 γ  T1                                T2                                |S1∩S2|  S3-closed?  #S3-orbits      orbit sizes
------------------------------------------------------------------------------------------------------------------------
 3  (3, —, SR)                        (3, —, SR)                             27         yes           5  [3, 6, 6, 6, 6]
 3  (3, —, SR)                        (4, [(0, 2)], SP)                      24         yes           4     [6, 6, 6, 6]
 3  (3, —, SP)                        (3, —, SP)                              6         yes           1              [6]
 3  (3, —, SP)                        (4, [(0, 2)], SP)                       6         yes           1              [6]
 4  (4, —, SR)                        (4, —, SR)                             81         yes          14  [3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]
 4  (4, [(0, 2)], SP)                 (4, [(0, 2)], SP)                      36         yes           6  [6, 6, 6, 6, 6, 6]
 4  (4, [(0, 2)], SP)                 (4, —, SR)                             36         yes           6  [6, 6, 6, 6, 6, 6]
 4  (4, —, SR)                        (4, [(0, 2)], SP)                      54         yes           9  [6, 6, 6, 6, 6, 6, 6, 6, 6]
 4  (3, [(0, 2)], SP)                 (4, [(0, 2)], SP)                      36         yes           6  [6, 6, 6, 6, 6, 6]
 4  (4, [(0, 2)], SP)                 (5, [(0, 2)], SP)                      12         yes           2           [6, 6]
 4  (4, [(0, 2)], SP)                 (6, [(0, 3)], SP)                       6         yes           1              [6]
 4  (4, [(0, 2)], SP)                 (6, [(0, 2), (3, 5)], SP)              36         yes           6  [6, 6, 6, 6, 6, 6]
 5  (5, [(0, 2)], SP)                 (3, —, SR)                             18         yes           3        [6, 6, 6]
 5  (5, [(0, 2)], SP)                 (5, [(0, 2)], SP)                      36         yes           6  [6, 6, 6, 6, 6, 6]
 5  (5, [(0, 2)], SP)                 (5, [(0, 3)], SP)                      36         yes           6  [6, 6, 6, 6, 6, 6]
 5  (5, [(0, 3)], SP)                 (5, [(0, 3)], SP)                      36         yes           6  [6, 6, 6, 6, 6, 6]
 5  (5, [(0, 2)], SR)                 (5, [(0, 2)], SP)                      90         yes          15  [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]
 6  (6, [(0, 3)], SP)                 (6, [(0, 3)], SP)                      36         yes           6  [6, 6, 6, 6, 6, 6]
 6  (6, [(0, 3)], SP)                 (6, [(0, 2), (3, 5)], SP)              36         yes           6  [6, 6, 6, 6, 6, 6]
 6  (6, [(0, 2), (3, 5)], SP)         (6, [(0, 2), (3, 5)], SP)             216         yes          36  [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]
 6  (6, [(0, 3)], SP)                 (3, —, SR)                              6         yes           1              [6]
 6  (6, [(0, 2), (3, 5)], SP)         (3, —, SR)                            108         yes          18  [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]
 6  (6, [(0, 2), (3, 5)], SP)         (4, [(0, 2)], SP)                     108         yes          18  [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]
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=== Combined (S_3 + cyclic) orbit canonical representatives ===
    Showing canonical rep, orbit size, and which (T_1, T_2) pairs contain it.

