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Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 6007 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,176)(123,150,173)(126,153,170)(129,156,167)(132,159,164)(135,162,161)(138,165,158)(141,168,155)(144,171,152)(146,174,149)(148,178,210)(151,181,207)(154,184,204)(157,187,201)(160,190,198)(163,193,195)(166,196,192)(169,199,189)(172,202,186)(175,205,183)(177,208,180)(179,212,247)(182,215,244)(185,218,241)(188,221,238)(191,224,235)(194,227,232)(197,230,229)(200,233,226)(203,236,223)(206,239,220)(209,242,217)(211,245,214)(213,249,287)(216,252,284)(219,255,281)(222,258,278)(225,261,275)(228,264,272)(231,267,269)(234,270,266)(237,273,263)(240,276,260)(243,279,257)(246,282,254)(248,285,251)(250,289,330)(253,292,327)(256,295,324)(259,298,321)(262,301,318)(265,304,315)(268,307,312)(271,310,309)(274,313,306)(277,316,303)(280,319,300)(283,322,297)(286,325,294)(288,328,291)(290,332,376)(293,335,373)(296,338,370)(299,341,367)(302,344,364)(305,347,361)(308,350,358)(311,353,355)(314,356,352)(317,359,349)(320,362,346)(323,365,343)(326,368,340)(329,371,337)(331,374,334)(333,378,425)(336,381,422)(339,384,419)(342,387,416)(345,390,413)(348,393,410)(351,396,407)(354,399,404)(357,402,401)(360,405,398)(363,408,395)(366,411,392)(369,414,389)(372,417,386)(375,420,383)(377,423,380)(379,427,477)(382,430,474)(385,433,471)(388,436,468)(391,439,465)(394,442,462)(397,445,459)(400,448,456)(403,451,453)(406,454,450)(409,457,447)(412,460,444)(415,463,441)(418,466,438)(421,469,435)(424,472,432)(426,475,429)(428,479,532)(431,482,529)(434,485,526)(437,488,523)(440,491,520)(443,494,517)(446,497,514)(449,500,511)(452,503,508)(455,506,505)(458,509,502)(461,512,499)(464,515,496)(467,518,493)(470,521,490)(473,524,487)(476,527,484)(478,530,481)(480,534,590)(483,537,587)(486,540,584)(489,543,581)(492,546,578)(495,549,575)(498,552,572)(501,555,569)(504,558,566)(507,561,563)(510,564,560)(513,567,557)(516,570,554)(519,573,551)(522,576,548)(525,579,545)(528,582,542)(531,585,539)(533,588,536)(535,592,651)(538,595,648)(541,598,645)(544,601,642)(547,604,639)(550,607,636)(553,610,633)(556,613,630)(559,616,627)(562,619,624)(565,622,621)(568,625,618)(571,628,615)(574,631,612)(577,634,609)(580,637,606)(583,640,603)(586,643,600)(589,646,597)(591,649,594)(593,653,715)(596,656,712)(599,659,709)(602,662,706)(605,665,703)(608,668,700)(611,671,697)(614,674,694)(617,677,691)(620,680,688)(623,683,685)(626,686,682)(629,689,679)(632,692,676)(635,695,673)(638,698,670)(641,701,667)(644,704,664)(647,707,661)(650,710,658)(652,713,655)(654,717,782)(657,720,779)(660,723,776)(663,726,773)(666,729,770)(669,732,767)(672,735,764)(675,738,761)(678,741,758)(681,744,755)(684,747,752)(687,750,749)(690,753,746)(693,756,743)(696,759,740)(699,762,737)(702,765,734)(705,768,731)(708,771,728)(711,774,725)(714,777,722)(716,780,719)(718,784,852)(721,787,849)(724,790,846)(727,793,843)(730,796,840)(733,799,837)(736,802,834)(739,805,831)(742,808,828)(745,811,825)(748,814,822)(751,817,819)(754,820,816)(757,823,813)(760,826,810)(763,829,807)(766,832,804)(769,835,801)(772,838,798)(775,841,795)(778,844,792)(781,847,789)(783,850,786)(785,854,925)(788,857,922)(791,860,919)(794,863,916)(797,866,913)(800,869,910)(803,872,907)(806,875,904)(809,878,901)(812,881,898)(815,884,895)(818,887,892)(821,890,889)(824,893,886)(827,896,883)(830,899,880)(833,902,877)(836,905,874)(839,908,871)(842,911,868)(845,914,865)(848,917,862)(851,920,859)(853,923,856)(855,927,1001)(858,930,998)(861,933,995)(864,936,992)(867,939,989)(870,942,986)(873,945,983)(876,948,980)(879,951,977)(882,954,974)(885,957,971)(888,960,968)(891,963,965)(894,966,962)(897,969,959)(900,972,956)(903,975,953)(906,978,950)(909,981,947)(912,984,944)(915,987,941)(918,990,938)(921,993,935)(924,996,932)(926,999,929)(928,1003,1080)(931,1006,1077)(934,1009,1074)(937,1012,1071)(940,1015,1068)(943,1018,1065)(946,1021,1062)(949,1024,1059)(952,1027,1056)(955,1030,1053)(958,1033,1050)(961,1036,1047)(964,1039,1044)(967