/* Summary of M12 orbits (by conjugation) of Hamming words that are close to the identity. This file: Distance up to 5 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. 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]. */ res05:=[ // Distance 0 or 1 from id. <0,1,1,g,0,1,[1,2,3,4,5,6,7,8,9,10,11,12]>, <1,12,11,g,1,1,[2,2,3,4,5,6,7,8,9,10,11,12]>, // Distance 2 from id. <2,66,1,g,2,1,[2,1,3,4,5,6,7,8,9,10,11,12]>, <2,66,20,g,2,1,[2,3,3,4,5,6,7,8,9,10,11,12]>, <2,66,10,g,2,1,[3,3,3,4,5,6,7,8,9,10,11,12]>, <2,66,90,g,2,1,[3,4,3,4,5,6,7,8,9,10,11,12]>, // Distance 3 from id. <3,220,6,g,3,1,[2,1,1,4,5,6,7,8,9,10,11,12]>, <3,220,27,g,3,1,[2,1,4,4,5,6,7,8,9,10,11,12]>, <3,220,2,g,3,1,[2,3,1,4,5,6,7,8,9,10,11,12]>, <3,220,54,g,3,1,[2,3,4,4,5,6,7,8,9,10,11,12]>, <3,220,27,g,3,1,[2,4,2,4,5,6,7,8,9,10,11,12]>, <3,220,54,g,3,1,[2,4,4,4,5,6,7,8,9,10,11,12]>, <3,220,432,g,3,1,[2,4,5,4,5,6,7,8,9,10,11,12]>, <3,220,9,g,3,1,[4,4,4,4,5,6,7,8,9,10,11,12]>, <3,220,216,g,3,1,[4,4,5,4,5,6,7,8,9,10,11,12]>, <3,220,216,g,3,1,[4,5,6,4,5,6,7,8,9,10,11,12]>, <3,220,72,g,3,1,[4,5,7,4,5,6,7,8,9,10,11,12]>, <3,220,144,g,3,1,[4,5,9,4,5,6,7,8,9,10,11,12]>, <3,220,72,g,3,1,[4,5,11,4,5,6,7,8,9,10,11,12]>, // Distance 4 from id. <4,495,12,g,4,1,[2,1,1,1,5,6,7,8,9,10,11,12]>, <4,495,12,g,4,1,[2,1,1,2,5,6,7,8,9,10,11,12]>, <4,495,24,g,4,1,[2,1,1,3,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,1,1,5,5,6,7,8,9,10,11,12]>, <4,495,3,y,4,3,[2,1,4,3,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,1,4,5,5,6,7,8,9,10,11,12]>, <4,495,48,g,4,1,[2,1,5,5,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,1,5,6,5,6,7,8,9,10,11,12]>, <4,495,48,y,4,2,[2,1,5,7,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,1,5,8,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,1,5,10,5,6,7,8,9,10,11,12]>, <4,495,24,g,4,1,[2,3,1,1,5,6,7,8,9,10,11,12]>, <4,495,64,g,4,1,[2,3,1,5,5,6,7,8,9,10,11,12]>, <4,495,6,y,4,3,[2,3,4,1,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,3,4,5,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,3,5,2,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,3,5,3,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,3,5,5,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,3,5,6,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,3,5,7,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,3,5,8,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,3,5,9,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,3,5,10,5,6,7,8,9,10,11,12]>, <4,495,192,y,4,2,[2,3,5,11,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,3,5,12,5,6,7,8,9,10,11,12]>, <4,495,32,g,4,1,[2,5,2,2,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,5,2,5,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,2,6,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,5,2,7,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,2,8,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,2,10,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,5,4,5,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,5,4,6,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,5,4,7,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,4,8,5,6,7,8,9,10,11,12]>, <4,495,96,y,4,2,[2,5,4,10,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,5,4,11,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,5,4,12,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,5,5,5,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,5,6,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,5,7,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,5,8,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,5,9,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,5,10,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