Enriched Problems in LG(5)

Frank Sottile
··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 2,2 75071  0.7507  3.0028 
 1,1,1,1 24929  0.2493  0.9972 
This computed 100000 Frobenius elements
This took 19.41 Hours

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 2,2 75305  0.7530  3.0122 
 1,1,1,1 24695  0.2470  0.9878 
This computed 100000 Frobenius elements
This took 2.36 Days

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 2,2 74780  0.7478  2.9912 
 1,1,1,1 25220  0.2522  1.0088 
This computed 100000 Frobenius elements
This took 1.30 Days

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 2,2 75013  0.7501  3.0005 
 1,1,1,1 24987  0.2499  0.9995 
This computed 100000 Frobenius elements
This took 16.49 Hours

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 2,2 75302  0.7530  3.0121 
 1,1,1,1 24698  0.2470  0.9879 
This computed 100000 Frobenius elements
This took 16.00 Hours

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 1,1,1,1 24925  0.2492  0.9970 
 2,2 75075  0.7508  3.0030 
This computed 100000 Frobenius elements
This took 7.18 Hours

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 1,1,1,1 25066  0.2507  1.0026 
 2,2 74934  0.7493  2.9974 
This computed 100000 Frobenius elements
This took 1.97 Hours

····· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 2,2 37531  0.3753  3.0025 
 1,1,2 24875  0.2487  1.9900 
 4 25028  0.2503  2.0022 
 1,1,1,1 12566  0.1257  1.0053 
This computed 100000 Frobenius elements
This took 3.18 Days

···· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 2,2 37592  0.3759  3.0074 
 1,1,1,1 12435  0.1244  0.9948 
 1,1,2 24746  0.2475  1.9797 
 4 25227  0.2523  2.0182 
This computed 100000 Frobenius elements
This took 15.03 Hours

···· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 2,2 37517  0.3752  3.0014 
 1,1,2 24898  0.2490  1.9918 
 4 25168  0.2517  2.0134 
 1,1,1,1 12417  0.1242  0.9934 
This computed 100000 Frobenius elements
This took 2.51 Days

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 2,2 37406  0.3741  2.9925 
 1,1,1,1 12533  0.1253  1.0026 
 4 25074  0.2507  2.0059 
 1,1,2 24987  0.2499  1.9990 
This computed 100000 Frobenius elements
This took 2.80 Days

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25118  0.2512  2.0094 
 2,2 37560  0.3756  3.0048 
 1,1,2 25030  0.2503  2.0024 
 1,1,1,1 12292  0.1229  0.9834 
This computed 100000 Frobenius elements
This took 2.12 Days

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 24958  0.2496  1.9966 
 2,2 37547  0.3755  3.0038 
 1,1,2 24823  0.2482  1.9858 
 1,1,1,1 12672  0.1267  1.0138 
This computed 100000 Frobenius elements
This took 2.99 Days

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 24948  0.2495  1.9958 
 1,1,2 25029  0.2503  2.0023 
 2,2 37623  0.3762  3.0098 
 1,1,1,1 12400  0.1240  0.9920 
This computed 100000 Frobenius elements
This took 2.26 Days

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25058  0.2506  2.0046 
 1,1,2 24941  0.2494  1.9953 
 2,2 37550  0.3755  3.0040 
 1,1,1,1 12451  0.1245  0.9961 
This computed 100000 Frobenius elements
This took 11.18 Hours

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 1,1,1,1 12527  0.1253  1.0022 
 2,2 37350  0.3735  2.9880 
 1,1,2 25006  0.2501  2.0005 
 4 25117  0.2512  2.0094 
This computed 100000 Frobenius elements
This took 1.10 Days

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25138  0.2514  2.0110 
 1,1,1,1 12498  0.1250  0.9998 
 1,1,2 24933  0.2493  1.9946 
 2,2 37431  0.3743  2.9945 
This computed 100000 Frobenius elements
This took 1.29 Days

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 2,2 37511  0.3751  3.0009 
 4 24996  0.2500  1.9997 
 1,1,1,1 12260  0.1226  0.9808 
 1,1,2 25233  0.2523  2.0186 
This computed 100000 Frobenius elements
This took 1.19 Days

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 1,1,2 24861  0.2486  1.9889 
 1,1,1,1 12515  0.1252  1.0012 
 4 24873  0.2487  1.9898 
 2,2 37751  0.3775  3.0201 
This computed 100000 Frobenius elements
This took 1.38 Days

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25195  0.2520  2.0156 
 1,1,2 24886  0.2489  1.9909 
 2,2 37479  0.3748  2.9983 
 1,1,1,1 12440  0.1244  0.9952 
This computed 100000 Frobenius elements
This took 17.30 Hours

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25222  0.2522  2.0178 
 1,1,1,1 12391  0.1239  0.9913 
 1,1,2 24931  0.2493  1.9945 
 2,2 37456  0.3746  2.9965 
This computed 100000 Frobenius elements
This took 18.50 Hours

