Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (37 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
21.13.129...161.1	$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 53 x^{16} - 899 x^{15} - 382 x^{14} + 2557 x^{13} + 1438 x^{12} - 4294 x^{11} - 3019 x^{10} + 4030 x^{9} + 3533 x^{8} - 1774 x^{7} - 2183 x^{6} + 69 x^{5} + 551 x^{4} + 110 x^{3} - 36 x^{2} - 13 x - 1$	$21$	[13,4]	$3^{3}\cdot 7^{14}\cdot 113\cdot 7985768699\cdot 78297036161$	$5$	$52.434023188$	$1684727121230.194$			?	$S_7\wr C_3$ (as 21T159)	trivial	$2$	$16$	$41466747060.9$
21.13.273...736.1	$x^{21} - 6 x^{19} - 4 x^{18} - 45 x^{17} - 60 x^{16} + 223 x^{15} + 486 x^{14} + 891 x^{13} + 1584 x^{12} - 918 x^{11} - 7428 x^{10} - 12146 x^{9} - 13032 x^{8} - 9933 x^{7} + 1246 x^{6} + 16092 x^{5} + 21528 x^{4} + 14992 x^{3} + 6048 x^{2} + 1344 x + 128$	$21$	[13,4]	$2^{14}\cdot 3^{24}\cdot 8388019^{3}$	$3$	$54.3328265076$				?	$C_3^7.(C_2^7.S_7)$ (as 21T152)	trivial	$2$	$16$	$59558850940.7$
21.13.464...432.1	$x^{21} - 42 x^{19} - 28 x^{18} + 729 x^{17} + 972 x^{16} - 6453 x^{15} - 13554 x^{14} + 27333 x^{13} + 94976 x^{12} - 14553 x^{11} - 328686 x^{10} - 312847 x^{9} + 372276 x^{8} + 958311 x^{7} + 546750 x^{6} - 438804 x^{5} - 927144 x^{4} - 695216 x^{3} - 284256 x^{2} - 63168 x - 6016$	$21$	[13,4]	$2^{14}\cdot 3^{21}\cdot 47^{2}\cdot 107^{3}\cdot 21557^{3}$	$5$	$55.7251630311$				?	$C_3^7.(C_2^7.S_7)$ (as 21T152)	trivial	$2$	$16$	$72288094145.7$
21.13.168...529.1	$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 54 x^{16} - 898 x^{15} - 396 x^{14} + 2541 x^{13} + 1511 x^{12} - 4209 x^{11} - 3210 x^{10} + 3829 x^{9} + 3846 x^{8} - 1479 x^{7} - 2499 x^{6} - 303 x^{5} + 537 x^{4} + 190 x^{3} - 15 x^{2} - 12 x - 1$	$21$	[13,4]	$7^{14}\cdot 41\cdot 167\cdot 5406197\cdot 671780022444019$	$5$	$59.2534848123$	$18247708437255.99$			?	$S_7\wr C_3$ (as 21T159)	trivial	$2$	$16$	$169796731730$
21.13.237...088.1	$x^{21} - 21 x^{19} - 10 x^{18} + 189 x^{17} + 180 x^{16} - 929 x^{15} - 1350 x^{14} + 2595 x^{13} + 5496 x^{12} - 3663 x^{11} - 13302 x^{10} + 495 x^{9} + 19764 x^{8} + 6885 x^{7} - 17594 x^{6} - 11664 x^{5} + 7392 x^{4} + 8032 x^{3} + 576 x^{2} - 768 x - 128$	$21$	[13,4]	$2^{14}\cdot 3^{21}\cdot 17\cdot 71^{3}\cdot 283583^{3}$	$5$	$60.2310613241$				?	$C_3^7.(C_2^7.S_7)$ (as 21T152)	trivial	$2$	$16$	$142663173463$
