q=8: theta ok True; U(a,b)U(c,d)=U(a+c,b+d+a th(c)) on 4096 quadruples, failures 0; M(c)U(a,b)M(c)^-1=U(a/c,b/(c th(c))) on 448 triples, failures 0; T^2=1, TM(c)T=M(1/c), M(c)M(1/c)=1: failures 0; form J=T preserved by all U(a,b), M(c), T: failures 0; condition (5) for all 63 pairs (a,b)!=(0,0): failures 0; => |G_q| = q^2(q-1)(q^2+1) = 29120
Sz(8): closure of <U(1,0), U(0,1), M(2), T> under right multiplication: 29120 elements; contains all U(a,b): True, all M(c): True; element orders {1: 1, 2: 455, 4: 3640, 5: 5824, 7: 12480, 13: 6720} (Sz(8): 1:1, 2:455, 4:3640, 5:5824, 7:12480, 13:6720)
q=32: theta ok True; U(a,b)U(c,d)=U(a+c,b+d+a th(c)) on 131072 quadruples, failures 0; M(c)U(a,b)M(c)^-1=U(a/c,b/(c th(c))) on 31744 triples, failures 0; T^2=1, TM(c)T=M(1/c), M(c)M(1/c)=1: failures 0; form J=T preserved by all U(a,b), M(c), T: failures 0; condition (5) for all 1023 pairs (a,b)!=(0,0): failures 0; => |G_q| = q^2(q-1)(q^2+1) = 32537600
q=128: theta ok True; U(a,b)U(c,d)=U(a+c,b+d+a th(c)) on 20000 quadruples, failures 0; M(c)U(a,b)M(c)^-1=U(a/c,b/(c th(c))) on 20000 triples, failures 0; T^2=1, TM(c)T=M(1/c), M(c)M(1/c)=1: failures 0; form J=T preserved by all U(a,b), M(c), T: failures 0; condition (5) for all 16383 pairs (a,b)!=(0,0): failures 0; => |G_q| = q^2(q-1)(q^2+1) = 34093383680
STRUCTURE failures: 0   (2s)