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 1,1,2 24823  0.2482  1.9858 
 2,2 37552  0.3755  3.0042 
 4 25162  0.2516  2.0130 
 1,1,1,1 12463  0.1246  0.9970 
This computed 100000 Frobenius elements
This took 2.59 Hours

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 1,1,1,1 12514  0.1251  1.0011 
 2,2 37522  0.3752  3.0018 
 4 24971  0.2497  1.9977 
 1,1,2 24993  0.2499  1.9994 
This computed 100000 Frobenius elements
This took 5.90 Hours

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 1,1,1,1 12488  0.1249  0.9990 
 1,1,2 24838  0.2484  1.9870 
 2,2 37578  0.3758  3.0062 
 4 25096  0.2510  2.0077 
This computed 100000 Frobenius elements
This took 6.53 Hours

···· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 4,4 468055  0.3120  59.9110 
 1,1,2,4 187987  0.1253  24.0623 
 1,1,1,1,2,2 140964  0.0940  18.0434 
 2,2,2,2 194991  0.1300  24.9588 
 2,6 249922  0.1666  31.9900 
 1,1,3,3 250101  0.1667  32.0129 
 1,1,1,1,1,1,1,1 7980  0.0053  1.0214 
This computed 1500000 Frobenius elements
This took 6.43 Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 1,1,1,1,2,2 373365  0.0933  17.9215 
 1,1,3,3 666714  0.1667  32.0023 
 2,2,2,2 520945  0.1302  25.0054 
 2,6 668104  0.1670  32.0690 
 4,4 1250767  0.3127  60.0368 
 1,1,2,4 499471  0.1249  23.9746 
 1,1,1,1,1,1,1,1 20634  0.0052  0.9904 
This computed 4000000 Frobenius elements
This took 13.67 Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 4,4 625018  0.3125  60.0017 
 1,1,1,1,2,2 187384  0.0937  17.9889 
 1,1,2,4 249098  0.1245  23.9134 
 2,6 334134  0.1671  32.0769 
 1,1,1,1,1,1,1,1 10245  0.0051  0.9835 
 2,2,2,2 260636  0.1303  25.0211 
 1,1,3,3 333485  0.1667  32.0146 
This computed 2000000 Frobenius elements
This took 17.26 Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 2,6 1667917  0.1668  32.0240 
 4,4 3129291  0.3129  60.0824 
 1,1,3,3 1667199  0.1667  32.0102 
 1,1,1,1,2,2 933642  0.0934  17.9259 
 2,2,2,2 1300352  0.1300  24.9668 
 1,1,2,4 1250710  0.1251  24.0136 
 1,1,1,1,1,1,1,1 50889  0.0051  0.9771 
This computed 10000000 Frobenius elements
This took 12.49 Days

···· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 2,6 125478  0.0837  32.1224 
 1,1,2,4 93046  0.0620  23.8198 
 1,1,6 125373  0.0836  32.0955 
 4,4 234927  0.1566  60.1413 
 2,2,4 140026  0.0934  35.8467 
 2,3,3 125008  0.0833  32.0020 
 1,1,3,3 125251  0.0835  32.0643 
 1,1,2,2,2 109215  0.0728  27.9590 
 8 187589  0.1251  48.0228 
 2,2,2,2 98005  0.0653  25.0893 
 1,1,1,1,2,2 69982  0.0467  17.9154 
 1,1,1,1,1,1,2 15565  0.0104  3.9846 
 1,1,1,1,4 46633  0.0311  11.9380 
 1,1,1,1,1,1,1,1 3902  0.0026  0.9989 
This computed 1500000 Frobenius elements
This took 33.69 Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 1,1,6 125191  0.0835  32.0489 
 1,1,1,1,2,2 70785  0.0472  18.1210 
 1,1,2,2,2 109101  0.0727  27.9299 
 4,4 234130  0.1561  59.9373 
 8 187536  0.1250  48.0092 
 2,3,3 124896  0.0833  31.9734 
 1,1,2,4 93374  0.0622  23.9037 
 2,2,2,2 97843  0.0652  25.0478 
 1,1,3,3 125374  0.0836  32.0957 
 2,2,4 140222  0.0935  35.8968 
 1,1,1,1,4 46549  0.0310  11.9165 
 2,6 125570  0.0837  32.1459 
 1,1,1,1,1,1,2 15496  0.0103  3.9670 
 1,1,1,1,1,1,1,1 3933  0.0026  1.0068 
This computed 1500000 Frobenius elements
This took 25.88 Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 8 622095  0.1244  47.7769 
 1,1,6 418159  0.0836  32.1146 
 2,3,3 418739  0.0837  32.1592 
 4,4 782050  0.1564  60.0614 
 1,1,1,1,2,2 233392  0.0467  17.9245 
 1,1,2,4 313625  0.0627  24.0864 
 2,2,2,2 323468  0.0647  24.8423 
 2,2,4 468543  0.0937  35.9841 
 2,6 417648  0.0835  32.0754 
 1,1,1,1,4 156371  0.0313  12.0093 
 1,1,2,2,2 366044  0.0732  28.1122 
 1,1,3,3 415390  0.0831  31.9020 
 1,1,1,1,1,1,1,1 12958  0.0026  0.9952 
 1,1,1,1,1,1,2 51518  0.0103  3.9566 
This computed 5000000 Frobenius elements
This took 86.17 Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 1,1,2,2,2 364344  0.0729  27.9816 
 1,1,3,3 416937  0.0834  32.0208 
 2,6 418193  0.0836  32.1172 
 4,4 783057  0.1566  60.1388 
 2,3,3 416638  0.0833  31.9978 
 1,1,6 415380  0.0831  31.9012 
 8 624451  0.1249  47.9578 
 2,2,2,2 326899  0.0654  25.1058 
 2,2,4 469055  0.0938  36.0234 
 1,1,1,1,1,1,1,1 12823  0.0026  0.9848 
 1,1,1,1,4 155995  0.0312  11.9804 
 1,1,2,4 311961  0.0624  23.9586 
 1,1,1,1,1,1,2 51471  0.0103  3.9530 
 1,1,1,1,2,2 232796  0.0466  17.8787 
This computed 5000000 Frobenius elements
This took 26.98 Days

···· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 2,2,4 311193  0.1556  119.4981 
 2,6 333780  0.1669  128.1715 
 8 250290  0.1251  96.1114 
 1,1,1,2,3 167396  0.0837  64.2801 
 1,1,3,3 111416  0.0557  42.7837 
 1,1,1,1,2,2 72985  0.0365  28.0262 
 1,1,2,2,2 62502  0.0313  24.0008 
 1,1,2,4 124872  0.0624  47.9508 
 4,4 187349  0.0937  71.9420 
 1,2,2,3 83396  0.0417  32.0241 
 2,2,2,2 57009  0.0285  21.8915 
 1,1,1,1,1,3 27728  0.0139  10.6476 
 1,3,4 166776  0.0834  64.0420 
 1,1,1,1,4 20941  0.0105  8.0413 
 1,1,1,1,1,1,2 20697  0.0103  7.9476 
 1,1,1,1,1,1,1,1 1670  0.0008  0.6413 
This computed 2000000 Frobenius elements
This took 21.13 Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 8 751666  0.1253  96.2133 
 2,6 999182  0.1665  127.8953 
 2,2,4 938845  0.1565  120.1722 
 1,2,2,3 248673  0.0414  31.8301 
 1,1,3,3 334055  0.0557  42.7590 
 1,3,4 499898  0.0833  63.9870 
 1,1,2,2,2 186125  0.0310  23.8240 
 1,1,1,2,3 500544  0.0834  64.0696 
 4,4 562855  0.0938  72.0455 
 2,2,2,2 171295  0.0285  21.9258 
 1,1,1,1,2,2 218512  0.0364  27.9695 
 1,1,2,4 375401  0.0626  48.0513 
 1,1,1,1,1,3 83050  0.0138  10.6304 
 1,1,1,1,4 62530  0.0104  8.0038 
 1,1,1,1,1,1,2 62385  0.0104  7.9853 
 1,1,1,1,1,1,1,1 4983  0.0008  0.6378 
This computed 5999999 Frobenius elements
This took 68.45 Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 2,2,2,2 28512  0.0285  21.8972 
 1,1,2,4 62428  0.0624  47.9447 
 1,1,1,2,3 83216  0.0832  63.9099 
 2,6 166971  0.1670  128.2337 
 1,3,4 82881  0.0829  63.6526 
 8 125037  0.1250  96.0284 
 4,4 94246  0.0942  72.3809 
 1,1,3,3 55627  0.0556  42.7215 
 2,2,4 155764  0.1558  119.6268 
 1,1,2,2,2 31398  0.0314  24.1137 
 1,1,1,1,1,3 14063  0.0141  10.8004 
 1,1,1,1,1,1,2 10474  0.0105  8.0440 
 1,1,1,1,4 10497  0.0105  8.0617 
 1,2,2,3 41697  0.0417  32.0233 
 1,1,1,1,2,2 36317  0.0363  27.8915 
 1,1,1,1,1,1,1,1 872  0.0009  0.6697 
This computed 1000000 Frobenius elements
This took 1.39 Days

··· = 16 in LG(5)
Cycle type Frequency Fraction Empirical
 4,12 11704692  0.0836  120.3911 
 1,5,5,5 28019751  0.2001  288.2032 
 4,4,4,4 19019789  0.1359  195.6321 
 1,1,1,1,3,3,3,3 5789477  0.0414  59.5489 
 2,2,6,6 17555039  0.1254  180.5661 
 1,1,2,3,3,6 11615650  0.0830  119.4753 
 1,1,2,4,4,4 17498033  0.1250  179.9798 
 8,8 17578907  0.1256  180.8116 
 2,2,2,2,2,2,2,2 5437247  0.0388  55.9260 
 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 61740  0.0004  0.6350 
 1,1,1,1,2,2,2,2,2,2 4313867  0.0308  44.3712 
 1,1,1,1,1,1,1,1,2,2,2,2 1405808  0.0100  14.4597 
This computed 140000000 Frobenius elements
This took 561.91 Days

Created Sat Nov 16 06:12:10 PM CST 2024 by Frank Sottile