n | even classes | homomorphisms (blocks) | = formula | transitive (blocks) | = recursion | transitive blocks | by criterion | by a walk | exceptional blocks | unresolved | exceptional homomorphisms | longest walk
2 | 1 (all) | 16 | True | 15 | True | 3 | 3 | 0 | 0 | 0 | 0 | 0
3 | 2 (all) | 486 | True | 440 | True | 10 | 9 | 1 | 0 | 0 | 0 | 23
4 | 3 (all) | 34176 | True | 31650 | True | 115 | 109 | 6 | 0 | 0 | 0 | 84
5 | 4 (all) | 3858240 | True | 3626064 | True | 516 | 500 | 16 | 0 | 0 | 0 | 151
6 | 6 (all) | 824354640 | True | 792600480 | True | 8471 | 8351 | 120 | 0 | 0 | 0 | 375
7 | 8 (all) | 268020990720 | True | 260690336640 | True | 57335 | 57139 | 196 | 0 | 0 | 0 | 704
8 | 12 (all) | 135486004792320 | True | 132905092496400 | True | 1108649 | 1105936 | 2713 | 0 | 0 | 0 | 891
9 | 16 (all) | 97519295217254400 | True | 96124376168956800 | True | 12119792 | 12111373 | 8405 | 14 | 0 | 522547200 | 1461
10 | 22 (all) | 97018295368129632000 | True | 95938557393889324800 | True | 244527705 | 244481861 | 45844 | 0 | 0 | 0 | 2545
exceptional blocks for n=9: 14 ; group orders: ['72'] ; orbit sizes under the moves: ['311040']
   exceptional homomorphisms for n=9: 522547200 = 1440 * 9! : True
ALL CHECKS PASSED
Consequences: for 2 <= n <= 8 and n = 10 every transitive homomorphism is related by the moves to a failing tuple;
for n = 9 the same holds outside the exceptional blocks.