  rep (1, 2, 1, 3)  |orbit| = 12  appears in 7 pair(s):
      γ=4  T_1=(4, —, SR)  T_2=(4, —, SR)
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(4, [(0, 2)], SP)
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(4, —, SR)
      γ=4  T_1=(4, —, SR)  T_2=(4, [(0, 2)], SP)
      γ=4  T_1=(3, [(0, 2)], SP)  T_2=(4, [(0, 2)], SP)
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(5, [(0, 2)], SP)
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
  rep (1, 2, 1, 2)  |orbit| = 6  appears in 6 pair(s):
      γ=4  T_1=(4, —, SR)  T_2=(4, —, SR)
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(4, [(0, 2)], SP)
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(4, —, SR)
      γ=4  T_1=(4, —, SR)  T_2=(4, [(0, 2)], SP)
      γ=4  T_1=(3, [(0, 2)], SP)  T_2=(4, [(0, 2)], SP)
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
  rep (1, 2, 2, 1)  |orbit| = 12  appears in 5 pair(s):
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(4, [(0, 2)], SP)
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(4, —, SR)
      γ=4  T_1=(3, [(0, 2)], SP)  T_2=(4, [(0, 2)], SP)
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(6, [(0, 3)], SP)
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
  rep (1, 2, 2, 3)  |orbit| = 24  appears in 5 pair(s):
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(4, [(0, 2)], SP)
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(4, —, SR)
      γ=4  T_1=(3, [(0, 2)], SP)  T_2=(4, [(0, 2)], SP)
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(5, [(0, 2)], SP)
      γ=4  T_1=(4, [(0, 2)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
  rep (1, 2, 3)  |orbit| = 6  appears in 4 pair(s):
      γ=3  T_1=(3, —, SR)  T_2=(3, —, SR)
      γ=3  T_1=(3, —, SR)  T_2=(4, [(0, 2)], SP)
      γ=3  T_1=(3, —, SP)  T_2=(3, —, SP)
      γ=3  T_1=(3, —, SP)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 1, 1, 3, 2)  |orbit| = 36  appears in 3 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(3, —, SR)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 1, 1, 3, 3)  |orbit| = 36  appears in 3 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(3, —, SR)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 1, 2, 1, 2)  |orbit| = 6  appears in 3 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(3, —, SR)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 1, 2, 3)  |orbit| = 30  appears in 3 pair(s):
      γ=5  T_1=(5, [(0, 2)], SP)  T_2=(5, [(0, 2)], SP)
      γ=5  T_1=(5, [(0, 2)], SP)  T_2=(5, [(0, 3)], SP)
      γ=5  T_1=(5, [(0, 2)], SR)  T_2=(5, [(0, 2)], SP)
  rep (1, 2, 2, 1, 3)  |orbit| = 30  appears in 3 pair(s):
      γ=5  T_1=(5, [(0, 2)], SP)  T_2=(3, —, SR)
      γ=5  T_1=(5, [(0, 2)], SP)  T_2=(5, [(0, 2)], SP)
      γ=5  T_1=(5, [(0, 2)], SP)  T_2=(5, [(0, 3)], SP)
  rep (1, 2, 2, 2, 3, 1)  |orbit| = 36  appears in 3 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(3, —, SR)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 2, 2, 3, 3)  |orbit| = 36  appears in 3 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(3, —, SR)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 3, 1, 3, 2)  |orbit| = 18  appears in 3 pair(s):
      γ=6  T_1=(6, [(0, 3)], SP)  T_2=(6, [(0, 3)], SP)
      γ=6  T_1=(6, [(0, 3)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 3, 2, 3, 1)  |orbit| = 36  appears in 3 pair(s):
      γ=6  T_1=(6, [(0, 3)], SP)  T_2=(6, [(0, 3)], SP)
      γ=6  T_1=(6, [(0, 3)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
      γ=6  T_1=(6, [(0, 3)], SP)  T_2=(3, —, SR)
  rep (1, 1, 2)  |orbit| = 18  appears in 2 pair(s):
      γ=3  T_1=(3, —, SR)  T_2=(3, —, SR)
      γ=3  T_1=(3, —, SR)  T_2=(4, [(0, 2)], SP)
