A5: GROUP degree=5 order=60 classes=5
   homomorphisms 286140 (sum over classes: True); transitive 256464; transitive blocks 122: by criterion 114, by a walk 8 (longest 146), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
A6: GROUP degree=6 order=360 classes=7
   homomorphisms 52889040 (sum over classes: True); transitive 50698080; transitive blocks 1680: by criterion 1680, by a walk 0 (longest 0), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
A7: GROUP degree=7 order=2520 classes=9
   homomorphisms 17051368320 (sum over classes: True); transitive 16579146240; transitive blocks 11583: by criterion 11455, by a walk 128 (longest 501), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
M11: GROUP degree=11 order=7920 classes=10
   homomorphisms 520349971680 (sum over classes: True); transitive 511027246080; transitive blocks 22145: by criterion 22113, by a walk 32 (longest 733), exceptional 0, unresolved 0
   transitive homomorphisms with image of order 11: 2108160; classes of transitive homomorphisms modulo conjugation: 64526304 (remainders 0, 0)
   = 64,526,304 as found by orb.c of the package, and 520,349,971,680 = 7920 * 65,700,754 homomorphisms: True
   every transitive homomorphism to this group is related by the moves to a failing tuple
PSL2_11: GROUP degree=12 order=660 classes=8
   homomorphisms 322614600 (sum over classes: True); transitive 312272400; transitive blocks 1792: by criterion 1774, by a walk 18 (longest 4096), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
PSL2_13: GROUP degree=14 order=1092 classes=9
   homomorphisms 1403441676 (sum over classes: True); transitive 1361767680; transitive blocks 2340: by criterion 2340, by a walk 0 (longest 0), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
PSL2_16: GROUP degree=17 order=4080 classes=17
   homomorphisms 72242507760 (sum over classes: True); transitive 68699923200; transitive blocks 9752: by criterion 67, by a walk 9685 (longest 4687), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
PSL2_17: GROUP degree=18 order=2448 classes=11
   homomorphisms 15448182336 (sum over classes: True); transitive 15075175680; transitive blocks 6831: by criterion 150, by a walk 6681 (longest 1725), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
PSL2_19: GROUP degree=20 order=3420 classes=12
   homomorphisms 41994056880 (sum over classes: True); transitive 41086990800; transitive blocks 8161: by criterion 204, by a walk 7957 (longest 9777), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
PSL2_23: GROUP degree=24 order=6072 classes=14
   homomorphisms 232249221336 (sum over classes: True); transitive 227954295360; transitive blocks 18280: by criterion 234, by a walk 18046 (longest 20001), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
PSL2_25: GROUP degree=26 order=7800 classes=15
   homomorphisms 489380533200 (sum over classes: True); transitive 480454416000; transitive blocks 29657: by criterion 694, by a walk 28963 (longest 2295), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
PSL2_27: GROUP degree=28 order=9828 classes=16
   homomorphisms 977509214136 (sum over classes: True); transitive 961731519840; transitive blocks 26136: by criterion 135, by a walk 26001 (longest 20001), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
PSL2_7: GROUP degree=8 order=168 classes=6
   homomorphisms 6097896 (sum over classes: True); transitive 5775840; transitive blocks 505: by criterion 491, by a walk 14 (longest 940), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
PSL2_8: GROUP degree=9 order=504 classes=9
   homomorphisms 145217016 (sum over classes: True); transitive 133993440; transitive blocks 1003: by criterion 991, by a walk 12 (longest 256), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
PSL3_3: GROUP degree=13 order=5616 classes=12
   homomorphisms 183316775616 (sum over classes: True); transitive 177246645120; transitive blocks 16593: by criterion 16549, by a walk 44 (longest 1916), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
PSU3_3: GROUP degree=28 order=6048 classes=14
   homomorphisms 244848695616 (sum over classes: True); transitive 242135308800; transitive blocks 28042: by criterion 290, by a walk 27752 (longest 2052), exceptional 0, unresolved 0
   every transitive homomorphism to this group is related by the moves to a failing tuple
S4: GROUP degree=4 order=24 classes=5
   homomorphisms 34176 (sum over classes: True); transitive 31650; transitive blocks 115: by criterion 109, by a walk 6 (longest 46), exceptional 0, unresolved 0
   agreement with r2_blk.c for n=4 (homomorphisms, transitive, blocks, criterion, walk, exceptional): True
   every transitive homomorphism to this group is related by the moves to a failing tuple
S5: GROUP degree=5 order=120 classes=7
   homomorphisms 3858240 (sum over classes: True); transitive 3626064; transitive blocks 516: by criterion 500, by a walk 16 (longest 183), exceptional 0, unresolved 0
   agreement with r2_blk.c for n=5 (homomorphisms, transitive, blocks, criterion, walk, exceptional): True
   every transitive homomorphism to this group is related by the moves to a failing tuple
S6: GROUP degree=6 order=720 classes=11
   homomorphisms 824354640 (sum over classes: True); transitive 792600480; transitive blocks 8471: by criterion 8351, by a walk 120 (longest 314), exceptional 0, unresolved 0
   agreement with r2_blk.c for n=6 (homomorphisms, transitive, blocks, criterion, walk, exceptional): True
   every transitive homomorphism to this group is related by the moves to a failing tuple
S7: GROUP degree=7 order=5040 classes=15
   homomorphisms 268020990720 (sum over classes: True); transitive 260690336640; transitive blocks 57335: by criterion 57139, by a walk 196 (longest 482), exceptional 0, unresolved 0
   agreement with r2_blk.c for n=7 (homomorphisms, transitive, blocks, criterion, walk, exceptional): True
   every transitive homomorphism to this group is related by the moves to a failing tuple
ALL CHECKS PASSED
