
(/VERSIONCHECK 2) 

(DEFUN |PGE;llli2gp| (|l| $)
  (SPADCALL (SPADCALL (ELT $ 8) |l| (QREFELT $ 13)) (QREFELT $ 15))) 

(DEFUN |PGE;li1n| (|n| $)
  (PROG (#0=#:G1836 |i|)
    (RETURN
      (SEQ (PROGN
             (LETT #0# NIL . #1=(|PGE;li1n|))
             (SEQ (LETT |i| 1 . #1#) G190
                  (COND ((QSGREATERP |i| |n|) (GO G191)))
                  (SEQ (EXIT (LETT #0# (CONS |i| #0#) . #1#)))
                  (LETT |i| (QSADD1 |i|) . #1#) (GO G190) G191
                  (EXIT (NREVERSE0 #0#)))))))) 

(DEFUN |PGE;youngGroup;LPg;3| (|l| $)
  (PROG (|n| #0=#:G1843 #1=#:G1844 |i| #2=#:G1845 |gens| |element|)
    (RETURN
      (SEQ (LETT |gens| NIL . #3=(|PGE;youngGroup;LPg;3|))
           (LETT |element| 1 . #3#)
           (SEQ (LETT |n| NIL . #3#) (LETT #0# |l| . #3#) G190
                (COND
                  ((OR (ATOM #0#)
                       (PROGN (LETT |n| (CAR #0#) . #3#) NIL))
                   #4=(GO G191)))
                (SEQ (EXIT (COND
                             ((< 1 |n|)
                              (SEQ (LETT |gens|
                                    (CONS
                                     (SPADCALL
                                      (PROGN
                                        (LETT #1# NIL . #3#)
                                        (SEQ (LETT |i| |element| . #3#)
                                         (LETT #2#
                                          (- (+ |element| |n|) 1) . #3#)
                                         G190 (COND ((> |i| #2#) #4#))
                                         (SEQ
                                          (EXIT
                                           (LETT #1#
                                            (CONS |i| #1#) . #3#)))
                                         (LETT |i| (+ |i| 1) . #3#)
                                         #5=(GO G190) G191
                                         (EXIT (NREVERSE0 #1#))))
                                      (QREFELT $ 18))
                                     |gens|) . #3#)
                                   (COND
                                     ((NULL (< |n| 3))
                                      (LETT |gens|
                                       (CONS
                                        (LIST
                                         (LIST |element|
                                          (+ |element| 1)))
                                        |gens|) . #3#)))
                                   (EXIT
                                    (LETT |element|
                                     (+ |element| |n|) . #3#)))))))
                (LETT #0# (CDR #0#) . #3#) #5# G191 (EXIT NIL))
           (EXIT (|PGE;llli2gp|
                     (COND
                       ((EQL (LENGTH |gens|) 0) (LIST (LIST (LIST 1))))
                       ('T |gens|))
                     $)))))) 

(DEFUN |PGE;youngGroup;PPg;4| (|lambda| $)
  (SPADCALL (SPADCALL |lambda| (QREFELT $ 21)) (QREFELT $ 19))) 

(DEFUN |PGE;rubiksGroup;Pg;5| ($)
  (PROG (|f| |r| |u| |d| |l| |b|)
    (RETURN
      (SEQ (LETT |f|
                 (LIST (LIST 11 13 15 17) (LIST 12 14 16 18)
                       (LIST 51 31 21 41) (LIST 53 33 23 43)
                       (LIST 52 32 22 42))
                 . #0=(|PGE;rubiksGroup;Pg;5|))
           (LETT |r|
                 (LIST (LIST 21 23 25 27) (LIST 22 24 26 28)
                       (LIST 13 37 67 43) (LIST 15 31 61 45)
                       (LIST 14 38 68 44)) . #0#)
           (LETT |u|
                 (LIST (LIST 31 33 35 37) (LIST 32 34 36 38)
                       (LIST 13 51 63 25) (LIST 11 57 61 23)
                       (LIST 12 58 62 24)) . #0#)
           (LETT |d|
                 (LIST (LIST 41 43 45 47) (LIST 42 44 46 48)
                       (LIST 17 21 67 55) (LIST 15 27 65 53)
                       (LIST 16 28 66 54)) . #0#)
           (LETT |l|
                 (LIST (LIST 51 53 55 57) (LIST 52 54 56 58)
                       (LIST 11 41 65 35) (LIST 17 47 63 33)
                       (LIST 18 48 64 34)) . #0#)
           (LETT |b|
                 (LIST (LIST 61 63 65 67) (LIST 62 64 66 68)
                       (LIST 45 25 35 55) (LIST 47 27 37 57)
                       (LIST 46 26 36 56)) . #0#)
           (EXIT (|PGE;llli2gp| (LIST |f| |r| |u| |d| |l| |b|) $)))))) 

(DEFUN |PGE;mathieu11;LPg;6| (|l| $)
  (PROG (|a|)
    (RETURN
      (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 24))
                 . #0=(|PGE;mathieu11;LPg;6|))
           (COND
             ((NULL (EQL (LENGTH |l|) 11))
              (EXIT (|error| "Exactly 11 integers for mathieu11 needed !"))))
           (LETT |a|
                 (LIST (LIST (SPADCALL |l| 1 (QREFELT $ 26))
                             (SPADCALL |l| 10 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 2 (QREFELT $ 26))
                             (SPADCALL |l| 8 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 3 (QREFELT $ 26))
                             (SPADCALL |l| 11 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 5 (QREFELT $ 26))
                             (SPADCALL |l| 7 (QREFELT $ 26)))) . #0#)
           (EXIT (|PGE;llli2gp|
                     (LIST |a|
                           (LIST (LIST (SPADCALL |l| 1 (QREFELT $ 26))
                                       (SPADCALL |l| 4 (QREFELT $ 26))
                                       (SPADCALL |l| 7 (QREFELT $ 26))
                                       (SPADCALL |l| 6 (QREFELT $ 26)))
                                 (LIST (SPADCALL |l| 2 (QREFELT $ 26))
                                       (SPADCALL |l| 11 (QREFELT $ 26))
                                       (SPADCALL |l| 10 (QREFELT $ 26))
                                       (SPADCALL |l| 9 (QREFELT $ 26)))))
                     $)))))) 

