p=11 al=1 be=3 : Q_8 closed with 8 matrices of determinant 1, non-abelian=1, elements of order 4: 6
elements of Q_8 other than +-1 with an eigenvalue in F_p: 0  (hypothesis (E) holds)
extension of order 10648: associativity, centrality of (0,s,1), inverses and the projection onto Gamma_p checked on 200000 random triples
|Gamma_p| = 968, conjugacy classes: 20
homomorphisms pi_1(S_2) -> Gamma_p: 4067504056
epimorphisms: 2550873600
epimorphisms with kappa = 0 (lift): 250905600 , of which J intransitive: 8015040
epimorphisms with kappa != 0 (do not lift): 2299968000 , of which J intransitive: 0
   kappa=1: 229996800 = 968 * 237600 (remainder 0) ; J intransitive: 0 = 968 * 0
   kappa=2: 229996800 = 968 * 237600 (remainder 0) ; J intransitive: 0 = 968 * 0
   kappa=3: 229996800 = 968 * 237600 (remainder 0) ; J intransitive: 0 = 968 * 0
   kappa=4: 229996800 = 968 * 237600 (remainder 0) ; J intransitive: 0 = 968 * 0
   kappa=5: 229996800 = 968 * 237600 (remainder 0) ; J intransitive: 0 = 968 * 0
   kappa=6: 229996800 = 968 * 237600 (remainder 0) ; J intransitive: 0 = 968 * 0
   kappa=7: 229996800 = 968 * 237600 (remainder 0) ; J intransitive: 0 = 968 * 0
   kappa=8: 229996800 = 968 * 237600 (remainder 0) ; J intransitive: 0 = 968 * 0
   kappa=9: 229996800 = 968 * 237600 (remainder 0) ; J intransitive: 0 = 968 * 0
   kappa=10: 229996800 = 968 * 237600 (remainder 0) ; J intransitive: 0 = 968 * 0
non-surjective homomorphisms with kappa != 0: 1368800400
surjectivity test compared with a closure computation on 175103 tuples (random sample): 0 disagreements
J = <x,[x,u],v> compared with <x,uxu^-1,v,wvw^-1> on 175031 tuples (random sample): 0 disagreements
RESULT p=11: every epimorphism which does not lift has J transitive