  rep (1, 1, 2, 2)  |orbit| = 12  appears in 2 pair(s):
      γ=4  T_1=(4, —, SR)  T_2=(4, —, SR)
      γ=4  T_1=(4, —, SR)  T_2=(4, [(0, 2)], SP)
  rep (1, 1, 2, 3)  |orbit| = 24  appears in 2 pair(s):
      γ=4  T_1=(4, —, SR)  T_2=(4, —, SR)
      γ=4  T_1=(4, —, SR)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 1, 1, 2, 2)  |orbit| = 36  appears in 2 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(3, —, SR)
  rep (1, 2, 1, 2, 1, 3)  |orbit| = 36  appears in 2 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(3, —, SR)
  rep (1, 2, 1, 2, 3, 3)  |orbit| = 36  appears in 2 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 1, 3, 2, 2)  |orbit| = 36  appears in 2 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(3, —, SR)
  rep (1, 2, 2, 1, 2, 3)  |orbit| = 36  appears in 2 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 2, 1, 3, 3)  |orbit| = 18  appears in 2 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 2, 3, 1)  |orbit| = 30  appears in 2 pair(s):
      γ=5  T_1=(5, [(0, 2)], SP)  T_2=(5, [(0, 2)], SP)
      γ=5  T_1=(5, [(0, 2)], SP)  T_2=(5, [(0, 3)], SP)
  rep (1, 2, 2, 3, 2, 1)  |orbit| = 36  appears in 2 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 3, 1, 2, 3)  |orbit| = 6  appears in 2 pair(s):
      γ=6  T_1=(6, [(0, 3)], SP)  T_2=(6, [(0, 3)], SP)
      γ=6  T_1=(6, [(0, 3)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
  rep (1, 2, 3, 3, 2, 1)  |orbit| = 18  appears in 2 pair(s):
      γ=6  T_1=(6, [(0, 3)], SP)  T_2=(6, [(0, 3)], SP)
      γ=6  T_1=(6, [(0, 3)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
  rep (1, 1, 1)  |orbit| = 3  appears in 1 pair(s):
      γ=3  T_1=(3, —, SR)  T_2=(3, —, SR)
  rep (1, 1, 1, 1)  |orbit| = 3  appears in 1 pair(s):
      γ=4  T_1=(4, —, SR)  T_2=(4, —, SR)
  rep (1, 1, 1, 2)  |orbit| = 24  appears in 1 pair(s):
      γ=4  T_1=(4, —, SR)  T_2=(4, —, SR)
  rep (1, 1, 2, 2, 3)  |orbit| = 30  appears in 1 pair(s):
      γ=5  T_1=(5, [(0, 2)], SR)  T_2=(5, [(0, 2)], SP)
  rep (1, 1, 2, 3, 2)  |orbit| = 30  appears in 1 pair(s):
      γ=5  T_1=(5, [(0, 2)], SR)  T_2=(5, [(0, 2)], SP)
  rep (1, 2, 1, 1, 2, 3)  |orbit| = 36  appears in 1 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
  rep (1, 2, 1, 2, 3, 2)  |orbit| = 36  appears in 1 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 1, 3, 2)  |orbit| = 30  appears in 1 pair(s):
      γ=5  T_1=(5, [(0, 2)], SP)  T_2=(3, —, SR)
  rep (1, 2, 1, 3, 2, 3)  |orbit| = 18  appears in 1 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
  rep (1, 2, 2, 1, 2, 1)  |orbit| = 36  appears in 1 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 2, 2, 1, 1)  |orbit| = 18  appears in 1 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
  rep (1, 2, 2, 2, 1, 3)  |orbit| = 36  appears in 1 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(6, [(0, 2), (3, 5)], SP)
  rep (1, 2, 2, 3, 1, 3)  |orbit| = 36  appears in 1 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(3, —, SR)
  rep (1, 2, 2, 3, 2, 3)  |orbit| = 36  appears in 1 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(4, [(0, 2)], SP)
  rep (1, 2, 3, 1, 2)  |orbit| = 30  appears in 1 pair(s):
      γ=5  T_1=(5, [(0, 3)], SP)  T_2=(5, [(0, 3)], SP)
  rep (1, 2, 3, 2, 1)  |orbit| = 30  appears in 1 pair(s):
      γ=5  T_1=(5, [(0, 3)], SP)  T_2=(5, [(0, 3)], SP)
  rep (1, 2, 3, 3, 1)  |orbit| = 30  appears in 1 pair(s):
      γ=5  T_1=(5, [(0, 3)], SP)  T_2=(5, [(0, 3)], SP)
  rep (1, 2, 3, 3, 2, 2)  |orbit| = 36  appears in 1 pair(s):
      γ=6  T_1=(6, [(0, 2), (3, 5)], SP)  T_2=(3, —, SR)

=== Rainbow pattern check ===
Found 1 canonical reps matching (a,b,c,b,c,a) pattern:
  (1, 2, 3, 2, 3, 1)  appears in 3 pair(s)