(DEFUN |PGE;mathieu11;Pg;7| ($)
  (SPADCALL (|PGE;li1n| 11 $) (QREFELT $ 27))) 

(DEFUN |PGE;mathieu12;LPg;8| (|l| $)
  (PROG (|a|)
    (RETURN
      (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 24))
                 . #0=(|PGE;mathieu12;LPg;8|))
           (COND
             ((NULL (EQL (LENGTH |l|) 12))
              (EXIT (|error| "Exactly 12 integers for mathieu12 needed !"))))
           (LETT |a|
                 (LIST (LIST (SPADCALL |l| 1 (QREFELT $ 26))
                             (SPADCALL |l| 2 (QREFELT $ 26))
                             (SPADCALL |l| 3 (QREFELT $ 26))
                             (SPADCALL |l| 4 (QREFELT $ 26))
                             (SPADCALL |l| 5 (QREFELT $ 26))
                             (SPADCALL |l| 6 (QREFELT $ 26))
                             (SPADCALL |l| 7 (QREFELT $ 26))
                             (SPADCALL |l| 8 (QREFELT $ 26))
                             (SPADCALL |l| 9 (QREFELT $ 26))
                             (SPADCALL |l| 10 (QREFELT $ 26))
                             (SPADCALL |l| 11 (QREFELT $ 26)))) . #0#)
           (EXIT (|PGE;llli2gp|
                     (LIST |a|
                           (LIST (LIST (SPADCALL |l| 1 (QREFELT $ 26))
                                       (SPADCALL |l| 6 (QREFELT $ 26))
                                       (SPADCALL |l| 5 (QREFELT $ 26))
                                       (SPADCALL |l| 8 (QREFELT $ 26))
                                       (SPADCALL |l| 3 (QREFELT $ 26))
                                       (SPADCALL |l| 7 (QREFELT $ 26))
                                       (SPADCALL |l| 4 (QREFELT $ 26))
                                       (SPADCALL |l| 2 (QREFELT $ 26))
                                       (SPADCALL |l| 9 (QREFELT $ 26))
                                       (SPADCALL |l| 10 (QREFELT $ 26)))
                                 (LIST (SPADCALL |l| 11 (QREFELT $ 26))
                                       (SPADCALL |l| 12 (QREFELT $ 26)))))
                     $)))))) 

(DEFUN |PGE;mathieu12;Pg;9| ($)
  (SPADCALL (|PGE;li1n| 12 $) (QREFELT $ 29))) 

(DEFUN |PGE;mathieu22;LPg;10| (|l| $)
  (PROG (|a| |b|)
    (RETURN
      (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 24))
                 . #0=(|PGE;mathieu22;LPg;10|))
           (COND
             ((NULL (EQL (LENGTH |l|) 22))
              (EXIT (|error| "Exactly 22 integers for mathieu22 needed !"))))
           (LETT |a|
                 (LIST (LIST (SPADCALL |l| 1 (QREFELT $ 26))
                             (SPADCALL |l| 2 (QREFELT $ 26))
                             (SPADCALL |l| 4 (QREFELT $ 26))
                             (SPADCALL |l| 8 (QREFELT $ 26))
                             (SPADCALL |l| 16 (QREFELT $ 26))
                             (SPADCALL |l| 9 (QREFELT $ 26))
                             (SPADCALL |l| 18 (QREFELT $ 26))
                             (SPADCALL |l| 13 (QREFELT $ 26))
                             (SPADCALL |l| 3 (QREFELT $ 26))
                             (SPADCALL |l| 6 (QREFELT $ 26))
                             (SPADCALL |l| 12 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 5 (QREFELT $ 26))
                             (SPADCALL |l| 10 (QREFELT $ 26))
                             (SPADCALL |l| 20 (QREFELT $ 26))
                             (SPADCALL |l| 17 (QREFELT $ 26))
                             (SPADCALL |l| 11 (QREFELT $ 26))
                             (SPADCALL |l| 22 (QREFELT $ 26))
                             (SPADCALL |l| 21 (QREFELT $ 26))
                             (SPADCALL |l| 19 (QREFELT $ 26))
                             (SPADCALL |l| 15 (QREFELT $ 26))
                             (SPADCALL |l| 7 (QREFELT $ 26))
                             (SPADCALL |l| 14 (QREFELT $ 26)))) . #0#)
           (LETT |b|
                 (LIST (LIST (SPADCALL |l| 1 (QREFELT $ 26))
                             (SPADCALL |l| 2 (QREFELT $ 26))
                             (SPADCALL |l| 6 (QREFELT $ 26))
                             (SPADCALL |l| 18 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 3 (QREFELT $ 26))
                             (SPADCALL |l| 15 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 5 (QREFELT $ 26))
                             (SPADCALL |l| 8 (QREFELT $ 26))
                             (SPADCALL |l| 21 (QREFELT $ 26))
                             (SPADCALL |l| 13 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 7 (QREFELT $ 26))
                             (SPADCALL |l| 9 (QREFELT $ 26))
                             (SPADCALL |l| 20 (QREFELT $ 26))
                             (SPADCALL |l| 12 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 10 (QREFELT $ 26))
                             (SPADCALL |l| 16 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 11 (QREFELT $ 26))
                             (SPADCALL |l| 19 (QREFELT $ 26))
                             (SPADCALL |l| 14 (QREFELT $ 26))
                             (SPADCALL |l| 22 (QREFELT $ 26)))) . #0#)
           (EXIT (|PGE;llli2gp| (LIST |a| |b|) $)))))) 