21.13.251...021.1	$x^{21} - 2 x^{20} - 15 x^{19} + 58 x^{18} + 22 x^{17} - 451 x^{16} + 666 x^{15} + 864 x^{14} - 3424 x^{13} + 1655 x^{12} + 5377 x^{11} - 4629 x^{10} - 8530 x^{9} + 10138 x^{8} + 6523 x^{7} - 9568 x^{6} - 4336 x^{5} + 6971 x^{4} - 397 x^{3} - 845 x^{2} - 78 x - 1$	$21$	[13,4]	$29^{19}\cdot 41^{2}\cdot 1567^{2}$	$3$	$60.3966354804$	$36574.31773966791$			?	$C_3^7:(C_2\times F_8)$ (as 21T112)	trivial	$2$	$16$	$197222417058$
21.13.309...228.1	$x^{21} - 5 x^{20} - 6 x^{19} + 63 x^{18} - 19 x^{17} - 327 x^{16} + 261 x^{15} + 911 x^{14} - 932 x^{13} - 1507 x^{12} + 1644 x^{11} + 1590 x^{10} - 1570 x^{9} - 1166 x^{8} + 816 x^{7} + 619 x^{6} - 241 x^{5} - 199 x^{4} + 49 x^{3} + 24 x^{2} - 3 x - 1$	$21$	[13,4]	$2^{2}\cdot 31\cdot 43\cdot 15053\cdot 102413451780923\cdot 3770285596717141$	$6$	$60.9954381057$				✓	$S_{21}$ (as 21T164)	trivial	$2$	$16$	$338584375527$
21.13.404...741.1	$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 45 x^{16} - 907 x^{15} - 270 x^{14} + 2685 x^{13} + 854 x^{12} - 5055 x^{11} - 1653 x^{10} + 6124 x^{9} + 2244 x^{8} - 4458 x^{7} - 2040 x^{6} + 1560 x^{5} + 960 x^{4} - 80 x^{3} - 123 x^{2} - 21 x - 1$	$21$	[13,4]	$7^{14}\cdot 59646183107903161080974909$	$2$	$61.7742371941$	$28261162488532.168$			?	$S_7\wr C_3$ (as 21T159)	trivial	$2$	$16$	$295522286712$
21.13.457...984.1	$x^{21} - 5 x^{20} - 6 x^{19} + 63 x^{18} - 19 x^{17} - 327 x^{16} + 261 x^{15} + 911 x^{14} - 932 x^{13} - 1507 x^{12} + 1644 x^{11} + 1590 x^{10} - 1570 x^{9} - 1166 x^{8} + 816 x^{7} + 619 x^{6} - 241 x^{5} - 200 x^{4} + 49 x^{3} + 25 x^{2} - 3 x - 1$	$21$	[13,4]	$2^{4}\cdot 103\cdot 426103\cdot 1287491\cdot 50609727688176358507171$	$5$	$62.1376410505$	$3.7963537258935434e+18$			✓	$S_{21}$ (as 21T164)	trivial	$2$	$16$	$572847412551$
21.13.579...937.1	$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 48 x^{16} - 904 x^{15} - 312 x^{14} + 2637 x^{13} + 1073 x^{12} - 4770 x^{11} - 2166 x^{10} + 5341 x^{9} + 2733 x^{8} - 3453 x^{7} - 2099 x^{6} + 1011 x^{5} + 825 x^{4} - x^{3} - 90 x^{2} - 18 x - 1$	$21$	[13,4]	$3^{28}\cdot 661493771\cdot 3828819218040827$	$3$	$62.8401794802$				?	$S_7\wr C_3$ (as 21T159)	trivial	$2$	$16$	$239334684795$
21.13.101...528.1	$x^{21} - 60 x^{19} - 8 x^{18} + 1224 x^{17} + 192 x^{16} - 10767 x^{15} - 4410 x^{14} + 45264 x^{13} + 54600 x^{12} - 156366 x^{11} - 233310 x^{10} + 726860 x^{9} + 270576 x^{8} - 2019843 x^{7} - 331208 x^{6} + 2676384 x^{5} + 103680 x^{4} - 922000 x^{3} + 242208 x^{2} - 161472 x - 107648$	$21$	[13,4]	$2^{14}\cdot 3^{21}\cdot 23^{3}\cdot 29^{2}\cdot 53\cdot 239^{3}\cdot 431^{3}$	$7$	$64.543106656$				?	$C_3^7.(C_2^7.S_7)$ (as 21T152)	trivial	$2$	$16$	$246815332729$
