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Label Polynomial Discriminant Galois group Class group
32.0.24788700386255228556692600250244140625.1 x32 - 2x31 + x29 + 14x28 - 23x27 - 25x26 + 77x25 + 32x24 - 233x23 + 130x22 + 275x21 - 204x20 - 500x19 + 369x18 + 976x17 - 775x16 - 1988x15 + 2706x14 + 1255x13 - 4074x12 + 870x11 + 3435x10 - 2784x9 - 528x8 + 1624x7 - 465x6 - 564x5 + 639x4 - 293x3 + 55x2 - x + 1 \( 5^{28}\cdot 13^{16} \) $C_8.A_4$ (as 32T402) Trivial (GRH)
32.0.47330370277129322496000000000000000000000000.1 x32 + x28 - x20 - x16 - x12 + x4 + 1 \( 2^{64}\cdot 3^{16}\cdot 5^{24} \) $C_2^3\times C_4$ (as 32T34) $[4]$ (GRH)
32.0.352701833122210710593389803720131611763844129.1 x32 - x31 + x29 - x28 + x26 - x25 + x23 - x22 + x20 - x19 + x17 - x16 + x15 - x13 + x12 - x10 + x9 - x7 + x6 - x4 + x3 - x + 1 \( 3^{16}\cdot 17^{30} \) $C_2\times C_{16}$ (as 32T32) $[5]$ (GRH)
32.0.515207889456069254383620937908064472169867121.1 x32 - 5x31 + 22x30 - 73x29 + 220x28 - 519x27 + 1255x26 - 2247x25 + 4413x24 - 6238x23 + 9744x22 - 10830x21 + 13240x20 - 10628x19 + 12053x18 - 5501x17 + 12591x16 - 3062x15 + 17256x14 + 194x13 + 18165x12 + 5659x11 + 13232x10 - 2318x9 - 319x8 - 13445x7 - 6940x6 - 4990x5 + 1466x4 + 2074x3 + 1626x2 + 264x + 79 \( 7^{16}\cdot 13^{28} \) $C_8.A_4$ (as 32T402) Trivial (GRH)
32.0.4722366482869645213696000000000000000000000000.1 x32 - x24 + x16 - x8 + 1 \( 2^{96}\cdot 5^{24} \) $C_2\times C_4^2$ (as 32T36) $[5]$ (GRH)
32.0.5512695749115635425536000000000000000000000000.1 x32 + x30 - 14x28 - 103x26 + 62x24 + 736x22 + 1892x20 + 4382x18 + 7111x16 + 4382x14 + 1892x12 + 736x10 + 62x8 - 103x6 - 14x4 + x2 + 1 \( 2^{32}\cdot 3^{16}\cdot 5^{24}\cdot 29^{8} \) $C_2^2\times C_2^2:C_4$ (as 32T262) $[2, 4]$ (GRH)
32.0.7669926418924454281216000000000000000000000000.1 x32 - 4x31 + 10x30 - 20x29 + 34x28 - 32x27 - 8x26 + 112x25 - 308x24 + 608x23 - 880x22 + 944x21 - 536x20 - 672x19 + 2960x18 - 6176x17 + 9744x16 - 12352x15 + 11840x14 - 5376x13 - 8576x12 + 30208x11 - 56320x10 + 77824x9 - 78848x8 + 57344x7 - 8192x6 - 65536x5 + 139264x4 - 163840x3 + 163840x2 - 131072x + 65536 \( 2^{64}\cdot 5^{24}\cdot 17^{8} \) $C_2\times C_4\times D_4$ (as 32T204) $[5]$ (GRH)
32.0.14648040110065267094876580444599852735215435776.1 x32 - x16 + 1 \( 2^{128}\cdot 3^{16} \) $C_2^2\times C_8$ (as 32T37) $[3, 3]$ (GRH)
32.0.14680252274932068764306928624388060814210236416.1 x32 - 4x30 + 10x28 - 32x26 + 83x24 - 208x22 + 458x20 - 956x18 + 2113x16 - 3824x14 + 7328x12 - 13312x10 + 21248x8 - 32768x6 + 40960x4 - 65536x2 + 65536 \( 2^{72}\cdot 3^{16}\cdot 13^{8}\cdot 97^{4} \) 32T12882 $[4]$ (GRH)