(DEFUN |PGE;mathieu22;Pg;11| ($)
  (SPADCALL (|PGE;li1n| 22 $) (QREFELT $ 31))) 

(DEFUN |PGE;mathieu23;LPg;12| (|l| $)
  (PROG (|a| |b|)
    (RETURN
      (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 24))
                 . #0=(|PGE;mathieu23;LPg;12|))
           (COND
             ((NULL (EQL (LENGTH |l|) 23))
              (EXIT (|error| "Exactly 23 integers for mathieu23 needed !"))))
           (LETT |a|
                 (LIST (LIST (SPADCALL |l| 1 (QREFELT $ 26))
                             (SPADCALL |l| 2 (QREFELT $ 26))
                             (SPADCALL |l| 3 (QREFELT $ 26))
                             (SPADCALL |l| 4 (QREFELT $ 26))
                             (SPADCALL |l| 5 (QREFELT $ 26))
                             (SPADCALL |l| 6 (QREFELT $ 26))
                             (SPADCALL |l| 7 (QREFELT $ 26))
                             (SPADCALL |l| 8 (QREFELT $ 26))
                             (SPADCALL |l| 9 (QREFELT $ 26))
                             (SPADCALL |l| 10 (QREFELT $ 26))
                             (SPADCALL |l| 11 (QREFELT $ 26))
                             (SPADCALL |l| 12 (QREFELT $ 26))
                             (SPADCALL |l| 13 (QREFELT $ 26))
                             (SPADCALL |l| 14 (QREFELT $ 26))
                             (SPADCALL |l| 15 (QREFELT $ 26))
                             (SPADCALL |l| 16 (QREFELT $ 26))
                             (SPADCALL |l| 17 (QREFELT $ 26))
                             (SPADCALL |l| 18 (QREFELT $ 26))
                             (SPADCALL |l| 19 (QREFELT $ 26))
                             (SPADCALL |l| 20 (QREFELT $ 26))
                             (SPADCALL |l| 21 (QREFELT $ 26))
                             (SPADCALL |l| 22 (QREFELT $ 26))
                             (SPADCALL |l| 23 (QREFELT $ 26)))) . #0#)
           (LETT |b|
                 (LIST (LIST (SPADCALL |l| 2 (QREFELT $ 26))
                             (SPADCALL |l| 16 (QREFELT $ 26))
                             (SPADCALL |l| 9 (QREFELT $ 26))
                             (SPADCALL |l| 6 (QREFELT $ 26))
                             (SPADCALL |l| 8 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 3 (QREFELT $ 26))
                             (SPADCALL |l| 12 (QREFELT $ 26))
                             (SPADCALL |l| 13 (QREFELT $ 26))
                             (SPADCALL |l| 18 (QREFELT $ 26))
                             (SPADCALL |l| 4 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 7 (QREFELT $ 26))
                             (SPADCALL |l| 17 (QREFELT $ 26))
                             (SPADCALL |l| 10 (QREFELT $ 26))
                             (SPADCALL |l| 11 (QREFELT $ 26))
                             (SPADCALL |l| 22 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 14 (QREFELT $ 26))
                             (SPADCALL |l| 19 (QREFELT $ 26))
                             (SPADCALL |l| 21 (QREFELT $ 26))
                             (SPADCALL |l| 20 (QREFELT $ 26))
                             (SPADCALL |l| 15 (QREFELT $ 26)))) . #0#)
           (EXIT (|PGE;llli2gp| (LIST |a| |b|) $)))))) 

(DEFUN |PGE;mathieu23;Pg;13| ($)
  (SPADCALL (|PGE;li1n| 23 $) (QREFELT $ 33))) 

