A7: degree 7, order 2520; elements of order 3: 350 (2 classes, sizes [70, 280]); involutions: 105 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 700; C-role solvable: 144; C and F: 126; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
  check of a hom of <A,B,C,F> against the literal relators: True
RESULT A7: homomorphisms J -> T with A != 1: NONE ; time 0.0 s
M11: degree 11, order 7920; elements of order 3: 440 (1 classes, sizes [440]); involutions: 165 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 440; C-role solvable: 36; C and F: 36; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
  check of a hom of <A,B,C,F> against the literal relators: True
RESULT M11: homomorphisms J -> T with A != 1: NONE ; time 0.0 s
L3_4: degree 21, order 20160; elements of order 3: 2240 (1 classes, sizes [2240]); involutions: 315 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 2240; C-role solvable: 180; C and F: 162; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
  check of a hom of <A,B,C,F> against the literal relators: True
RESULT L3_4: homomorphisms J -> T with A != 1: NONE ; time 0.1 s
U3_3: degree 28, order 6048; elements of order 3: 728 (2 classes, sizes [56, 672]); involutions: 63 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 1456; C-role solvable: 36; C and F: 18; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
  check of a hom of <A,B,C,F> against the literal relators: True
RESULT U3_3: homomorphisms J -> T with A != 1: NONE ; time 0.1 s
L3_3: degree 13, order 5616; elements of order 3: 728 (2 classes, sizes [624, 104]); involutions: 117 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 1456; C-role solvable: 18; C and F: 0; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
RESULT L3_3: homomorphisms J -> T with A != 1: NONE ; time 0.1 s
U4_2: degree 27, order 25920; elements of order 3: 800 (4 classes, sizes [40, 40, 480, 240]); involutions: 315 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 3200; C-role solvable: 162; C and F: 162; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
  check of a hom of <A,B,C,F> against the literal relators: True
RESULT U4_2: homomorphisms J -> T with A != 1: NONE ; time 0.1 s
A8: degree 8, order 20160; elements of order 3: 1232 (2 classes, sizes [112, 1120]); involutions: 315 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 2464; C-role solvable: 342; C and F: 306; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
  check of a hom of <A,B,C,F> against the literal relators: True
RESULT A8: homomorphisms J -> T with A != 1: NONE ; time 0.1 s
M12: degree 12, order 95040; elements of order 3: 4400 (2 classes, sizes [1760, 2640]); involutions: 891 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 8800; C-role solvable: 108; C and F: 108; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
  check of a hom of <A,B,C,F> against the literal relators: True
RESULT M12: homomorphisms J -> T with A != 1: NONE ; time 0.4 s
A9: degree 9, order 181440; elements of order 3: 5768 (3 classes, sizes [168, 3360, 2240]); involutions: 1323 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 17304; C-role solvable: 648; C and F: 594; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
  check of a hom of <A,B,C,F> against the literal relators: True
RESULT A9: homomorphisms J -> T with A != 1: NONE ; time 0.7 s
U3_4: degree 65, order 62400; elements of order 3: 4160 (1 classes, sizes [4160]); involutions: 195 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 4160; C-role solvable: 0; C and F: 0; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
RESULT U3_4: homomorphisms J -> T with A != 1: NONE ; time 0.2 s
L3_5: degree 31, order 372000; elements of order 3: 15500 (1 classes, sizes [15500]); involutions: 775 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 15500; C-role solvable: 96; C and F: 0; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
RESULT L3_5: homomorphisms J -> T with A != 1: NONE ; time 0.8 s
M22: degree 22, order 443520; elements of order 3: 12320 (1 classes, sizes [12320]); involutions: 1155 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 12320; C-role solvable: 864; C and F: 792; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
  check of a hom of <A,B,C,F> against the literal relators: True
RESULT M22: homomorphisms J -> T with A != 1: NONE ; time 0.8 s
J1: degree 266, order 175560; elements of order 3: 5852 (1 classes, sizes [5852]); involutions: 1463 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 5852; C-role solvable: 0; C and F: 0; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
RESULT J1: homomorphisms J -> T with A != 1: NONE ; time 0.7 s
U3_5: degree 50, order 126000; elements of order 3: 3500 (1 classes, sizes [3500]); involutions: 525 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 3500; C-role solvable: 504; C and F: 432; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
  check of a hom of <A,B,C,F> against the literal relators: True
RESULT U3_5: homomorphisms J -> T with A != 1: NONE ; time 0.2 s
S4_4: degree 85, order 979200; elements of order 3: 10880 (2 classes, sizes [5440, 5440]); involutions: 4335 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 21760; C-role solvable: 360; C and F: 360; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
  check of a hom of <A,B,C,F> against the literal relators: True
RESULT S4_4: homomorphisms J -> T with A != 1: NONE ; time 3.4 s
J2: degree 100, order 604800; elements of order 3: 17360 (2 classes, sizes [560, 16800]); involutions: 2835 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 34720; C-role solvable: 96; C and F: 36; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
  check of a hom of <A,B,C,F> against the literal relators: True
RESULT J2: homomorphisms J -> T with A != 1: NONE ; time 3.7 s
L3_7: degree 57, order 1876896; elements of order 3: 52136 (1 classes, sizes [52136]); involutions: 2793 (class sizes recomputed as conjugation orbits: all equal to the GAP class sizes)
pairs (a,b) tested: 52136; C-role solvable: 648; C and F: 108; C and D (= hom of J): 0; C and E: 0; all four (= hom of K): 0
  check of an L-hom (a,b,c) against the literal relators: True
  check of a hom of <A,B,C,F> against the literal relators: True
RESULT L3_7: homomorphisms J -> T with A != 1: NONE ; time 3.1 s