21.13.886...232.1	$x^{21} + 24 x^{19} - 16 x^{18} - 36 x^{17} + 48 x^{16} - 3472 x^{15} + 6912 x^{14} - 11088 x^{13} + 18304 x^{12} + 107136 x^{11} - 407040 x^{10} + 691648 x^{9} - 928512 x^{8} - 63744 x^{7} + 4379648 x^{6} - 10036224 x^{5} + 11501568 x^{4} - 7729152 x^{3} + 3096576 x^{2} - 688128 x + 65536$	$21$	[13,4]	$2^{38}\cdot 3^{21}\cdot 11\cdot 809^{6}$	$4$	$79.8499708379$					$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147)	trivial	$2$	$16$	$26033728843700$
21.13.128...792.1	$x^{21} - 9 x^{19} - 6 x^{18} - 36 x^{17} - 48 x^{16} + 362 x^{15} + 756 x^{14} + 828 x^{13} + 976 x^{12} - 3024 x^{11} - 12576 x^{10} - 18674 x^{9} - 17352 x^{8} - 9186 x^{7} + 11260 x^{6} + 36504 x^{5} + 44208 x^{4} + 30112 x^{3} + 12096 x^{2} + 2688 x + 256$	$21$	[13,4]	$2^{42}\cdot 3^{21}\cdot 809^{6}$	$3$	$81.2874838617$					$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147)	trivial	$2$	$16$	$91102872861900$
21.13.216...533.1	$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 57 x^{16} - 895 x^{15} - 438 x^{14} + 2493 x^{13} + 1730 x^{12} - 3910 x^{11} - 3695 x^{10} + 2962 x^{9} + 4125 x^{8} - 418 x^{7} - 2147 x^{6} - 599 x^{5} + 347 x^{4} + 190 x^{3} + 4 x^{2} - 9 x - 1$	$21$	[13,4]	$229^{7}\cdot 92077\cdot 82827653\cdot 85991827177$	$4$	$83.3190643455$	$12254894810420.373$			?	$S_7\wr C_3.C_2$ (as 21T162)	trivial	$2$	$16$	$4943549820250$
21.13.304...464.1	$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 44 x^{16} - 908 x^{15} - 256 x^{14} + 2701 x^{13} + 781 x^{12} - 5138 x^{11} - 1458 x^{10} + 6313 x^{9} + 1901 x^{8} - 4745 x^{7} - 1695 x^{6} + 1879 x^{5} + 877 x^{4} - 201 x^{3} - 146 x^{2} - 22 x - 1$	$21$	[13,4]	$2^{14}\cdot 37^{7}\cdot 113\cdot 8273\cdot 385537\cdot 54305277821449$	$6$	$84.6807775469$	$42718137712460.88$			?	$S_7\wr C_3.C_2$ (as 21T162)	trivial	$2$	$16$	$5098826311570$
21.13.360...272.1	$x^{21} - 3 x^{19} - 2 x^{18} - 108 x^{17} - 144 x^{16} + 141 x^{15} + 378 x^{14} + 2520 x^{13} + 6104 x^{12} + 2646 x^{11} - 8652 x^{10} - 21233 x^{9} - 36324 x^{8} - 49287 x^{7} - 49534 x^{6} - 39852 x^{5} - 27864 x^{4} - 15696 x^{3} - 6048 x^{2} - 1344 x - 128$	$21$	[13,4]	$2^{14}\cdot 3^{21}\cdot 29^{18}$	$3$	$85.3673729135$				?	$C_3^7:C_2\wr C_7$ (as 21T123)	trivial	$2$	$16$	$6544435479500$