32.0.23790908696561643372461609312578223409406672896.1 x32 - 8x30 + 32x28 - 80x26 + 127x24 - 80x22 - 224x20 + 936x18 - 2175x16 + 3744x14 - 3584x12 - 5120x10 + 32512x8 - 81920x6 + 131072x4 - 131072x2 + 65536 \( 2^{96}\cdot 3^{16}\cdot 17^{8} \) $C_2^2\times C_2^2:C_4$ (as 32T262) $[12]$ (GRH)
32.0.35190667333271321019306672876612934335729762304.1 x32 - x30 + x28 - x26 + x24 - x22 + x20 - x18 + x16 - x14 + x12 - x10 + x8 - x6 + x4 - x2 + 1 \( 2^{32}\cdot 17^{30} \) $C_2\times C_{16}$ (as 32T32) $[8]$ (GRH)
32.0.87993561227221187133696000000000000000000000000.1 x32 - 5x30 + 19x28 - 70x26 + 215x24 - 590x22 + 1466x20 - 3340x18 + 7009x16 - 13360x14 + 23456x12 - 37760x10 + 55040x8 - 71680x6 + 77824x4 - 81920x2 + 65536 \( 2^{32}\cdot 3^{16}\cdot 5^{24}\cdot 41^{8} \) $C_2^2\times C_2^2:C_4$ (as 32T262) $[4, 4]$ (GRH)
32.0.366225584701948244050176000000000000000000000000.1 x32 - 3x30 + 4x28 - 9x26 + 27x24 - 93x22 + 188x20 - 279x18 + 581x16 - 1116x14 + 3008x12 - 5952x10 + 6912x8 - 9216x6 + 16384x4 - 49152x2 + 65536 \( 2^{32}\cdot 3^{16}\cdot 5^{24}\cdot 7^{16} \) $C_2^3\times C_4$ (as 32T34) n/a
32.0.520402924666472696020370152488960000000000000000.1 x32 - 47x24 + 2208x16 - 47x8 + 1 \( 2^{96}\cdot 3^{16}\cdot 5^{16} \) $C_2^3\times C_4$ (as 32T34) $[20]$ (GRH)
32.0.550026747803854214004736000000000000000000000000.1 x32 + 6x28 + 315x24 - 2036x20 + 5109x16 - 2036x12 + 315x8 + 6x4 + 1 \( 2^{64}\cdot 5^{24}\cdot 29^{8} \) $C_2^2\times C_2^2:C_4$ (as 32T262) $[3, 6]$ (GRH)
32.0.845222867573683465013147373404160000000000000000.1 x32 - 6x30 - 64x29 + 18x28 + 120x27 + 884x26 + 1360x25 + 2453x24 - 592x23 + 11300x22 + 12152x21 - 15370x20 + 39248x19 + 6590x18 - 25344x17 + 75876x16 - 25344x15 + 6590x14 + 39248x13 - 15370x12 + 12152x11 + 11300x10 - 592x9 + 2453x8 + 1360x7 + 884x6 + 120x5 + 18x4 - 64x3 - 6x2 + 1 \( 2^{64}\cdot 3^{16}\cdot 5^{16}\cdot 17^{8} \) $C_2^3\times D_4$ (as 32T273) $[4, 4]$ (GRH)
32.0.1033818800357475102568684143000990752577071087616.1 x32 - 4x31 + 8x30 - 16x29 + 25x28 - 24x27 + 24x26 - 20x25 - 36x23 + 152x22 - 256x21 + 425x20 - 584x19 + 296x18 + 4x17 + 113x16 + 8x15 + 1184x14 - 4672x13 + 6800x12 - 8192x11 + 9728x10 - 4608x9 - 10240x7 + 24576x6 - 49152x5 + 102400x4 - 131072x3 + 131072x2 - 131072x + 65536 \( 2^{64}\cdot 3^{16}\cdot 41^{8}\cdot 113^{4} \) 32T12882 $[3, 6]$ (GRH)
