SIMPLE GROUPS 10^8 <= |T| < 1000000000
SKIP 101130708 L(2,587) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 104263632 L(2,593) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 107460600 L(2,599) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 108540600 L(2,601) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 111823968 L(2,607) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 115172892 L(2,613) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 117442248 L(2,617) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 118588020 L(2,619) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 122070000 L(2,625) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 125619480 L(2,631) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 131687040 L(2,641) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 132923532 L(2,643) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 134217216 L(2,512) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 135419688 L(2,647) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP B(2,7) = O(5,7) ~ C(2,7) = S(4,7) order 138297600 degree 
400 involutions 52675 classes3 2 pairs 876 C-role 16 C+F 8 C+D (hom of J) 
0 all four (hom of K) 0 time 13 s
SKIP 139222212 L(2,653) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 143095260 L(2,659) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 144402060 L(2,661) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 152410272 L(2,673) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 155144028 L(2,677) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 159305652 L(2,683) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 164969340 L(2,691) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 172235700 L(2,701) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP D(4,2) = O+(8,2) order 174182400 degree 120 involutions 69615 classes3 
5 pairs 1326 C-role 20 C+F 19 C+D (hom of J) 0 all four (hom of K) 0 time 3 s
SKIP 178200060 L(2,709) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 185847120 L(2,719) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 192119928 L(2,727) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 193709880 L(2,729) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 196916052 L(2,733) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP 2D(4,2) = O-(8,2) order 197406720 degree 119 involutions 69615 classes3 
3 pairs 1632 C-role 10 C+F 7 C+D (hom of J) 0 all four (hom of K) 0 time 4 s
SKIP 201791340 L(2,739) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 205085832 L(2,743) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP 3D(4,2) order 211341312 degree 819 involutions 69615 classes3 2 pairs 
1170 C-role 2 C+F 1 C+D (hom of J) 0 all four (hom of K) 0 time 35 s
SKIP 211782000 L(2,751) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(2,11) = L(3,11)  order 212427600 degree 133 involutions 
16093 classes3 1 pairs 14762 C-role 10 C+F 2 C+D (hom of J) 
0 all four (hom of K) 0 time 1 s
SKIP 216898668 L(2,757) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 220355160 L(2,761) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 227377920 L(2,769) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 230944572 L(2,773) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(12) order 239500800 degree 12 involutions 63855 classes3 4 pairs 
3396 C-role 14 C+F 12 C+D (hom of J) 0 all four (hom of K) 0 time 1 s
SKIP 243721308 L(2,787) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP M(24) order 244823040 degree 24 involutions 43263 classes3 2 pairs 
2242 C-role 25 C+F 15 C+D (hom of J) 0 all four (hom of K) 0 time 0 s
GROUP G(2,4) order 251596800 degree 416 involutions 69615 classes3 2 pairs 
8618 C-role 12 C+F 3 C+D (hom of J) 0 all four (hom of K) 0 time 21 s
SKIP 253130388 L(2,797) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 264737160 L(2,809) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 266705460 L(2,811) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(2,13) = L(3,13)  order 270178272 degree 183 involutions 
30927 classes3 1 pairs 13108 C-role 36 C+F 0 C+D (hom of J) 
0 all four (hom of K) 0 time 39 s
SKIP 276693420 L(2,821) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 278720472 L(2,823) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 282804228 L(2,827) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 284860980 L(2,829) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 295294440 L(2,839) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 297411240 L(2,841) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 310324812 L(2,853) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 314710968 L(2,857) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 316919460 L(2,859) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 321367392 L(2,863) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 337262628 L(2,877) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 341898480 L(2,881) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 344232252 L(2,883) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 348931608 L(2,887) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 373070868 L(2,907) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 378028560 L(2,911) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 388075320 L(2,919) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 400882080 L(2,929) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 411328008 L(2,937) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 416618340 L(2,941) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 424638588 L(2,947) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 432761112 L(2,953) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 443751360 L(2,961) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 452115048 L(2,967) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 457748820 L(2,971) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 466286928 L(2,977) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 474930552 L(2,983) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 486620640 L(2,991) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 495512988 L(2,997) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 513621360 L(2,1009) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 519754092 L(2,1013) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 529044420 L(2,1019) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 532165620 L(2,1021) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 547955880 L(2,1031) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 551150952 L(2,1033) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 560810640 L(2,1039) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 577159800 L(2,1049) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 580467300 L(2,1051) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 597194460 L(2,1061) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 600577992 L(2,1063) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 610805220 L(2,1069) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 642182208 L(2,1087) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 649297740 L(2,1091) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 652875132 L(2,1093) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 660069288 L(2,1097) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 670959312 L(2,1103) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 681968460 L(2,1109) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 696833748 L(2,1117) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 708123372 L(2,1123) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 719534280 L(2,1129) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 762422400 L(2,1151) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 766403712 L(2,1153) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 786518292 L(2,1163) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 802861020 L(2,1171) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP 2A(2,13) = U(3,13) order 811273008 degree 2198 involutions 
26533 classes3 1 pairs 28760 C-role 14 C+F 2 C+D (hom of J) 
0 all four (hom of K) 0 time 39 s
SKIP 823605780 L(2,1181) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 836222508 L(2,1187) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 848967432 L(2,1193) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 866161200 L(2,1201) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 892384692 L(2,1213) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP Mc order 898128000 degree 275 involutions 22275 classes3 2 pairs 
1186 C-role 28 C+F 26 C+D (hom of J) 0 all four (hom of K) 0 time 4 s
SKIP 901242048 L(2,1217) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 914637672 L(2,1223) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 928165380 L(2,1229) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 932704080 L(2,1231) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 946408908 L(2,1237) : PSL(2,q), Jambor 2015 Prop. 12.2
SKIP 974220000 L(2,1249) : PSL(2,q), Jambor 2015 Prop. 12.2
GROUP A(3,4) = L(4,4) ~ D(3,4) = O+(6,4)  order 987033600 degree 
85 involutions 69615 classes3 4 pairs 5154 C-role 22 C+F 8 C+D (hom of J) 
0 all four (hom of K) 0 time 7 s
SKIP 997807860 L(2,1259) : PSL(2,q), Jambor 2015 Prop. 12.2
SUMMARY searched 12 groups; with a homomorphism of J: [  ]; of K: [  ]