(DEFUN |PGE;mathieu24;LPg;14| (|l| $)
  (PROG (|a| |b|)
    (RETURN
      (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 24))
                 . #0=(|PGE;mathieu24;LPg;14|))
           (COND
             ((NULL (EQL (LENGTH |l|) 24))
              (EXIT (|error| "Exactly 24 integers for mathieu24 needed !"))))
           (LETT |a|
                 (LIST (LIST (SPADCALL |l| 1 (QREFELT $ 26))
                             (SPADCALL |l| 16 (QREFELT $ 26))
                             (SPADCALL |l| 10 (QREFELT $ 26))
                             (SPADCALL |l| 22 (QREFELT $ 26))
                             (SPADCALL |l| 24 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 2 (QREFELT $ 26))
                             (SPADCALL |l| 12 (QREFELT $ 26))
                             (SPADCALL |l| 18 (QREFELT $ 26))
                             (SPADCALL |l| 21 (QREFELT $ 26))
                             (SPADCALL |l| 7 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 4 (QREFELT $ 26))
                             (SPADCALL |l| 5 (QREFELT $ 26))
                             (SPADCALL |l| 8 (QREFELT $ 26))
                             (SPADCALL |l| 6 (QREFELT $ 26))
                             (SPADCALL |l| 17 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 9 (QREFELT $ 26))
                             (SPADCALL |l| 11 (QREFELT $ 26))
                             (SPADCALL |l| 13 (QREFELT $ 26))
                             (SPADCALL |l| 19 (QREFELT $ 26))
                             (SPADCALL |l| 15 (QREFELT $ 26)))) . #0#)
           (LETT |b|
                 (LIST (LIST (SPADCALL |l| 1 (QREFELT $ 26))
                             (SPADCALL |l| 22 (QREFELT $ 26))
                             (SPADCALL |l| 13 (QREFELT $ 26))
                             (SPADCALL |l| 14 (QREFELT $ 26))
                             (SPADCALL |l| 6 (QREFELT $ 26))
                             (SPADCALL |l| 20 (QREFELT $ 26))
                             (SPADCALL |l| 3 (QREFELT $ 26))
                             (SPADCALL |l| 21 (QREFELT $ 26))
                             (SPADCALL |l| 8 (QREFELT $ 26))
                             (SPADCALL |l| 11 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 2 (QREFELT $ 26))
                             (SPADCALL |l| 10 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 4 (QREFELT $ 26))
                             (SPADCALL |l| 15 (QREFELT $ 26))
                             (SPADCALL |l| 18 (QREFELT $ 26))
                             (SPADCALL |l| 17 (QREFELT $ 26))
                             (SPADCALL |l| 16 (QREFELT $ 26))
                             (SPADCALL |l| 5 (QREFELT $ 26))
                             (SPADCALL |l| 9 (QREFELT $ 26))
                             (SPADCALL |l| 19 (QREFELT $ 26))
                             (SPADCALL |l| 12 (QREFELT $ 26))
                             (SPADCALL |l| 7 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 23 (QREFELT $ 26))
                             (SPADCALL |l| 24 (QREFELT $ 26)))) . #0#)
           (EXIT (|PGE;llli2gp| (LIST |a| |b|) $)))))) 

(DEFUN |PGE;mathieu24;Pg;15| ($)
  (SPADCALL (|PGE;li1n| 24 $) (QREFELT $ 35))) 