32.0.1156745857256138299057661301456078800598048178176.1 x32 + 10x30 - 28x29 + 56x28 - 208x27 + 604x26 - 876x25 + 2547x24 - 5760x23 + 7684x22 - 11384x21 + 37676x20 - 21776x19 + 12262x18 - 135456x17 + 96553x16 + 443172x15 + 1107228x14 + 758160x13 - 662400x12 - 2309040x11 - 1681344x10 + 1407456x9 + 4596912x8 + 3872448x7 - 62208x6 - 4385664x5 - 3545856x4 + 3919104x2 + 3359232x + 1679616 \( 2^{72}\cdot 3^{16}\cdot 13^{8}\cdot 17^{8} \) $C_2\times D_4^2$ (as 32T1016) $[2, 6]$ (GRH)
32.0.1250223652010309685753479160887484565582275390625.1 x32 - x31 + 2x30 - 3x29 + 5x28 - 8x27 + 13x26 - 21x25 + 34x24 - 55x23 + 89x22 - 144x21 + 233x20 - 377x19 + 610x18 - 987x17 + 1597x16 + 987x15 + 610x14 + 377x13 + 233x12 + 144x11 + 89x10 + 55x9 + 34x8 + 21x7 + 13x6 + 8x5 + 5x4 + 3x3 + 2x2 + x + 1 \( 5^{16}\cdot 17^{30} \) $C_2\times C_{16}$ (as 32T32) $[17]$ (GRH)
32.0.1461501637330902918203684832716283019655932542976.1 x32 + 1 \( 2^{160} \) $C_2\times C_{16}$ (as 32T32) $[17]$ (GRH)
32.2.1478570811461626154162295475745342334411977277407.1 x32 - x - 1 \( -\,191\cdot 19329543076986451\cdot 400485847292917407445603765627 \) $S_{32}$ (as 32T2801324) Trivial (GRH)
32.0.2294081869728198830572049522437155246734619140625.1 x32 - 11x31 + 68x30 - 336x29 + 1315x28 - 4335x27 + 12498x26 - 30713x25 + 67152x24 - 127199x23 + 211471x22 - 307078x21 + 387026x20 - 419617x19 + 359728x18 - 149755x17 - 229142x16 + 581095x15 - 441722x14 - 315448x13 + 1021466x12 - 946897x11 + 366311x10 - 50246x9 + 132237x8 - 215882x7 + 157773x6 - 97500x5 + 79930x4 - 54894x3 + 25063x2 - 7709x + 3131 \( 3^{32}\cdot 5^{28}\cdot 7^{16} \) $C_8.A_4$ (as 32T402) Trivial (GRH)
32.0.5037920877776643425304576000000000000000000000000.1 x32 - 2x31 + 3x30 - 2x29 - 12x27 + 17x26 - 24x25 + 3x24 + 8x23 + 101x22 - 128x21 + 208x20 - 34x19 + 39x18 - 726x17 + 877x16 - 1452x15 + 156x14 - 272x13 + 3328x12 - 4096x11 + 6464x10 + 1024x9 + 768x8 - 12288x7 + 17408x6 - 24576x5 - 16384x3 + 49152x2 - 65536x + 65536 \( 2^{48}\cdot 3^{16}\cdot 5^{24}\cdot 17^{8} \) $C_2\times C_4\times D_4$ (as 32T204) $[4, 4]$ (GRH)
32.0.6142666889587199870339155304469168186187744140625.1 x32 - 4x31 + 38x30 - 130x29 + 699x28 - 2191x27 + 8745x26 - 25571x25 + 83386x24 - 222738x23 + 612551x22 - 1445800x21 + 3366820x20 - 6839883x19 + 13440516x18 - 23161945x17 + 38310126x16 - 55684805x15 + 77474162x14 - 94829103x13 + 110710129x12 - 113727761x11 + 110357640x10 - 94103904x9 + 74479117x8 - 51698016x7 + 32429638x6 - 17496051x5 + 7973462x4 - 3036857x3 + 868340x2 - 166271x + 16531 \( 5^{28}\cdot 67^{16} \) $C_8.A_4$ (as 32T402) Trivial (GRH)