21.13.702...912.1	$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 50 x^{16} - 902 x^{15} - 340 x^{14} + 2605 x^{13} + 1219 x^{12} - 4584 x^{11} - 2516 x^{10} + 4843 x^{9} + 3119 x^{8} - 2799 x^{7} - 2259 x^{6} + 563 x^{5} + 741 x^{4} + 71 x^{3} - 64 x^{2} - 16 x - 1$	$21$	[13,4]	$2^{14}\cdot 37^{7}\cdot 3637897767851\cdot 12409911498371$	$4$	$88.1189074606$	$64877949175492.88$			?	$S_7\wr C_3.C_2$ (as 21T162)	trivial	$2$	$16$	$8986268282460$
21.13.165...672.1	$x^{21} - 6 x^{19} - 4 x^{18} - 63 x^{17} - 84 x^{16} + 269 x^{15} + 594 x^{14} + 1692 x^{13} + 3544 x^{12} + 54 x^{11} - 9804 x^{10} - 22883 x^{9} - 42156 x^{8} - 52446 x^{7} - 27556 x^{6} + 17064 x^{5} + 39024 x^{4} + 29536 x^{3} + 12096 x^{2} + 2688 x + 256$	$21$	[13,4]	$2^{14}\cdot 3^{21}\cdot 149^{6}\cdot 211^{6}$	$4$	$91.7907635323$					$C_3^7.(C_2^7.A_7)$ (as 21T151)	trivial	$2$	$16$	$166762897303000$
21.13.185...528.1	$x^{21} - 24 x^{19} - 16 x^{18} + 162 x^{17} + 216 x^{16} - 9 x^{15} - 162 x^{14} - 1890 x^{13} - 4776 x^{12} - 3780 x^{11} + 1128 x^{10} + 9800 x^{9} + 26208 x^{8} + 42027 x^{7} + 44894 x^{6} + 37692 x^{5} + 27288 x^{4} + 15632 x^{3} + 6048 x^{2} + 1344 x + 128$	$21$	[13,4]	$2^{14}\cdot 3^{21}\cdot 1009^{9}$	$3$	$92.2974806899$				?	$C_3^7:C_2\wr D_7$ (as 21T131)	trivial	$2$	$16$	$12956091666000$
21.13.960...112.1	$x^{21} - 21 x^{19} - 20 x^{18} + 189 x^{17} + 360 x^{16} - 801 x^{15} - 2700 x^{14} + 675 x^{13} + 10344 x^{12} + 7857 x^{11} - 18828 x^{10} - 33233 x^{9} + 4536 x^{8} + 51237 x^{7} + 34828 x^{6} - 20304 x^{5} - 37896 x^{4} - 15392 x^{3} + 1440 x^{2} + 2112 x + 320$	$21$	[13,4]	$2^{24}\cdot 3^{21}\cdot 73^{12}\cdot 239$	$4$	$99.8087228609$				?	$C_3^7.C_2\wr C_7:C_3$ (as 21T137)	trivial	$2$	$16$	$169091612739000$
21.13.205...696.1	$x^{21} - 21 x^{19} - 14 x^{18} + 117 x^{17} + 156 x^{16} + 133 x^{15} + 162 x^{14} - 1593 x^{13} - 4512 x^{12} - 3321 x^{11} + 2034 x^{10} + 8709 x^{9} + 18180 x^{8} + 23313 x^{7} + 11554 x^{6} - 9612 x^{5} - 19800 x^{4} - 14800 x^{3} - 6048 x^{2} - 1344 x - 128$	$21$	[13,4]	$2^{33}\cdot 3^{21}\cdot 73^{12}$	$3$	$103.496177705$				?	$C_3^7.C_2\wr C_7:C_3$ (as 21T137)	trivial	$2$	$16$	$240112609207000$