(DEFUN |PGE;janko2;LPg;16| (|l| $)
  (PROG (|a| |b|)
    (RETURN
      (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 24))
                 . #0=(|PGE;janko2;LPg;16|))
           (COND
             ((NULL (EQL (LENGTH |l|) 100))
              (EXIT (|error| "Exactly 100 integers for janko2 needed !"))))
           (LETT |a|
                 (LIST (LIST (SPADCALL |l| 2 (QREFELT $ 26))
                             (SPADCALL |l| 3 (QREFELT $ 26))
                             (SPADCALL |l| 4 (QREFELT $ 26))
                             (SPADCALL |l| 5 (QREFELT $ 26))
                             (SPADCALL |l| 6 (QREFELT $ 26))
                             (SPADCALL |l| 7 (QREFELT $ 26))
                             (SPADCALL |l| 8 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 9 (QREFELT $ 26))
                             (SPADCALL |l| 10 (QREFELT $ 26))
                             (SPADCALL |l| 11 (QREFELT $ 26))
                             (SPADCALL |l| 12 (QREFELT $ 26))
                             (SPADCALL |l| 13 (QREFELT $ 26))
                             (SPADCALL |l| 14 (QREFELT $ 26))
                             (SPADCALL |l| 15 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 16 (QREFELT $ 26))
                             (SPADCALL |l| 17 (QREFELT $ 26))
                             (SPADCALL |l| 18 (QREFELT $ 26))
                             (SPADCALL |l| 19 (QREFELT $ 26))
                             (SPADCALL |l| 20 (QREFELT $ 26))
                             (SPADCALL |l| 21 (QREFELT $ 26))
                             (SPADCALL |l| 22 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 23 (QREFELT $ 26))
                             (SPADCALL |l| 24 (QREFELT $ 26))
                             (SPADCALL |l| 25 (QREFELT $ 26))
                             (SPADCALL |l| 26 (QREFELT $ 26))
                             (SPADCALL |l| 27 (QREFELT $ 26))
                             (SPADCALL |l| 28 (QREFELT $ 26))
                             (SPADCALL |l| 29 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 30 (QREFELT $ 26))
                             (SPADCALL |l| 31 (QREFELT $ 26))
                             (SPADCALL |l| 32 (QREFELT $ 26))
                             (SPADCALL |l| 33 (QREFELT $ 26))
                             (SPADCALL |l| 34 (QREFELT $ 26))
                             (SPADCALL |l| 35 (QREFELT $ 26))
                             (SPADCALL |l| 36 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 37 (QREFELT $ 26))
                             (SPADCALL |l| 38 (QREFELT $ 26))
                             (SPADCALL |l| 39 (QREFELT $ 26))
                             (SPADCALL |l| 40 (QREFELT $ 26))
                             (SPADCALL |l| 41 (QREFELT $ 26))
                             (SPADCALL |l| 42 (QREFELT $ 26))
                             (SPADCALL |l| 43 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 44 (QREFELT $ 26))
                             (SPADCALL |l| 45 (QREFELT $ 26))
                             (SPADCALL |l| 46 (QREFELT $ 26))
                             (SPADCALL |l| 47 (QREFELT $ 26))
                             (SPADCALL |l| 48 (QREFELT $ 26))
                             (SPADCALL |l| 49 (QREFELT $ 26))
                             (SPADCALL |l| 50 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 51 (QREFELT $ 26))
                             (SPADCALL |l| 52 (QREFELT $ 26))
                             (SPADCALL |l| 53 (QREFELT $ 26))
                             (SPADCALL |l| 54 (QREFELT $ 26))
                             (SPADCALL |l| 55 (QREFELT $ 26))
                             (SPADCALL |l| 56 (QREFELT $ 26))
                             (SPADCALL |l| 57 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 58 (QREFELT $ 26))
                             (SPADCALL |l| 59 (QREFELT $ 26))
                             (SPADCALL |l| 60 (QREFELT $ 26))
                             (SPADCALL |l| 61 (QREFELT $ 26))
                             (SPADCALL |l| 62 (QREFELT $ 26))
                             (SPADCALL |l| 63 (QREFELT $ 26))
                             (SPADCALL |l| 64 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 65 (QREFELT $ 26))
                             (SPADCALL |l| 66 (QREFELT $ 26))
                             (SPADCALL |l| 67 (QREFELT $ 26))
                             (SPADCALL |l| 68 (QREFELT $ 26))
                             (SPADCALL |l| 69 (QREFELT $ 26))
                             (SPADCALL |l| 70 (QREFELT $ 26))
                             (SPADCALL |l| 71 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 72 (QREFELT $ 26))
                             (SPADCALL |l| 73 (QREFELT $ 26))
                             (SPADCALL |l| 74 (QREFELT $ 26))
                             (SPADCALL |l| 75 (QREFELT $ 26))
                             (SPADCALL |l| 76 (QREFELT $ 26))
                             (SPADCALL |l| 77 (QREFELT $ 26))
                             (SPADCALL |l| 78 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 79 (QREFELT $ 26))
                             (SPADCALL |l| 80 (QREFELT $ 26))
                             (SPADCALL |l| 81 (QREFELT $ 26))
                             (SPADCALL |l| 82 (QREFELT $ 26))
                             (SPADCALL |l| 83 (QREFELT $ 26))
                             (SPADCALL |l| 84 (QREFELT $ 26))
                             (SPADCALL |l| 85 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 86 (QREFELT $ 26))
                             (SPADCALL |l| 87 (QREFELT $ 26))
                             (SPADCALL |l| 88 (QREFELT $ 26))
                             (SPADCALL |l| 89 (QREFELT $ 26))
                             (SPADCALL |l| 90 (QREFELT $ 26))
                             (SPADCALL |l| 91 (QREFELT $ 26))
                             (SPADCALL |l| 92 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 93 (QREFELT $ 26))
                             (SPADCALL |l| 94 (QREFELT $ 26))
                             (SPADCALL |l| 95 (QREFELT $ 26))
                             (SPADCALL |l| 96 (QREFELT $ 26))
                             (SPADCALL |l| 97 (QREFELT $ 26))
                             (SPADCALL |l| 98 (QREFELT $ 26))
                             (SPADCALL |l| 99 (QREFELT $ 26)))) . #0#)
           (LETT |b|
                 (LIST (LIST (SPADCALL |l| 1 (QREFELT $ 26))
                             (SPADCALL |l| 74 (QREFELT $ 26))
                             (SPADCALL |l| 83 (QREFELT $ 26))
                             (SPADCALL |l| 21 (QREFELT $ 26))
                             (SPADCALL |l| 36 (QREFELT $ 26))
                             (SPADCALL |l| 77 (QREFELT $ 26))
                             (SPADCALL |l| 44 (QREFELT $ 26))
                             (SPADCALL |l| 80 (QREFELT $ 26))
                             (SPADCALL |l| 64 (QREFELT $ 26))
                             (SPADCALL |l| 2 (QREFELT $ 26))
                             (SPADCALL |l| 34 (QREFELT $ 26))
                             (SPADCALL |l| 75 (QREFELT $ 26))
                             (SPADCALL |l| 48 (QREFELT $ 26))
                             (SPADCALL |l| 17 (QREFELT $ 26))
                             (SPADCALL |l| 100 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 3 (QREFELT $ 26))
                             (SPADCALL |l| 15 (QREFELT $ 26))
                             (SPADCALL |l| 31 (QREFELT $ 26))
                             (SPADCALL |l| 52 (QREFELT $ 26))
                             (SPADCALL |l| 19 (QREFELT $ 26))
                             (SPADCALL |l| 11 (QREFELT $ 26))
                             (SPADCALL |l| 73 (QREFELT $ 26))
                             (SPADCALL |l| 79 (QREFELT $ 26))
                             (SPADCALL |l| 26 (QREFELT $ 26))
                             (SPADCALL |l| 56 (QREFELT $ 26))
                             (SPADCALL |l| 41 (QREFELT $ 26))
                             (SPADCALL |l| 99 (QREFELT $ 26))
                             (SPADCALL |l| 39 (QREFELT $ 26))
                             (SPADCALL |l| 84 (QREFELT $ 26))
                             (SPADCALL |l| 90 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 4 (QREFELT $ 26))
                             (SPADCALL |l| 57 (QREFELT $ 26))
                             (SPADCALL |l| 86 (QREFELT $ 26))
                             (SPADCALL |l| 63 (QREFELT $ 26))
                             (SPADCALL |l| 85 (QREFELT $ 26))
                             (SPADCALL |l| 95 (QREFELT $ 26))
                             (SPADCALL |l| 82 (QREFELT $ 26))
                             (SPADCALL |l| 97 (QREFELT $ 26))
                             (SPADCALL |l| 98 (QREFELT $ 26))
                             (SPADCALL |l| 81 (QREFELT $ 26))
                             (SPADCALL |l| 8 (QREFELT $ 26))
                             (SPADCALL |l| 69 (QREFELT $ 26))
                             (SPADCALL |l| 38 (QREFELT $ 26))
                             (SPADCALL |l| 43 (QREFELT $ 26))
                             (SPADCALL |l| 58 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 5 (QREFELT $ 26))
                             (SPADCALL |l| 66 (QREFELT $ 26))
                             (SPADCALL |l| 49 (QREFELT $ 26))
                             (SPADCALL |l| 59 (QREFELT $ 26))
                             (SPADCALL |l| 61 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 6 (QREFELT $ 26))
                             (SPADCALL |l| 68 (QREFELT $ 26))
                             (SPADCALL |l| 89 (QREFELT $ 26))
                             (SPADCALL |l| 94 (QREFELT $ 26))
                             (SPADCALL |l| 92 (QREFELT $ 26))
                             (SPADCALL |l| 20 (QREFELT $ 26))
                             (SPADCALL |l| 13 (QREFELT $ 26))
                             (SPADCALL |l| 54 (QREFELT $ 26))
                             (SPADCALL |l| 24 (QREFELT $ 26))
                             (SPADCALL |l| 51 (QREFELT $ 26))
                             (SPADCALL |l| 87 (QREFELT $ 26))
                             (SPADCALL |l| 27 (QREFELT $ 26))
                             (SPADCALL |l| 76 (QREFELT $ 26))
                             (SPADCALL |l| 23 (QREFELT $ 26))
                             (SPADCALL |l| 67 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 7 (QREFELT $ 26))
                             (SPADCALL |l| 72 (QREFELT $ 26))
                             (SPADCALL |l| 22 (QREFELT $ 26))
                             (SPADCALL |l| 35 (QREFELT $ 26))
                             (SPADCALL |l| 30 (QREFELT $ 26))
                             (SPADCALL |l| 70 (QREFELT $ 26))
                             (SPADCALL |l| 47 (QREFELT $ 26))
                             (SPADCALL |l| 62 (QREFELT $ 26))
                             (SPADCALL |l| 45 (QREFELT $ 26))
                             (SPADCALL |l| 46 (QREFELT $ 26))
                             (SPADCALL |l| 40 (QREFELT $ 26))
                             (SPADCALL |l| 28 (QREFELT $ 26))
                             (SPADCALL |l| 65 (QREFELT $ 26))
                             (SPADCALL |l| 93 (QREFELT $ 26))
                             (SPADCALL |l| 42 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 9 (QREFELT $ 26))
                             (SPADCALL |l| 71 (QREFELT $ 26))
                             (SPADCALL |l| 37 (QREFELT $ 26))
                             (SPADCALL |l| 91 (QREFELT $ 26))
                             (SPADCALL |l| 18 (QREFELT $ 26))
                             (SPADCALL |l| 55 (QREFELT $ 26))
                             (SPADCALL |l| 96 (QREFELT $ 26))
                             (SPADCALL |l| 60 (QREFELT $ 26))
                             (SPADCALL |l| 16 (QREFELT $ 26))
                             (SPADCALL |l| 53 (QREFELT $ 26))
                             (SPADCALL |l| 50 (QREFELT $ 26))
                             (SPADCALL |l| 25 (QREFELT $ 26))
                             (SPADCALL |l| 32 (QREFELT $ 26))
                             (SPADCALL |l| 14 (QREFELT $ 26))
                             (SPADCALL |l| 33 (QREFELT $ 26)))
                       (LIST (SPADCALL |l| 10 (QREFELT $ 26))
                             (SPADCALL |l| 78 (QREFELT $ 26))
                             (SPADCALL |l| 88 (QREFELT $ 26))
                             (SPADCALL |l| 29 (QREFELT $ 26))
                             (SPADCALL |l| 12 (QREFELT $ 26)))) . #0#)
           (EXIT (|PGE;llli2gp| (LIST |a| |b|) $)))))) 

