CONTROLS
GROUP A6 order 360 degree 6 involutions 45 classes3 2 pairs 32 C-role 4 C+F 
4 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
GROUP PSL(2,7) order 168 degree 7 involutions 21 classes3 1 pairs 20 C-role 
4 C+F 2 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
GROUP PSU(3,5) order 126000 degree 50 involutions 525 classes3 1 pairs 
118 C-role 14 C+F 12 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
GROUP PSp(4,4) order 979200 degree 85 involutions 4335 classes3 2 pairs 
224 C-role 2 C+F 2 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SIMPLE GROUPS 60 <= |T| < 604800
GROUP A(5) ~ A(1,4) = L(2,4) ~ B(1,4) = O(3,4) ~ C(1,4) = S(2,4) ~ 2A(1,4) = U\
(2,4) ~ A(1,5) = L(2,5) ~ B(1,5) = O(3,5) ~ C(1,5) = S(2,5) ~ 2A(1,5) = U(2,5)\
 order 60 degree 5 involutions 15 classes3 1 pairs 8 C-role 0 C+F 
0 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 168 L(2,7) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(6) ~ A(1,9) = L(2,9) ~ B(1,9) = O(3,9) ~ C(1,9) = S(2,9) ~ 2A(1,9) = U\
(2,9) order 360 degree 6 involutions 45 classes3 2 pairs 32 C-role 4 C+F 
4 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 504 L(2,8) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 660 L(2,11) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 1092 L(2,13) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 2448 L(2,17) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(7) order 2520 degree 7 involutions 105 classes3 2 pairs 75 C-role 
10 C+F 8 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 3420 L(2,19) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 4080 L(2,16) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(2,3) = L(3,3)  order 5616 degree 13 involutions 117 classes3 2 pairs 
116 C-role 2 C+F 0 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
GROUP 2A(2,3) = U(3,3) order 6048 degree 28 involutions 63 classes3 2 pairs 
104 C-role 4 C+F 2 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 6072 L(2,23) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 7800 L(2,25) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP M(11) order 7920 degree 11 involutions 165 classes3 1 pairs 30 C-role 
2 C+F 2 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 9828 L(2,27) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 12180 L(2,29) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 14880 L(2,31) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(8) ~ A(3,2) = L(4,2) ~ D(3,2) = O+(6,2) order 20160 degree 
8 involutions 315 classes3 2 pairs 108 C-role 10 C+F 8 C+D (hom of J) 
0 all four (hom of K) 0 time 0 s
GROUP A(2,4) = L(3,4) order 20160 degree 21 involutions 315 classes3 1 pairs 
256 C-role 20 C+F 18 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 25308 L(2,37) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP B(2,3) = O(5,3) ~ C(2,3) = S(4,3) ~ 2A(3,2) = U(4,2) ~ 2D(3,2) = O-(6,2)\
 order 25920 degree 40 involutions 315 classes3 4 pairs 114 C-role 2 C+F 
2 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 29120 2B(2,8) = 2C(2,8) = Sz(8) : 3 does not divide |T|
SKIP 32736 L(2,32) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 34440 L(2,41) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 39732 L(2,43) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 51888 L(2,47) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 58800 L(2,49) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP 2A(2,4) = U(3,4) order 62400 degree 65 involutions 195 classes3 1 pairs 
284 C-role 0 C+F 0 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 74412 L(2,53) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP M(12) order 95040 degree 12 involutions 891 classes3 2 pairs 243 C-role 
2 C+F 2 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 102660 L(2,59) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 113460 L(2,61) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP 2A(2,5) = U(3,5) order 126000 degree 126 involutions 525 classes3 
1 pairs 118 C-role 14 C+F 12 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 150348 L(2,67) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP J(1) order 175560 degree 266 involutions 1463 classes3 1 pairs 
200 C-role 0 C+F 0 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 178920 L(2,71) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(9) order 181440 degree 9 involutions 1323 classes3 3 pairs 284 C-role 
7 C+F 6 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 194472 L(2,73) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 246480 L(2,79) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 262080 L(2,64) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 265680 L(2,81) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 285852 L(2,83) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 352440 L(2,89) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(2,5) = L(3,5)  order 372000 degree 31 involutions 775 classes3 
1 pairs 650 C-role 4 C+F 0 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
GROUP M(22) order 443520 degree 22 involutions 1155 classes3 1 pairs 
364 C-role 24 C+F 22 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 456288 L(2,97) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 515100 L(2,101) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 546312 L(2,103) : PSL(2,q), Jambor 2015 Prop. 12.2
SUMMARY searched 16 groups; with a homomorphism of J: [  ]; of K: [  ]