,5,11,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,5,12,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,6,6,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,6,7,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,5,6,8,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,6,9,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,6,10,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,6,11,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,6,12,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,7,6,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,5,7,7,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,7,9,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,7,10,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,7,11,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,7,12,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,5,8,6,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,8,9,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,8,10,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,8,11,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,8,12,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,9,9,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,9,10,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,5,9,11,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,9,12,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,10,9,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,10,10,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,5,10,12,5,6,7,8,9,10,11,12]>, <4,495,96,y,4,2,[2,5,11,9,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[2,5,11,10,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[2,5,12,10,5,6,7,8,9,10,11,12]>, <4,495,8,g,4,1,[5,5,5,5,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[5,5,5,6,5,6,7,8,9,10,11,12]>, <4,495,32,g,4,1,[5,5,5,7,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[5,5,6,6,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[5,5,6,7,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[5,5,6,8,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[5,5,6,9,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[5,5,6,10,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[5,5,6,11,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[5,5,6,12,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[5,5,7,6,5,6,7,8,9,10,11,12]>, <4,495,24,g,4,1,[5,5,7,7,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[5,5,7,10,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[5,5,8,6,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[5,5,8,9,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[5,5,8,10,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[5,5,8,12,5,6,7,8,9,10,11,12]>, <4,495,48,g,4,1,[5,5,10,10,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[5,5,10,12,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[5,6,7,8,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[5,6,7,9,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[5,6,7,10,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[5,6,7,11,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[5,6,7,12,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[5,6,8,10,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[5,6,8,12,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[5,6,9,7,5,6,7,8,9,10,11,12]>, <4,495,64,g,4,1,[5,6,10,8,5,6,7,8,9,10,11,12]>, <4,495,48,g,4,1,[5,6,10,9,5,6,7,8,9,10,11,12]>, <4,495,24,g,4,1,[5,6,11,7,5,6,7,8,9,10,11,12]>, <4,495,96,g,4,1,[5,7,6,8,5,6,7,8,9,10,11,12]>, <4,495,192,g,4,1,[5,7,6,12,5,6,7,8,9,10,11,12]>, <4,495,24,y,4,2,[5,7,10,12,5,6,7,8,9,10,11,12]>, <4,495,16,y,4,2,[5,9,6,12,5,6,7,8,9,10,11,12]>, <4,495,64,g,4,1,[5,10,8,6,5,6,7,8,9,10,11,12]>, // Distance 