(DEFUN |PGE;janko2;Pg;17| ($)
  (SPADCALL (|PGE;li1n| 100 $) (QREFELT $ 37))) 

(DEFUN |PGE;abelianGroup;LPg;18| (|l| $)
  (PROG (|n| #0=#:G1879 #1=#:G1880 |i| #2=#:G1881 |gens| |element|)
    (RETURN
      (SEQ (LETT |gens| NIL . #3=(|PGE;abelianGroup;LPg;18|))
           (LETT |element| 1 . #3#)
           (SEQ (LETT |n| NIL . #3#) (LETT #0# |l| . #3#) G190
                (COND
                  ((OR (ATOM #0#)
                       (PROGN (LETT |n| (CAR #0#) . #3#) NIL))
                   #4=(GO G191)))
                (SEQ (EXIT (COND
                             ((< 1 |n|)
                              (SEQ (LETT |gens|
                                    (CONS
                                     (SPADCALL
                                      (PROGN
                                        (LETT #1# NIL . #3#)
                                        (SEQ (LETT |i| |element| . #3#)
                                         (LETT #2#
                                          (- (+ |element| |n|) 1) . #3#)
                                         G190 (COND ((> |i| #2#) #4#))
                                         (SEQ
                                          (EXIT
                                           (LETT #1#
                                            (CONS |i| #1#) . #3#)))
                                         (LETT |i| (+ |i| 1) . #3#)
                                         #5=(GO G190) G191
                                         (EXIT (NREVERSE0 #1#))))
                                      (QREFELT $ 18))
                                     |gens|) . #3#)
                                   (EXIT
                                    (LETT |element|
                                     (+ |element| |n|) . #3#)))))))
                (LETT #0# (CDR #0#) . #3#) #5# G191 (EXIT NIL))
           (EXIT (|PGE;llli2gp|
                     (COND
                       ((EQL (LENGTH |gens|) 0) (LIST (LIST (LIST 1))))
                       ('T |gens|))
                     $)))))) 