21.13.246...408.1	$x^{21} + 24 x^{19} - 16 x^{18} - 297 x^{17} + 396 x^{16} - 7881 x^{15} + 15498 x^{14} + 14859 x^{13} - 64880 x^{12} + 659124 x^{11} - 2003016 x^{10} + 1978298 x^{9} + 876312 x^{8} - 11936907 x^{7} + 41795214 x^{6} - 77901372 x^{5} + 84911832 x^{4} - 56319248 x^{3} + 22504608 x^{2} - 5001024 x + 476288$	$21$	[13,4]	$2^{14}\cdot 3^{29}\cdot 61^{2}\cdot 8388019^{3}$	$4$	$104.398440234$				?	$C_3^7.(C_2^6.S_7)$ (as 21T149)	trivial	$2$	$16$	$61555633715100$
21.13.921...696.1	$x^{21} - 6 x^{19} - 4 x^{18} - 126 x^{17} - 168 x^{16} + 862 x^{15} + 1836 x^{14} + 1548 x^{13} + 1136 x^{12} - 8370 x^{11} - 30396 x^{10} - 35873 x^{9} - 6948 x^{8} + 27087 x^{7} + 39230 x^{6} + 35532 x^{5} + 26712 x^{4} + 15568 x^{3} + 6048 x^{2} + 1344 x + 128$	$21$	[13,4]	$2^{14}\cdot 3^{19}\cdot 7\cdot 1601^{9}$	$4$	$111.152985899$				?	$C_3^7:C_2\wr D_7$ (as 21T131)	trivial	$2$	$16$	$388660756503000$
21.13.104...608.1	$x^{21} - 24 x^{19} - 16 x^{18} + 135 x^{17} + 180 x^{16} + 519 x^{15} + 918 x^{14} - 4653 x^{13} - 13904 x^{12} - 7236 x^{11} + 16440 x^{10} + 49612 x^{9} + 101808 x^{8} + 105621 x^{7} - 51646 x^{6} - 286524 x^{5} - 369432 x^{4} - 255248 x^{3} - 102816 x^{2} - 22848 x - 2176$	$21$	[13,4]	$2^{14}\cdot 3^{21}\cdot 17^{2}\cdot 29^{18}$	$4$	$111.809196954$				?	$C_3^7:C_2\wr C_7$ (as 21T123)	trivial	$2$	$16$	$166388749255000$
21.13.241...944.1	$x^{21} - 21 x^{19} - 3 x^{18} + 189 x^{17} + 54 x^{16} - 1021 x^{15} - 405 x^{14} + 3975 x^{13} + 2216 x^{12} - 11943 x^{11} - 10797 x^{10} + 23903 x^{9} + 36558 x^{8} - 17487 x^{7} - 64299 x^{6} - 27972 x^{5} + 34740 x^{4} + 45128 x^{3} + 20304 x^{2} + 3936 x + 256$	$21$	[13,4]	$2^{12}\cdot 3^{21}\cdot 11\cdot 53\cdot 149^{6}\cdot 211^{6}$	$6$	$116.3664972$				?	$C_3^7.(C_2^7.A_7)$ (as 21T151)	trivial	$2$	$16$	$834348991285000$
21.13.837...496.1	$x^{21} - 27 x^{19} - 18 x^{18} + 171 x^{17} + 228 x^{16} + 589 x^{15} + 1026 x^{14} - 5067 x^{13} - 15184 x^{12} - 15093 x^{11} - 6006 x^{10} + 26188 x^{9} + 105696 x^{8} + 177387 x^{7} + 165758 x^{6} + 98172 x^{5} + 43416 x^{4} + 17424 x^{3} + 6048 x^{2} + 1344 x + 128$	$21$	[13,4]	$2^{14}\cdot 3^{31}\cdot 587^{9}$	$3$	$123.47177805$					$C_3^7:(C_2^6:D_7)$ (as 21T122)	trivial	$2$	$16$	$1150144579010000$
21.13.678...176.1	$x^{21} - 6 x^{19} - 4 x^{18} - 126 x^{17} - 168 x^{16} + 322 x^{15} + 756 x^{14} + 4554 x^{13} + 10912 x^{12} + 5454 x^{11} - 13020 x^{10} - 60139 x^{9} - 164556 x^{8} - 259701 x^{7} - 251642 x^{6} - 171396 x^{5} - 97416 x^{4} - 48624 x^{3} - 18144 x^{2} - 4032 x - 384$	$21$	[13,4]	$2^{14}\cdot 3^{35}\cdot 587^{9}$	$3$	$152.211666618$					$C_3^7:(C_2^6:D_7)$ (as 21T122)	trivial	$2$	$16$	$9751020542440000$
