# Black box algorithm to find standard generators of Fi24' set F 0 # Have we found element 1? set G 0 # Have we found element 2? set V 0 # Timeout counter for "semi-standard" part set Y 0 # Timeout counter for conjugating part lbl SEMISTD rand 1 ord 1 A incr V if V gt 1000 then timeout if A notin 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 & 23 24 26 27 28 29 30 33 35 36 39 42 45 60 then fail if F eq 0 then if A in 20 28 60 then div A 2 B pwr B 1 2 set F 1 endif endif if G eq 0 then if A eq 39 then div A 3 C pwr C 1 3 set G 1 # This is an element of order 3 and it must be # in class 3A or 3E (50/50) endif endif if F eq 0 then jmp SEMISTD if G eq 0 then jmp SEMISTD set X 0 # Number of times we have tried to prove element is in 3D set Z 0 # Are we definitely in class 3E? lbl CONJUGATE incr Y if Y gt 1000 then timeout rand 4 cjr 3 4 mu 2 3 5 ord 5 D if D notin 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 20 21 23 24 & 26 27 28 29 30 33 35 36 39 42 45 then # This is not Fi24'! fail endif if D in 7 8 10 11 14 15 16 17 18 20 21 23 24 26 27 28 29 30 33 & 35 36 39 42 45 then # The element of order 3 is in class 3E (not 3A). set Z 1 endif if Z eq 0 then if D in 2 3 4 5 6 9 12 then # The chances are that our element of order 3 is in # class 3A, so go back to the beginning. set G 0 jmp SEMISTD endif endif if D noteq 29 then jmp CONJUGATE pwr 3 5 6 mu 6 3 7 ord 7 E if E noteq 33 then jmp CONJUGATE oup 2 2 3