(DEFUN |PGE;alternatingGroup;LPg;19| (|l| $)
  (PROG (#0=#:G1889 |i| #1=#:G1890 |tmp| |gens|)
    (RETURN
      (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 24))
                 . #2=(|PGE;alternatingGroup;LPg;19|))
           (EXIT (COND
                   ((EQL (LENGTH |l|) 0)
                    (|error| "Cannot construct alternating group on empty set"))
                   ((< (LENGTH |l|) 3)
                    (|PGE;llli2gp|
                        (LIST (LIST (LIST
                                     (SPADCALL |l| 1 (QREFELT $ 26)))))
                        $))
                   ((EQL (LENGTH |l|) 3)
                    (|PGE;llli2gp|
                        (LIST (LIST (LIST
                                     (SPADCALL |l| 1 (QREFELT $ 26))
                                     (SPADCALL |l| 2 (QREFELT $ 26))
                                     (SPADCALL |l| 3 (QREFELT $ 26)))))
                        $))
                   ('T
                    (SEQ (LETT |tmp|
                               (PROGN
                                 (LETT #0# NIL . #2#)
                                 (SEQ (LETT |i| 3 . #2#)
                                      (LETT #1# (LENGTH |l|) . #2#)
                                      G190
                                      (COND ((> |i| #1#) (GO G191)))
                                      (SEQ
                                       (EXIT
                                        (LETT #0#
                                         (CONS
                                          (SPADCALL |l| |i|
                                           (QREFELT $ 26))
                                          #0#) . #2#)))
                                      (LETT |i| (+ |i| 1) . #2#)
                                      (GO G190) G191
                                      (EXIT (NREVERSE0 #0#)))) . #2#)
                         (LETT |gens|
                               (LIST (LIST |tmp|)
                                     (LIST
                                      (LIST
                                       (SPADCALL |l| 1 (QREFELT $ 26))
                                       (SPADCALL |l| 2 (QREFELT $ 26))
                                       (SPADCALL |l| 3 (QREFELT $ 26))))) . #2#)
                         (EXIT (COND
                                 ((ODDP (LENGTH |l|))
                                  (|PGE;llli2gp| |gens| $))
                                 ('T
                                  (SEQ (SPADCALL |gens| 1
                                        (CONS
                                         (LIST
                                          (SPADCALL |l| 1
                                           (QREFELT $ 26))
                                          (SPADCALL |l| 2
                                           (QREFELT $ 26)))
                                         (SPADCALL |gens| 1
                                          (QREFELT $ 41)))
                                        (QREFELT $ 42))
                                       (EXIT (|PGE;llli2gp| |gens| $)))))))))))))) 

(DEFUN |PGE;alternatingGroup;PiPg;20| (|n| $)
  (SPADCALL (|PGE;li1n| |n| $) (QREFELT $ 43))) 

(DEFUN |PGE;symmetricGroup;LPg;21| (|l| $)
  (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 24))
             |PGE;symmetricGroup;LPg;21|)
       (EXIT (COND
               ((EQL (LENGTH |l|) 0)
                (|error| "Cannot construct symmetric group on empty set !"))
               ((< (LENGTH |l|) 3) (|PGE;llli2gp| (LIST (LIST |l|)) $))
               ('T
                (|PGE;llli2gp|
                    (LIST (LIST |l|)
                          (LIST (LIST (SPADCALL |l| 1 (QREFELT $ 26))
                                      (SPADCALL |l| 2 (QREFELT $ 26)))))
                    $)))))) 

(DEFUN |PGE;symmetricGroup;PiPg;22| (|n| $)
  (SPADCALL (|PGE;li1n| |n| $) (QREFELT $ 46))) 

(DEFUN |PGE;cyclicGroup;LPg;23| (|l| $)
  (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 24))
             |PGE;cyclicGroup;LPg;23|)
       (EXIT (COND
               ((EQL (LENGTH |l|) 0)
                (|error| "Cannot construct cyclic group on empty set"))
               ('T (|PGE;llli2gp| (LIST (LIST |l|)) $)))))) 

(DEFUN |PGE;cyclicGroup;PiPg;24| (|n| $)
  (SPADCALL (|PGE;li1n| |n| $) (QREFELT $ 48))) 

(DEFUN |PGE;dihedralGroup;LPg;25| (|l| $)
  (PROG (#0=#:G1903 |i| #1=#:G1904 |tmp|)
    (RETURN
      (SEQ (LETT |l| (SPADCALL |l| (QREFELT $ 24))
                 . #2=(|PGE;dihedralGroup;LPg;25|))
           (EXIT (COND
                   ((< (LENGTH |l|) 3)
                    (|error| "in dihedralGroup: Minimum of 3 elements needed !"))
                   ('T
                    (SEQ (LETT |tmp|
                               (PROGN
                                 (LETT #0# NIL . #2#)
                                 (SEQ (LETT |i| 1 . #2#)
                                      (LETT #1#
                                       (QUOTIENT2 (LENGTH |l|) 2) . #2#)
                                      G190
                                      (COND
                                        ((QSGREATERP |i| #1#)
                                         (GO G191)))
                                      (SEQ
                                       (EXIT
                                        (LETT #0#
                                         (CONS
                                          (LIST
                                           (SPADCALL |l| |i|
                                            (QREFELT $ 26))
                                           (SPADCALL |l|
                                            (+ (- (LENGTH |l|) |i|) 1)
                                            (QREFELT $ 26)))
                                          #0#) . #2#)))
                                      (LETT |i| (QSADD1 |i|) . #2#)
                                      (GO G190) G191
                                      (EXIT (NREVERSE0 #0#)))) . #2#)
                         (EXIT (|PGE;llli2gp| (LIST (LIST |l|) |tmp|)
                                   $)))))))))) 