21.13.148...864.1	$x^{21} + 36 x^{19} - 24 x^{18} - 108 x^{17} + 144 x^{16} - 7608 x^{15} + 15120 x^{14} + 6768 x^{13} - 42688 x^{12} + 402624 x^{11} - 1212288 x^{10} - 86528 x^{9} + 5658624 x^{8} - 8884608 x^{7} + 761600 x^{6} + 13312512 x^{5} - 18994176 x^{4} + 13400064 x^{3} - 5419008 x^{2} + 1204224 x - 114688$	$21$	[13,4]	$2^{14}\cdot 3^{21}\cdot 7^{3}\cdot 43^{18}$	$4$	$157.998159882$				?	$C_3^7:C_2\wr C_7$ (as 21T123)	trivial	$2$	$16$	$8586842734230000$
21.13.164...800.1	$x^{21} - 3 x^{19} - 2 x^{18} - 108 x^{17} - 144 x^{16} + 195 x^{15} + 486 x^{14} + 3321 x^{13} + 8064 x^{12} + 1674 x^{11} - 17508 x^{10} - 42797 x^{9} - 79956 x^{8} - 97365 x^{7} - 40522 x^{6} + 56700 x^{5} + 101304 x^{4} + 74256 x^{3} + 30240 x^{2} + 6720 x + 640$	$21$	[13,4]	$2^{15}\cdot 3^{21}\cdot 5^{2}\cdot 7^{12}\cdot 173^{9}$	$5$	$158.776795793$				?	$C_3^7.C_2\wr F_7$ (as 21T142)	trivial	$2$	$16$	$32075783443900000$
21.13.148...736.1	$x^{21} - 6 x^{19} - 4 x^{18} - 81 x^{17} - 108 x^{16} + 342 x^{15} + 756 x^{14} + 2610 x^{13} + 5728 x^{12} - 216 x^{11} - 16944 x^{10} - 42271 x^{9} - 84348 x^{8} - 108792 x^{7} - 59304 x^{6} + 31968 x^{5} + 77472 x^{4} + 59008 x^{3} + 24192 x^{2} + 5376 x + 512$	$21$	[13,4]	$2^{39}\cdot 3^{39}\cdot 13^{16}$	$3$	$196.723743928$					$C_3^7.C_2\wr F_7$ (as 21T142)	trivial	$2$	$16$	$115513437952000000$
21.13.758...400.1	$x^{21} - 6 x^{19} - 4 x^{18} - 432 x^{17} - 576 x^{16} + 1752 x^{15} + 3888 x^{14} + 50544 x^{13} + 128448 x^{12} - 74304 x^{11} - 617088 x^{10} - 1868864 x^{9} - 4518144 x^{8} - 5331840 x^{7} + 699136 x^{6} + 10160640 x^{5} + 13741056 x^{4} + 9590784 x^{3} + 3870720 x^{2} + 860160 x + 81920$	$21$	[13,4]	$2^{14}\cdot 3^{22}\cdot 5^{2}\cdot 7^{12}\cdot 173^{9}\cdot 307$	$6$	$212.621653968$				?	$C_3^7.C_2\wr F_7$ (as 21T142)	trivial	$2$	$16$	$473704900323000000$
21.13.883...288.1	$x^{21} - 12 x^{19} - 8 x^{18} - 324 x^{17} - 432 x^{16} + 2880 x^{15} + 6048 x^{14} + 37728 x^{13} + 90752 x^{12} - 96768 x^{11} - 582144 x^{10} - 1895872 x^{9} - 4845312 x^{8} - 6218496 x^{7} - 1158144 x^{6} + 7271424 x^{5} + 10764288 x^{4} + 7647232 x^{3} + 3096576 x^{2} + 688128 x + 65536$	$21$	[13,4]	$2^{35}\cdot 3^{40}\cdot 7\cdot 13^{15}\cdot 59$	$5$	$214.17162041$				?	$C_3^7.C_2\wr F_7$ (as 21T142)	trivial	$2$	$16$	$616524970790000000$