5 from id. <5,792,20,g,5,1,[2,1,1,1,1,6,7,8,9,10,11,12]>, <5,792,60,g,5,1,[2,1,1,1,2,6,7,8,9,10,11,12]>, <5,792,120,y,5,4,[2,1,1,1,3,6,7,8,9,10,11,12]>, <5,792,120,y,5,2,[2,1,1,1,6,6,7,8,9,10,11,12]>, <5,792,60,y,5,2,[2,1,1,1,7,6,7,8,9,10,11,12]>, <5,792,120,y,5,2,[2,1,1,1,9,6,7,8,9,10,11,12]>, <5,792,120,y,5,3,[2,1,1,1,10,6,7,8,9,10,11,12]>, <5,792,120,y,5,5,[2,1,1,2,3,6,7,8,9,10,11,12]>, <5,792,120,y,5,3,[2,1,1,2,6,6,7,8,9,10,11,12]>, <5,792,60,y,5,3,[2,1,1,2,7,6,7,8,9,10,11,12]>, <5,792,120,y,5,2,[2,1,1,2,8,6,7,8,9,10,11,12]>, <5,792,60,y,5,3,[2,1,1,2,10,6,7,8,9,10,11,12]>, <5,792,60,y,5,4,[2,1,1,2,12,6,7,8,9,10,11,12]>, <5,792,60,y,5,5,[2,1,1,3,3,6,7,8,9,10,11,12]>, <5,792,120,y,5,8,[2,1,1,3,4,6,7,8,9,10,11,12]>, <5,792,120,r,4,1,[2,1,1,3,6,6,7,8,9,10,11,12]>, <5,792,120,r,4,1,[2,1,1,3,7,6,7,8,9,10,11,12]>, <5,792,120,y,5,5,[2,1,1,3,8,6,7,8,9,10,11,12]>, <5,792,120,y,5,6,[2,1,1,3,9,6,7,8,9,10,11,12]>, <5,792,120,y,5,4,[2,1,1,3,10,6,7,8,9,10,11,12]>, <5,792,120,y,5,4,[2,1,1,3,11,6,7,8,9,10,11,12]>, <5,792,120,y,5,6,[2,1,1,3,12,6,7,8,9,10,11,12]>, <5,792,60,r,4,1,[2,1,1,5,4,6,7,8,9,10,11,12]>, <5,792,120,y,5,5,[2,1,1,5,6,6,7,8,9,10,11,12]>, <5,792,120,y,5,5,[2,1,1,5,7,6,7,8,9,10,11,12]>, <5,792,120,y,5,4,[2,1,1,5,8,6,7,8,9,10,11,12]>, <5,792,120,y,5,6,[2,1,1,5,9,6,7,8,9,10,11,12]>, <5,792,120,y,5,6,[2,1,1,5,10,6,7,8,9,10,11,12]>, <5,792,120,y,5,4,[2,1,1,5,11,6,7,8,9,10,11,12]>, <5,792,120,r,4,1,[2,1,1,5,12,6,7,8,9,10,11,12]>, <5,792,120,y,5,4,[2,1,1,6,6,6,7,8,9,10,11,12]>, <5,792,120,y,5,5,[2,1,1,6,7,6,7,8,9,10,11,12]>, <5,792,120,y,5,3,[2,1,1,6,8,6,7,8,9,10,11,12]>, <5,792,120,y,5,4,[2,1,1,6,9,6,7,8,9,10,11,12]>, <5,792,120,r,4,1,[2,1,1,6,10,6,7,8,9,10,11,12]>, <5,792,120,y,5,4,[2,1,1,6,11,6,7,8,9,10,11,12]>, <5,792,60,y,5,6,[2,1,1,6,12,6,7,8,9,10,11,12]>, <5,792,120,y,5,3,[2,1,1,7,6,6,7,8,9,10,11,12]>, <5,792,60,y,5,3,[2,1,1,7,7,6,7,8,9,10,11,12]>, <5,792,120,y,5,3,[2,1,1,7,8,6,7,8,9,10,11,12]>, <5,792,120,y,5,3,[2,1,1,7,9,6,7,8,9,10,11,12]>, <5,792,120,y,5,4,[2,1,1,7,10,6,7,8,9,10,11,12]>, <5,792,120,y,5,2,[2,1,1,7,11,6,7,8,9,10,11,12]>, <5,792,120,y,5,2,[2,1,1,8,6,6,7,8,9,10,11,12]>, <5,792,120,g,5,1,[2,1,1,8,8,6,7,8,9,10,11,12]>, <5,792,120,y,5,3,[2,1,1,8,9,6,7,8,9,10,11,12]>, <5,792,120,y,5,2,[2,1,1,8,10,6,7,8,9,10,11,12]>, <5,792,60,y,5,3,[2,1,1,8,11,6,7,8,9,10,11,12]>, <5,792,120,y,5,3,[2,1,1,9,6,6,7,8,9,10,11,12]>, <5,792,120,y,5,2,[2,1,1,9,8,6,7,8,9,10,11,12]>, <5,792,120,y,5,3,[2,1,1,9,9,6,7,8,9,10,11,12]>, <5,792,60,y,5,5,[2,1,1,9,10,6,7,8,9,10,11,12]>, <5,792,120,y,5,4,[2,1,1,10,6,6,7,8,9,10,11,12]>, <5,792,120,y,5,3,[2,1,1,10,8,6,7,8,9,10,11,12]>, <5,792,60,r,4,1,[2,1,1,10,9,6,7,8,9,10,11,12]>, <5,792,120,y,5,3,[2,1,1,11,6,6,7,8,9,10,11,12]>, <5,792,60,y,5,3,[2,1,1,11,8,6,7,8,9,10,11,12]>, <5,792,60,y,5,5,[2,1,1,12,6,6,7,8,9,10,11,12]>, <5,792,60,r,4,1,[2,1,4,3,6,6,7,8,9,10,11,12]>, <5,792,15,r,3,1,[2,1,4,3,7,6,7,8,9,10,11,12]>, <5,792,30,r,4,1,[2,1,4,3,10,6,7,8,9,10,11,12]>, <5,792,20,y,5,12,[2,1,4,5,3,6,7,8,9,10,11,12]>, <5,792,120,r,4,1,[2,1,4,5,6,6,7,8,9,10,11,12]>, <5,792,60,r,4,1,[2,1,4,5,7,6,7,8,9,10,11,12]>, <5,792,120,y,5,8,[2,1,4,5,8,6,7,8,9,10,11,12]>, <5,792,120,y,5,8,[2,1,4,5,10,6,7,8,9,10,11,12]>, <5,792,60,y,5,6,[2,1,4,6,4,6,7,8,9,10,11,12]>, <5,792,120,y,5,5,[2,1,4,6,6,6,7,8,9,10,11,12]>, <5,792,120,r,4,1,[2,1,4,6,7,6,7,8,9,10,11,12]>, <5,792,120,y,5,6,[2,1,4,6,8,6,7,8,9,10,11,12]>, <5,792,120,y,5,6,[2,1,4,6,9,6,7,8,9,10,11,12]>, <5,792,120,r,4,1,[2,1,4,6,10,6,7,8,9,10,11,12]>, <5,792,120,y,5,6,[2,1,4,6,11,6,7,8,9,10,11,12]>, <5,792,120,y,5,6,[2,1,4,6,12,6,7,8,9,10,11,12]>, <5,792,30,y,5,4,[2,1,4,7,4,6,7,8,9,10,11,12]>, 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