32.0.6649076259173893054484111016591360000000000000000.1 x32 - 8x31 + 22x30 - 40x29 + 178x28 - 712x27 + 1264x26 + 844x25 - 9359x24 + 23304x23 - 31738x22 + 20712x21 + 4242x20 - 53384x19 + 309318x18 - 1090772x17 + 2225756x16 - 2949980x15 + 2866688x14 - 2095500x13 + 1173576x12 - 535544x11 + 258862x10 - 119572x9 + 42617x8 - 13676x7 + 3860x6 - 916x5 + 264x4 - 80x3 + 20x2 - 4x + 1 \( 2^{72}\cdot 3^{16}\cdot 5^{16}\cdot 11^{8} \) $C_2^3\times D_4$ (as 32T273) $[2, 12]$ (GRH)
32.0.7790452574060543254749837160138952789467349385216.1 x32 - 16x31 + 156x30 - 1096x29 + 6134x28 - 28580x27 + 114266x26 - 399684x25 + 1239490x24 - 3440780x23 + 8605010x22 - 19473044x21 + 39982438x20 - 74587072x19 + 126485556x18 - 194983784x17 + 273242634x16 - 348358772x15 + 405080242x14 - 431986068x13 + 426399702x12 - 394223580x11 + 344722538x10 - 285681476x9 + 222647745x8 - 160135088x7 + 103163456x6 - 57484000x5 + 26721528x4 - 9914240x3 + 2744800x2 - 506176x + 48016 \( 2^{64}\cdot 3^{24}\cdot 11^{8}\cdot 17^{8} \) $C_2\times D_4^2$ (as 32T1016) $[2, 12]$ (GRH)
32.0.8779518136340480467664896000000000000000000000000.1 x32 + 13x28 + 78x24 + 356x20 + 1505x16 + 5696x12 + 19968x8 + 53248x4 + 65536 \( 2^{64}\cdot 5^{24}\cdot 41^{8} \) $C_2^2\times C_2^2:C_4$ (as 32T262) $[2, 2, 8]$ (GRH)
32.0.36539993586348786372837376000000000000000000000000.1 x32 - x28 - 15x24 + 31x20 + 209x16 + 496x12 - 3840x8 - 4096x4 + 65536 \( 2^{64}\cdot 5^{24}\cdot 7^{16} \) $C_2^3\times C_4$ (as 32T34) n/a
32.0.42655280577413385127292283461599409580230712890625.1 x32 - 2x31 - 14x30 + 32x29 + 110x28 - 256x27 - 822x26 + 1761x25 + 5076x24 - 6234x23 - 33617x22 + 7049x21 + 145847x20 + 80587x19 - 200297x18 - 1040496x17 + 909785x16 - 126545x15 + 4807173x14 - 6468687x13 + 4092091x12 - 12326083x11 + 15573178x10 - 9966741x9 + 15430857x8 - 15762104x7 + 7858456x6 - 7358464x5 + 5444944x4 - 823424x3 + 88384x2 - 5760x + 256 \( 3^{16}\cdot 5^{24}\cdot 7^{16}\cdot 29^{8} \) $C_2^2\times C_2^2:C_4$ (as 32T262) n/a
32.0.44580746322432044939368312527587514829553937678336.1 x32 + 2x30 + 9x28 + 4x26 + 26x24 - 45x22 + 10x20 - 403x18 - 171x16 - 1612x14 + 160x12 - 2880x10 + 6656x8 + 4096x6 + 36864x4 + 32768x2 + 65536 \( 2^{32}\cdot 3^{24}\cdot 61^{16} \) $C_2^2\times \SL(2,3)$ (as 32T405) $[2, 10]$ (GRH)
32.0.51922968585348276285304963292200960000000000000000.1 x32 + 2207x16 + 1 \( 2^{128}\cdot 5^{16} \) $C_2^2\times C_8$ (as 32T37) $[17]$ (GRH)
32.0.59647719207059933350876409342295283657151229198336.1 x32 - x30 + x28 - 8x26 + 20x24 - 16x22 + 32x20 - 128x18 + 64x16 - 512x14 + 512x12 - 1024x10 + 5120x8 - 8192x6 + 4096x4 - 16384x2 + 65536 \( 2^{44}\cdot 3^{16}\cdot 4093^{8} \) 32T34907 $[2, 8]$ (GRH)