21.13.793...776.1	$x^{21} - 30 x^{19} - 20 x^{18} - 621 x^{17} - 828 x^{16} + 17247 x^{15} + 35046 x^{14} + 66051 x^{13} + 119024 x^{12} - 1844262 x^{11} - 6476388 x^{10} - 4483504 x^{9} + 11041056 x^{8} + 23943879 x^{7} + 14457846 x^{6} - 7997076 x^{5} - 19421064 x^{4} - 14795696 x^{3} - 6066144 x^{2} - 1348032 x - 128384$	$21$	[13,4]	$2^{14}\cdot 3^{28}\cdot 17^{2}\cdot 29^{18}\cdot 59^{2}$	$5$	$237.777369955$				?	$C_3^7:(C_2^3:F_8)$ (as 21T120)	trivial	$2$	$16$	$292713654111000000$
21.13.218...544.1	$x^{21} + 24 x^{19} - 16 x^{18} - 459 x^{17} + 612 x^{16} - 11355 x^{15} + 22302 x^{14} + 46044 x^{13} - 159128 x^{12} + 1546074 x^{11} - 4684332 x^{10} + 4473917 x^{9} + 2650860 x^{8} - 37055628 x^{7} + 136617936 x^{6} - 258599088 x^{5} + 283109760 x^{4} - 187999040 x^{3} + 75140352 x^{2} - 16697856 x + 1590272$	$21$	[13,4]	$2^{12}\cdot 3^{28}\cdot 149^{6}\cdot 211^{6}\cdot 1553^{2}$	$5$	$249.511730497$					$C_3^7.C_2^6:A_7$ (as 21T148)	trivial	$2$	$16$	$6636766064500000000$
21.13.508...416.1	$x^{21} - 9 x^{19} - 6 x^{18} - 135 x^{17} - 180 x^{16} + 993 x^{15} + 2106 x^{14} + 4887 x^{13} + 9600 x^{12} - 23031 x^{11} - 103602 x^{10} - 97025 x^{9} + 87948 x^{8} + 258951 x^{7} + 196462 x^{6} - 6804 x^{5} - 122472 x^{4} - 101808 x^{3} - 42336 x^{2} - 9408 x - 896$	$21$	[13,4]	$2^{32}\cdot 3^{22}\cdot 7^{14}\cdot 11^{18}$	$4$	$259.761440337$				?	$C_3^7.C_2^3:F_8:C_3$ (as 21T127)	trivial	$2$	$16$	$5620145735590000000$
21.13.140...264.1	$x^{21} + 15 x^{19} - 10 x^{18} - 540 x^{17} + 720 x^{16} - 6774 x^{15} + 13068 x^{14} + 74556 x^{13} - 220112 x^{12} + 892728 x^{11} - 2334288 x^{10} - 783346 x^{9} + 13135176 x^{8} - 39968658 x^{7} + 94308324 x^{6} - 155188008 x^{5} + 162971856 x^{4} - 106988384 x^{3} + 42662592 x^{2} - 9480576 x + 902912$	$21$	[13,4]	$2^{44}\cdot 3^{28}\cdot 809^{6}\cdot 3527^{2}$	$4$	$272.635096078$					$C_3^7.C_2^6:\GL(3,2)$ (as 21T145)	trivial	$2$	$16$	$16363118441400000000$
21.13.100...904.1	$x^{21} + 33 x^{19} - 22 x^{18} - 540 x^{17} + 720 x^{16} - 21597 x^{15} + 42714 x^{14} - 65736 x^{13} + 105688 x^{12} + 1371762 x^{11} - 4859580 x^{10} + 9685343 x^{9} - 16976412 x^{8} - 2163123 x^{7} + 96125046 x^{6} - 220676508 x^{5} + 253088568 x^{4} - 170110352 x^{3} + 68154912 x^{2} - 15145536 x + 1442432$	$21$	[13,4]	$2^{14}\cdot 3^{28}\cdot 29^{18}\cdot 59^{2}\cdot 191^{2}$	$5$	$299.382341374$				?	$C_3^7:(C_2^3:F_8)$ (as 21T120)	trivial	$2$	$16$	$4153536235960000000$