,8,9,10,11,12]>,
<7,792,120,y,7,20,[8,8,9,9,8,8,9,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,9,9,8,8,10,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,9,9,8,8,11,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,9,9,8,8,12,8,9,10,11,12]>,
<7,792,60,y,7,20,[8,8,9,9,8,9,8,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,9,9,8,9,10,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,9,9,8,9,11,8,9,10,11,12]>,
<7,792,120,y,7,32,[8,8,9,9,8,9,12,8,9,10,11,12]>,
<7,792,120,y,7,30,[8,8,9,9,8,10,8,8,9,10,11,12]>,
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