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 604800 <= |T| < 100000000
GROUP HJ = J(2) = F(5-) order 604800 degree 100 involutions 2835 classes3 
2 pairs 581 C-role 4 C+F 1 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 612468 L(2,107) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 647460 L(2,109) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 721392 L(2,113) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 885720 L(2,121) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 976500 L(2,125) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP B(2,4) = O(5,4) ~ C(2,4) = S(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
SKIP 1024128 L(2,127) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 1123980 L(2,131) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 1285608 L(2,137) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 1342740 L(2,139) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP B(3,2) = O(7,2) ~ C(3,2) = S(6,2) order 1451520 degree 63 involutions 
5103 classes3 3 pairs 302 C-role 8 C+F 7 C+D (hom of J) 0 all four (hom of K) 
0 time 0 s
SKIP 1653900 L(2,149) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 1721400 L(2,151) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(10) order 1814400 degree 10 involutions 5355 classes3 3 pairs 
743 C-role 10 C+F 7 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
GROUP A(2,7) = L(3,7)  order 1876896 degree 57 involutions 2793 classes3 
1 pairs 1472 C-role 18 C+F 3 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 1934868 L(2,157) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 2097024 L(2,128) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 2165292 L(2,163) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 2328648 L(2,167) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 2413320 L(2,169) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 2588772 L(2,173) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 2867580 L(2,179) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 2964780 L(2,181) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP 2A(3,3) = U(4,3) ~ 2D(3,3) = O-(6,3) order 3265920 degree 
280 involutions 2835 classes3 4 pairs 1018 C-role 50 C+F 48 C+D (hom of J) 
0 all four (hom of K) 0 time 0 s
SKIP 3483840 L(2,191) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 3594432 L(2,193) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 3822588 L(2,197) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 3940200 L(2,199) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP G(2,3) order 4245696 degree 351 involutions 7371 classes3 5 pairs 
1460 C-role 5 C+F 2 C+D (hom of J) 0 all four (hom of K) 0 time 1 s
GROUP B(2,5) = O(5,5) ~ C(2,5) = S(4,5) order 4680000 degree 156 involutions 
10075 classes3 2 pairs 234 C-role 6 C+F 6 C+D (hom of J) 
0 all four (hom of K) 0 time 1 s
SKIP 4696860 L(2,211) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP 2A(2,8) = U(3,8) order 5515776 degree 513 involutions 3591 classes3 
3 pairs 1136 C-role 0 C+F 0 C+D (hom of J) 0 all four (hom of K) 0 time 3 s
SKIP 5544672 L(2,223) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP 2A(2,7) = U(3,7) order 5663616 degree 344 involutions 2107 classes3 
1 pairs 2468 C-role 8 C+F 1 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 5848428 L(2,227) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 6004380 L(2,229) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(3,3) = L(4,3) ~ D(3,3) = O+(6,3)  order 6065280 degree 40 involutions 
7371 classes3 4 pairs 1618 C-role 6 C+F 4 C+D (hom of J) 
0 all four (hom of K) 0 time 0 s
SKIP 6324552 L(2,233) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 6825840 L(2,239) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 6998640 L(2,241) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 7174332 L(2,243) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 7906500 L(2,251) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 8487168 L(2,257) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 9095592 L(2,263) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 9732420 L(2,269) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 9951120 L(2,271) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(4,2) = L(5,2)  order 9999360 degree 31 involutions 6975 classes3 
2 pairs 700 C-role 14 C+F 12 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
GROUP M(23) order 10200960 degree 23 involutions 3795 classes3 1 pairs 
356 C-role 16 C+F 14 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 10626828 L(2,277) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 11093880 L(2,281) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 11332452 L(2,283) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 12068640 L(2,289) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 12576732 L(2,293) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP 2A(4,2) = U(5,2) order 13685760 degree 165 involutions 3135 classes3 
6 pairs 782 C-role 2 C+F 2 C+D (hom of J) 0 all four (hom of K) 0 time 1 s
SKIP 14467068 L(2,307) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 15039960 L(2,311) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 15331992 L(2,313) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 15927348 L(2,317) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(2,8) = L(3,8)  order 16482816 degree 73 involutions 4599 classes3 
1 pairs 4160 C-role 16 C+F 2 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 16776960 L(2,256) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP 2F(4,2)' = Ree(2)' = Tits order 17971200 degree 1600 involutions 
13455 classes3 1 pairs 1564 C-role 8 C+F 6 C+D (hom of J) 
0 all four (hom of K) 0 time 2 s
SKIP 18132180 L(2,331) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 19136208 L(2,337) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(11) order 19958400 degree 11 involutions 18315 classes3 3 pairs 
1331 C-role 10 C+F 7 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
SKIP 20176632 L(2,343) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 20890788 L(2,347) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 21254100 L(2,349) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 21993312 L(2,353) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 23133960 L(2,359) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 23522760 L(2,361) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 24715248 L(2,367) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 25947372 L(2,373) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 27219780 L(2,379) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 28090752 L(2,383) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 29431740 L(2,389) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 31285188 L(2,397) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 32240400 L(2,401) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 32537600 2B(2,32) = 2C(2,32) = Sz(32) : 3 does not divide |T|
SKIP 34208760 L(2,409) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 36779820 L(2,419) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 37309020 L(2,421) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 40031280 L(2,431) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 40591152 L(2,433) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 42302040 L(2,439) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(2,9) = L(3,9)  order 42456960 degree 91 involutions 7371 classes3 
2 pairs 6836 C-role 8 C+F 4 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
GROUP 2A(2,9) = U(3,9) order 42573600 degree 730 involutions 5913 classes3 
2 pairs 6800 C-role 10 C+F 2 C+D (hom of J) 0 all four (hom of K) 0 time 1 s
SKIP 43468932 L(2,443) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP HS order 44352000 degree 100 involutions 21175 classes3 1 pairs 
399 C-role 13 C+F 12 C+D (hom of J) 0 all four (hom of K) 0 time 4 s
SKIP 45259200 L(2,449) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 47721768 L(2,457) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 48985860 L(2,461) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 49626192 L(2,463) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP J(3) order 50232960 degree 6156 involutions 26163 classes3 2 pairs 
1346 C-role 8 C+F 6 C+D (hom of J) 0 all four (hom of K) 0 time 54 s
SKIP 50923548 L(2,467) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 54950880 L(2,479) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 57750408 L(2,487) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 59185140 L(2,491) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 62125500 L(2,499) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 63631512 L(2,503) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 65935860 L(2,509) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 70710120 L(2,521) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP 2A(2,11) = U(3,11) order 70915680 degree 1332 involutions 
13431 classes3 1 pairs 3494 C-role 36 C+F 12 C+D (hom of J) 
0 all four (hom of K) 0 time 622 s
SKIP 71527572 L(2,523) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 74017680 L(2,529) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 79169940 L(2,541) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 81833388 L(2,547) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 86404068 L(2,557) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 89226492 L(2,563) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 92109720 L(2,569) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 93084420 L(2,571) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 96049728 L(2,577) : PSL(2,q), Jambor 2015 Prop. 12.2
SUMMARY searched 22 groups; with a homomorphism of J: [  ]; of K: [  ]
