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 2.99 GHz-Days

·· = 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 8.74 GHz-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 4.80 GHz-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 2.54 GHz-Days

·· = 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 2.47 GHz-Days

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 2,2 75075  0.7508  3.0030 
 1,1,1,1 24925  0.2492  0.9970 
This computed 100000 Frobenius elements
This took 1.11 GHz-Days

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 2,2 74934  0.7493  2.9974 
 1,1,1,1 25066  0.2507  1.0026 
This computed 100000 Frobenius elements
This took 7.27 GHz-Hours

····· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25028  0.2503  2.0022 
 2,2 37531  0.3753  3.0025 
 1,1,2 24875  0.2487  1.9900 
 1,1,1,1 12566  0.1257  1.0053 
This computed 100000 Frobenius elements
This took 11.75 GHz-Days

···· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25227  0.2523  2.0182 
 2,2 37592  0.3759  3.0074 
 1,1,2 24746  0.2475  1.9797 
 1,1,1,1 12435  0.1244  0.9948 
This computed 100000 Frobenius elements
This took 2.32 GHz-Days

···· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25168  0.2517  2.0134 
 2,2 37517  0.3752  3.0014 
 1,1,2 24898  0.2490  1.9918 
 1,1,1,1 12417  0.1242  0.9934 
This computed 100000 Frobenius elements
This took 9.29 GHz-Days

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25074  0.2507  2.0059 
 2,2 37406  0.3741  2.9925 
 1,1,2 24987  0.2499  1.9990 
 1,1,1,1 12533  0.1253  1.0026 
This computed 100000 Frobenius elements
This took 10.36 GHz-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 7.85 GHz-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 11.05 GHz-Days

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 24948  0.2495  1.9958 
 2,2 37623  0.3762  3.0098 
 1,1,2 25029  0.2503  2.0023 
 1,1,1,1 12400  0.1240  0.9920 
This computed 100000 Frobenius elements
This took 8.35 GHz-Days

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25058  0.2506  2.0046 
 2,2 37550  0.3755  3.0040 
 1,1,2 24941  0.2494  1.9953 
 1,1,1,1 12451  0.1245  0.9961 
This computed 100000 Frobenius elements
This took 1.72 GHz-Days

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25117  0.2512  2.0094 
 2,2 37350  0.3735  2.9880 
 1,1,2 25006  0.2501  2.0005 
 1,1,1,1 12527  0.1253  1.0022 
This computed 100000 Frobenius elements
This took 4.08 GHz-Days

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25138  0.2514  2.0110 
 2,2 37431  0.3743  2.9945 
 1,1,2 24933  0.2493  1.9946 
 1,1,1,1 12498  0.1250  0.9998 
This computed 100000 Frobenius elements
This took 4.76 GHz-Days

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 24996  0.2500  1.9997 
 2,2 37511  0.3751  3.0009 
 1,1,2 25233  0.2523  2.0186 
 1,1,1,1 12260  0.1226  0.9808 
This computed 100000 Frobenius elements
This took 4.40 GHz-Days

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 24873  0.2487  1.9898 
 2,2 37751  0.3775  3.0201 
 1,1,2 24861  0.2486  1.9889 
 1,1,1,1 12515  0.1252  1.0012 
This computed 100000 Frobenius elements
This took 5.12 GHz-Days

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25195  0.2520  2.0156 
 2,2 37479  0.3748  2.9983 
 1,1,2 24886  0.2489  1.9909 
 1,1,1,1 12440  0.1244  0.9952 
This computed 100000 Frobenius elements
This took 2.67 GHz-Days

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25222  0.2522  2.0178 
 2,2 37456  0.3746  2.9965 
 1,1,2 24931  0.2493  1.9945 
 1,1,1,1 12391  0.1239  0.9913 
This computed 100000 Frobenius elements
This took 2.85 GHz-Days

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25162  0.2516  2.0130 
 2,2 37552  0.3755  3.0042 
 1,1,2 24823  0.2482  1.9858 
 1,1,1,1 12463  0.1246  0.9970 
This computed 100000 Frobenius elements
This took 9.59 GHz-Hours

··· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 24971  0.2497  1.9977 
 2,2 37522  0.3752  3.0018 
 1,1,2 24993  0.2499  1.9994 
 1,1,1,1 12514  0.1251  1.0011 
This computed 100000 Frobenius elements
This took 21.85 GHz-Hours

·· = 4 in LG(5)
Cycle type Frequency Fraction Empirical
 4 25096  0.2510  2.0077 
 2,2 37578  0.3758  3.0062 
 1,1,2 24838  0.2484  1.9870 
 1,1,1,1 12488  0.1249  0.9990 
This computed 100000 Frobenius elements
This took 1.01 GHz-Days

···· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 4,4 468055  0.3120  59.9110 
 2,6 249922  0.1666  31.9900 
 2,2,2,2 194991  0.1300  24.9588 
 1,1,3,3 250101  0.1667  32.0129 
 1,1,2,4 187987  0.1253  24.0623 
 1,1,1,1,2,2 140964  0.0940  18.0434 
 1,1,1,1,1,1,1,1 7980  0.0053  1.0214 
This computed 1500000 Frobenius elements
This took 23.80 GHz-Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 4,4 1250767  0.3127  60.0368 
 2,6 668104  0.1670  32.0690 
 2,2,2,2 520945  0.1302  25.0054 
 1,1,3,3 666714  0.1667  32.0023 
 1,1,2,4 499471  0.1249  23.9746 
 1,1,1,1,2,2 373365  0.0933  17.9215 
 1,1,1,1,1,1,1,1 20634  0.0052  0.9904 
This computed 4000000 Frobenius elements
This took 50.59 GHz-Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 4,4 625018  0.3125  60.0017 
 2,6 334134  0.1671  32.0769 
 2,2,2,2 260636  0.1303  25.0211 
 1,1,3,3 333485  0.1667  32.0146 
 1,1,2,4 249098  0.1245  23.9134 
 1,1,1,1,2,2 187384  0.0937  17.9889 
 1,1,1,1,1,1,1,1 10245  0.0051  0.9835 
This computed 2000000 Frobenius elements
This took 63.86 GHz-Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 4,4 3129291  0.3129  60.0824 
 2,6 1667917  0.1668  32.0240 
 2,2,2,2 1300352  0.1300  24.9668 
 1,1,3,3 1667199  0.1667  32.0102 
 1,1,2,4 1250710  0.1251  24.0136 
 1,1,1,1,2,2 933642  0.0934  17.9259 
 1,1,1,1,1,1,1,1 50889  0.0051  0.9771 
This computed 10000000 Frobenius elements
This took 46.21 GHz-Days

···· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 8 187589  0.1251  48.0228 
 4,4 234927  0.1566  60.1413 
 2,6 125478  0.0837  32.1224 
 2,3,3 125008  0.0833  32.0020 
 2,2,4 140026  0.0934  35.8467 
 2,2,2,2 98005  0.0653  25.0893 
 1,1,6 125373  0.0836  32.0955 
 1,1,3,3 125251  0.0835  32.0643 
 1,1,2,4 93046  0.0620  23.8198 
 1,1,2,2,2 109215  0.0728  27.9590 
 1,1,1,1,4 46633  0.0311  11.9380 
 1,1,1,1,2,2 69982  0.0467  17.9154 
 1,1,1,1,1,1,2 15565  0.0104  3.9846 
 1,1,1,1,1,1,1,1 3902  0.0026  0.9989 
This computed 1500000 Frobenius elements
This took 124.65 GHz-Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 8 187536  0.1250  48.0092 
 4,4 234130  0.1561  59.9373 
 2,6 125570  0.0837  32.1459 
 2,3,3 124896  0.0833  31.9734 
 2,2,4 140222  0.0935  35.8968 
 2,2,2,2 97843  0.0652  25.0478 
 1,1,6 125191  0.0835  32.0489 
 1,1,3,3 125374  0.0836  32.0957 
 1,1,2,4 93374  0.0622  23.9037 
 1,1,2,2,2 109101  0.0727  27.9299 
 1,1,1,1,4 46549  0.0310  11.9165 
 1,1,1,1,2,2 70785  0.0472  18.1210 
 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 95.76 GHz-Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 8 622095  0.1244  47.7769 
 4,4 782050  0.1564  60.0614 
 2,6 417648  0.0835  32.0754 
 2,3,3 418739  0.0837  32.1592 
 2,2,4 468543  0.0937  35.9841 
 2,2,2,2 323468  0.0647  24.8423 
 1,1,6 418159  0.0836  32.1146 
 1,1,3,3 415390  0.0831  31.9020 
 1,1,2,4 313625  0.0627  24.0864 
 1,1,2,2,2 366044  0.0732  28.1122 
 1,1,1,1,4 156371  0.0313  12.0093 
 1,1,1,1,2,2 233392  0.0467  17.9245 
 1,1,1,1,1,1,2 51518  0.0103  3.9566 
 1,1,1,1,1,1,1,1 12958  0.0026  0.9952 
This computed 5000000 Frobenius elements
This took 318.81 GHz-Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 8 624451  0.1249  47.9578 
 4,4 783057  0.1566  60.1388 
 2,6 418193  0.0836  32.1172 
 2,3,3 416638  0.0833  31.9978 
 2,2,4 469055  0.0938  36.0234 
 2,2,2,2 326899  0.0654  25.1058 
 1,1,6 415380  0.0831  31.9012 
 1,1,3,3 416937  0.0834  32.0208 
 1,1,2,4 311961  0.0624  23.9586 
 1,1,2,2,2 364344  0.0729  27.9816 
 1,1,1,1,4 155995  0.0312  11.9804 
 1,1,1,1,2,2 232796  0.0466  17.8787 
 1,1,1,1,1,1,2 51471  0.0103  3.9530 
 1,1,1,1,1,1,1,1 12823  0.0026  0.9848 
This computed 5000000 Frobenius elements
This took 99.83 GHz-Days

···· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 8 250290  0.1251  144.1670 
 4,4 187349  0.0937  107.9130 
 2,6 333780  0.1669  192.2573 
 2,2,4 311193  0.1556  179.2472 
 2,2,2,2 57009  0.0285  32.8372 
 1,3,4 166776  0.0834  96.0630 
 1,2,2,3 83396  0.0417  48.0361 
 1,1,3,3 111416  0.0557  64.1756 
 1,1,2,4 124872  0.0624  71.9263 
 1,1,2,2,2 62502  0.0313  36.0012 
 1,1,1,2,3 167396  0.0837  96.4201 
 1,1,1,1,4 20941  0.0105  12.0620 
 1,1,1,1,2,2 72985  0.0365  42.0394 
 1,1,1,1,1,3 27728  0.0139  15.9713 
 1,1,1,1,1,1,2 20697  0.0103  11.9215 
 1,1,1,1,1,1,1,1 1670  0.0008  0.9619 
This computed 2000000 Frobenius elements
This took 78.17 GHz-Days

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 8 1875494  0.1250  144.0379 
 4,4 1407908  0.0939  108.1273 
 2,6 2497184  0.1665  191.7837 
 2,2,4 2347885  0.1565  180.3176 
 2,2,2,2 429632  0.0286  32.9957 
 1,3,4 1250659  0.0834  96.0506 
 1,2,2,3 624657  0.0416  47.9737 
 1,1,3,3 832915  0.0555  63.9679 
 1,1,2,4 936132  0.0624  71.8949 
 1,1,2,2,2 467505  0.0312  35.9044 
 1,1,1,2,3 1250818  0.0834  96.0628 
 1,1,1,1,4 155862  0.0104  11.9702 
 1,1,1,1,2,2 546610  0.0364  41.9796 
 1,1,1,1,1,3 208341  0.0139  16.0006 
 1,1,1,1,1,1,2 155691  0.0104  11.9571 
 1,1,1,1,1,1,1,1 12707  0.0008  0.9759 
This computed 15000000 Frobenius elements
This took 1.78 GHz-Years

··· = 8 in LG(5)
Cycle type Frequency Fraction Empirical
 8 12493026  0.1249  143.9197 
 4,4 9386138  0.0939  108.1283 
 2,6 16698798  0.1670  192.3702 
 2,2,4 15599975  0.1560  179.7117 
 2,2,2,2 2856963  0.0286  32.9122 
 1,3,4 8335630  0.0834  96.0265 
 1,2,2,3 4176986  0.0418  48.1189 
 1,1,3,3 5568506  0.0557  64.1492 
 1,1,2,4 6236425  0.0624  71.8436 
 1,1,2,2,2 3128640  0.0313  36.0419 
 1,1,1,2,3 8320205  0.0832  95.8488 
 1,1,1,1,4 1043535  0.0104  12.0215 
 1,1,1,1,2,2 3644807  0.0364  41.9882 
 1,1,1,1,1,3 1383668  0.0138  15.9399 
 1,1,1,1,1,1,2 1038371  0.0104  11.9620 
 1,1,1,1,1,1,1,1 88327  0.0009  1.0175 
This computed 100000000 Frobenius elements
This took 2.28 GHz-Years

··· = 16 in LG(5)
Cycle type Frequency Fraction Empirical
 8,8 17578907  0.1256  241.0822 
 4,4,4,4 19019789  0.1359  260.8428 
 4,12 11704692  0.0836  160.5215 
 2,2,6,6 17555039  0.1254  240.7548 
 2,2,2,2,2,2,2,2 5437247  0.0388  74.5680 
 1,5,5,5 28019751  0.2001  384.2709 
 1,1,2,4,4,4 17498033  0.1250  239.9730 
 1,1,2,3,3,6 11615650  0.0830  159.3003 
 1,1,1,1,3,3,3,3 5789477  0.0414  79.3985 
 1,1,1,1,2,2,2,2,2,2 4313867  0.0308  59.1616 
 1,1,1,1,1,1,1,1,2,2,2,2 1405808  0.0100  19.2797 
 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 61740  0.0004  0.8467 
This computed 140000000 Frobenius elements
This took 5.69 GHz-Years

Created Tue Jan 14 10:12:56 PM CST 2025 by Frank Sottile