32.0.90220386589172305242198553166127486468521067544576.1 x32 - 4x28 + 22x24 - 36x20 + 209x16 - 576x12 + 5632x8 - 16384x4 + 65536 \( 2^{76}\cdot 89^{4}\cdot 257^{8} \) 32T96908 $[24]$ (GRH)
32.0.97424180758632937220739951448553101324025212174336.1 x32 - 10x28 + 27x24 + 150x20 - 1215x16 + 2400x12 + 6912x8 - 40960x4 + 65536 \( 2^{72}\cdot 223^{8}\cdot 241^{4} \) 32T96908 $[2, 8]$ (GRH)
32.0.111539154030155436264757885742310633531656776974336.1 x32 + 7x30 + 23x28 + 38x26 + 11x24 - 94x22 - 186x20 - 24x18 + 385x16 - 96x14 - 2976x12 - 6016x10 + 2816x8 + 38912x6 + 94208x4 + 114688x2 + 65536 \( 2^{32}\cdot 3^{16}\cdot 89^{4}\cdot 1327^{8} \) 32T96908 $[3, 6]$ (GRH)
32.0.113341328678310292663197722067951895712000278265856.1 x32 + 31x24 + 705x16 + 7936x8 + 65536 \( 2^{96}\cdot 3^{16}\cdot 7^{16} \) $C_2^3\times C_4$ (as 32T34) $[4, 4, 4]$ (GRH)
32.0.126945864674316252168838917102904812361796913463296.1 x32 + 2x30 + x28 - 6x26 - 28x24 - 58x22 + 9x20 + 230x18 + 593x16 + 920x14 + 144x12 - 3712x10 - 7168x8 - 6144x6 + 4096x4 + 32768x2 + 65536 \( 2^{32}\cdot 3^{16}\cdot 137^{4}\cdot 1087^{8} \) 32T96908 $[12]$ (GRH)
32.0.133516116647406931991162570051420160000000000000000.1 x32 - 2x31 - 16x30 + 24x29 + 141x28 - 120x27 - 852x26 - 70x25 + 4216x24 + 4978x23 - 15640x22 - 47344x21 + 45797x20 + 270436x19 - 110380x18 - 986938x17 + 284105x16 + 1973876x15 - 441520x14 - 2163488x13 + 732752x12 + 1515008x11 - 1000960x10 - 637184x9 + 1079296x8 + 35840x7 - 872448x6 + 245760x5 + 577536x4 - 196608x3 - 262144x2 + 65536x + 65536 \( 2^{48}\cdot 3^{16}\cdot 5^{16}\cdot 13^{8}\cdot 97^{4} \) 32T12882 $[20]$ (GRH)
32.0.170408552095468407540899423358812160000000000000000.1 x32 - 24x30 + 407x28 - 3048x26 + 15745x24 - 51120x22 + 120578x20 - 196608x18 + 236974x16 - 196608x14 + 120578x12 - 51120x10 + 15745x8 - 3048x6 + 407x4 - 24x2 + 1 \( 2^{64}\cdot 3^{24}\cdot 5^{16}\cdot 11^{8} \) $C_2^3\times D_4$ (as 32T273) $[2, 4, 8]$ (GRH)
32.0.184085596562491198850839682056048266622946116632576.1 x32 - 28x30 + 502x28 - 5304x26 + 40319x24 - 205348x22 + 769870x20 - 2005384x18 + 3886261x16 - 5310988x14 + 5324752x12 - 3494768x10 + 1644300x8 - 452512x6 + 81152x4 - 1184x2 + 16 \( 2^{64}\cdot 3^{16}\cdot 7^{16}\cdot 17^{8} \) $C_2^3\times D_4$ (as 32T273) n/a
32.0.272292877590407567597186433188495333554574218609249.1 x32 - x31 - x30 + 3x29 - x28 - 5x27 + 7x26 + 3x25 - 17x24 + 11x23 + 23x22 - 45x21 - x20 + 91x19 - 89x18 - 93x17 + 271x16 - 186x15 - 356x14 + 728x13 - 16x12 - 1440x11 + 1472x10 + 1408x9 - 4352x8 + 1536x7 + 7168x6 - 10240x5 - 4096x4 + 24576x3 - 16384x2 - 32768x + 65536 \( 7^{16}\cdot 17^{30} \) $C_2\times C_{16}$ (as 32T32) $[3, 15]$ (GRH)