(DEFUN |PGE;dihedralGroup;PiPg;26| (|n| $)
  (COND
    ((EQL |n| 1) (SPADCALL 2 (QREFELT $ 47)))
    ((EQL |n| 2)
     (|PGE;llli2gp| (LIST (LIST (LIST 1 2)) (LIST (LIST 3 4))) $))
    ('T (SPADCALL (|PGE;li1n| |n| $) (QREFELT $ 50))))) 

(DEFUN |PermutationGroupExamples| ()
  (PROG ()
    (RETURN
      (PROG (#0=#:G1907)
        (RETURN
          (COND
            ((LETT #0#
                   (HGET |$ConstructorCache|
                         '|PermutationGroupExamples|)
                   . #1=(|PermutationGroupExamples|))
             (|CDRwithIncrement| (CDAR #0#)))
            ('T
             (UNWIND-PROTECT
               (PROG1 (CDDAR (HPUT |$ConstructorCache|
                                   '|PermutationGroupExamples|
                                   (LIST
                                    (CONS NIL
                                     (CONS 1
                                      (|PermutationGroupExamples;|))))))
                 (LETT #0# T . #1#))
               (COND
                 ((NOT #0#)
                  (HREM |$ConstructorCache|
                        '|PermutationGroupExamples|))))))))))) 

(DEFUN |PermutationGroupExamples;| ()
  (PROG (|dv$| $ |pv$|)
    (RETURN
      (PROGN
        (LETT |dv$| '(|PermutationGroupExamples|)
              . #0=(|PermutationGroupExamples|))
        (LETT $ (GETREFV 52) . #0#)
        (QSETREFV $ 0 |dv$|)
        (QSETREFV $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#))
        (|haddProp| |$ConstructorCache| '|PermutationGroupExamples| NIL
            (CONS 1 $))
        (|stuffDomainSlots| $)
        $)))) 

(MAKEPROP '|PermutationGroupExamples| '|infovec|
    (LIST '#(NIL NIL NIL NIL NIL NIL (|List| 17) (|Permutation| 25)
             (0 . |cycles|) (|List| 7) (|Mapping| 7 6) (|List| 6)
             (|ListFunctions2| 6 7) (5 . |map|) (|PermutationGroup| 25)
             (11 . |coerce|) (16 . |One|) (|List| 25) (20 . |list|)
             |PGE;youngGroup;LPg;3| (|Partition|) (25 . |convert|)
             |PGE;youngGroup;PPg;4| |PGE;rubiksGroup;Pg;5|
             (30 . |removeDuplicates|) (|Integer|) (35 . |elt|)
             |PGE;mathieu11;LPg;6| |PGE;mathieu11;Pg;7|
             |PGE;mathieu12;LPg;8| |PGE;mathieu12;Pg;9|
             |PGE;mathieu22;LPg;10| |PGE;mathieu22;Pg;11|
             |PGE;mathieu23;LPg;12| |PGE;mathieu23;Pg;13|
             |PGE;mathieu24;LPg;14| |PGE;mathieu24;Pg;15|
             |PGE;janko2;LPg;16| |PGE;janko2;Pg;17| (|List| 44)
             |PGE;abelianGroup;LPg;18| (41 . |elt|) (47 . |setelt|)
             |PGE;alternatingGroup;LPg;19| (|PositiveInteger|)
             |PGE;alternatingGroup;PiPg;20| |PGE;symmetricGroup;LPg;21|
             |PGE;symmetricGroup;PiPg;22| |PGE;cyclicGroup;LPg;23|
             |PGE;cyclicGroup;PiPg;24| |PGE;dihedralGroup;LPg;25|
             |PGE;dihedralGroup;PiPg;26|)
          '#(|youngGroup| 54 |symmetricGroup| 64 |rubiksGroup| 74
             |mathieu24| 78 |mathieu23| 87 |mathieu22| 96 |mathieu12|
             105 |mathieu11| 114 |janko2| 123 |dihedralGroup| 132
             |cyclicGroup| 142 |alternatingGroup| 152 |abelianGroup|
             162)
          'NIL
          (CONS (|makeByteWordVec2| 1 'NIL)
                (CONS '#()
                      (CONS '#()
                            (|makeByteWordVec2| 51
                                '(1 7 0 6 8 2 12 9 10 11 13 1 14 0 9 15
                                  0 7 0 16 1 6 0 17 18 1 20 17 0 21 1
                                  17 0 0 24 2 17 25 0 25 26 2 11 6 0 25
                                  41 3 11 6 0 25 6 42 1 0 14 20 22 1 0
                                  14 17 19 1 0 14 44 47 1 0 14 17 46 0
                                  0 14 23 1 0 14 17 35 0 0 14 36 1 0 14
                                  17 33 0 0 14 34 0 0 14 32 1 0 14 17
                                  31 1 0 14 17 29 0 0 14 30 1 0 14 17
                                  27 0 0 14 28 0 0 14 38 1 0 14 17 37 1
                                  0 14 17 50 1 0 14 44 51 1 0 14 44 49
                                  1 0 14 17 48 1 0 14 44 45 1 0 14 17
                                  43 1 0 14 39 40)))))
          '|lookupComplete|)) 

(MAKEPROP '|PermutationGroupExamples| 'NILADIC T) 