32.0.301756981416745756154944013144439800625000000000000.1 x32 + 46x30 + 899x28 + 9779x26 + 65207x24 + 277346x22 + 763587x20 + 1370784x18 + 1627006x16 + 1296861x14 + 701262x12 + 257219x10 + 63092x8 + 10001x6 + 959x4 + 49x2 + 1 \( 2^{12}\cdot 3^{24}\cdot 5^{16}\cdot 41^{4}\cdot 167^{8} \) 32T96908 $[18]$ (GRH)
32.0.334285232879825411498534254159851729760457815228416.1 x32 - x30 - 3x28 + 20x26 - 12x24 - 64x22 + 160x20 + 64x18 - 704x16 + 256x14 + 2560x12 - 4096x10 - 3072x8 + 20480x6 - 12288x4 - 16384x2 + 65536 \( 2^{44}\cdot 3^{16}\cdot 5077^{8} \) 32T34907 $[4, 4]$ (GRH)
32.0.351509915919708142388734226325389286150171856470016.1 x32 + 8x24 + 64x20 + 16x16 + 1024x12 + 2048x8 + 65536 \( 2^{76}\cdot 17^{12}\cdot 41^{8} \) 32T96908 $[2, 24]$ (GRH)
32.0.361280028614042283247927296000000000000000000000000.1 x32 + 2x30 - 56x28 - 824x26 + 992x24 + 23552x22 + 121088x20 + 560896x18 + 1820416x16 + 2243584x14 + 1937408x12 + 1507328x10 + 253952x8 - 843776x6 - 229376x4 + 32768x2 + 65536 \( 2^{48}\cdot 3^{16}\cdot 5^{24}\cdot 29^{8} \) $C_2^2\times C_2^2:C_4$ (as 32T262) n/a
32.0.361280028614042283247927296000000000000000000000000.2 x32 - 2x30 - 56x28 + 824x26 + 992x24 - 23552x22 + 121088x20 - 560896x18 + 1820416x16 - 2243584x14 + 1937408x12 - 1507328x10 + 253952x8 + 843776x6 - 229376x4 - 32768x2 + 65536 \( 2^{48}\cdot 3^{16}\cdot 5^{24}\cdot 29^{8} \) $C_2^2\times C_2^2:C_4$ (as 32T262) n/a
32.0.368622913612148362854567389427658855145582683488256.1 x32 - 6x28 + 49x24 - 248x20 + 1072x16 - 3968x12 + 12544x8 - 24576x4 + 65536 \( 2^{64}\cdot 41^{4}\cdot 1277^{8} \) 32T96908 $[4, 8]$ (GRH)
32.0.385049567410499609358247677435067162906957579288576.1 x32 + 40x24 + 16x20 + 784x16 + 256x12 + 10240x8 + 65536 \( 2^{72}\cdot 17^{4}\cdot 997^{8} \) 32T96908 $[2, 20]$ (GRH)
32.0.480960519379403029833827263813614000556122650443776.1 x32 + 20x30 + 236x28 + 1948x26 + 12276x24 + 58148x22 + 212422x20 + 567784x18 + 1013620x16 + 772588x14 + 788932x12 + 1345276x10 + 364625x8 - 228564x6 + 145744x4 - 25856x2 + 4096 \( 2^{48}\cdot 3^{16}\cdot 13^{8}\cdot 17^{16} \) $C_2^2\times C_2^2\wr C_2$ (as 32T1369) $[2, 2, 4]$ (GRH)
32.0.480960519379403029833827263813614000556122650443776.2 x32 + 3x28 + 13x24 - 108x20 - 384x16 - 1728x12 + 3328x8 + 12288x4 + 65536 \( 2^{48}\cdot 3^{16}\cdot 13^{8}\cdot 17^{16} \) $C_2^2\times C_2^2\wr C_2$ (as 32T1369) $[2, 4, 8]$ (GRH)
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