,1042,1041)(970,1045,1038)(973,1048,1035)(976,1051,1032)(979,1054,1029)(982,1057,1026)(985,1060,1023)(988,1063,1020)(991,1066,1017)(994,1069,1014)(997,1072,1011)(1000,1075,1008)(1002,1078,1005)(1004,1082,1162)(1007,1085,1159)(1010,1088,1156)(1013,1091,1153)(1016,1094,1150)(1019,1097,1147)(1022,1100,1144)(1025,1103,1141)(1028,1106,1138)(1031,1109,1135)(1034,1112,1132)(1037,1115,1129)(1040,1118,1126)(1043,1121,1123)(1046,1124,1120)(1049,1127,1117)(1052,1130,1114)(1055,1133,1111)(1058,1136,1108)(1061,1139,1105)(1064,1142,1102)(1067,1145,1099)(1070,1148,1096)(1073,1151,1093)(1076,1154,1090)(1079,1157,1087)(1081,1160,1084)(1083,1164,1247)(1086,1167,1244)(1089,1170,1241)(1092,11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0,3196,3335,3477,3622,3770,3921,4072,4220,4362,4498,4628,4752,4870,4982,5088,5188,5282,5370,5452,5528,5402,5217,5008,4775,4518,4237,3935,3633,3343,3065,2799,2545,2303,2073,1855,1649,1455,1273,1103,945,799,665,543,433,335,249,288,329,372,418,467,519,574,632,693,757,824,894,967,1043,1122,1204,1289,1377,1468,1562,1659,1759,1862,1968,2077,2189,2304,2422,2543,2667,2794,2924,3057,3193,3332,3474,3619,3767,3918,4069,4217,4359,4495,4625,4749,4867,4979,5085,5185,5279,5367,5449,5314,5117,4896,4651,4382,4089,3784,3488,3204,2932,2672,2424,2188,1964,1752,1552,1364,1188,1024,872,732,604,488,384,292,212,248,286,326,369,415,464,516,571,629,690,754,821,891,964,1040,1119,1201,1286,1374,1465,1559,1656,1756,1859,1965,2074,2186,2301,2419,2540,2664,2791,2921,3054,3190,3329,3471,3616,3764,3915,4066,4214,4356,4492,4622,4746,4864,4976,5082,5182,5276,5364,5220,5011,4778,4521,4240,3938,3636,3346,3068,2802,2548,2306,2076,1858,1652,1458,1276,1106,948,802,668,546,436,338,252,178,211,246,283,323,366,412,461,513,568,626,687,751,818,888,961,1037,1116,1198,1283,1371,1462,1556,1653,1753,1856,1962,2071,2183,2298,2416,2537,2661,2788,2918,3051,3187,3326,3468,3613,3761,3912,4063,4211,4353,4489,4619,4743,4861,4973,5079,5179,5273,5120,4899,4654,4385,4092,3787,3491,3207,2935,2675,2427,2191,1967,1755,1555,1367,1191,1027,875,735,607,491,387,295,215,147,177,209,243,280,320,363,409,458,510,565,623,684,748,815,885,958,1034,1113,1195,1280,1368,1459,1553,1650,1750,1853,1959,2068,2180,2295,2413,2534,2658,2785,2915,3048,3184,3323,3465,3610,3758,3909,4060,4208,4350,4486,4616,4740,4858,4970,5076,5176,5014,4781,4524,4243,3941,3639,3349,3071,2805,2551,2309,2079,1861,1655,1461,1279,1109,951,805,671,549,439,341,255,181,119,146,175,206,240,277,317,360,406,455,507,562,620,681,745,812,882,955,1031,1110,1192,1277,1365,1456,1550,1647,1747,1850,1956,2065,2177,2292,2410,2531,2655,2782,2912,3045,3181,3320,3462,3607,3755,3906,4057,4205,4347,4483,4613,4737,4855,4967,5073,4902,4657,4388,4095,3790,3494,3210,2938,2678,2430,2194,1970,1758,1558,1370,1194,1030,878,738,610,494,390,298,218,150,94,118,144,172,203,237,274,314,357,403,452,504,559,617,678,742,809,879,952,1028,1107,1189,1274,1362,1453,1547,1644,1744,1847,1953,2062,2174,2289,2407,2528,2652,2779,2909,3042,3178,3317,3459,3604,3752,3903,4054,4202,4344,4480,4610,4734,4852,4964,4784,4527,4246,3944,3642,3352,3074,2808,2554,2312,2082,1864,1658,1464,1282,1112,954,808,674,552,442,344,258,184,122,72,93,116,141,169,200,234,271,311,354,400,449,501,556,614,675,739,806,876,949,1025,1104,1186,1271,1359,1450,1544,1641,1741,1844,1950,2059,2171,2286,2404,2525,2649,2776,2906,3039,3175,3314,3456,3601,3749,3900,4051,4199,4341,4477,4607,4731,4849,4660,4391,4098,3793,3497,3213,2941,2681,2433,2197,1973,1761,1561,1373,1197,1033,881,741,613,497,393,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,397,446,498,553,611,672,736,803,873,946,1022,1101,1183,1268,1356,1447,1541,1638,1738,1841,1947,2056,2168,2283,2401,2522,2646,2773,2903,3036,3172,3311,3453,3598,3746,3897,4048,4196,4338,4474,4604,4728,4530,4249,3947,3645,3355,3077,2811,2557,2315,2085,1867,1661,1467,1285,1115,957,811,677,555,445,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,394,443,495,550,608,669,733,800,870,943,1019,1098,1180,1265,1353,1444,1538,1635,1735,1838,1944,2053,2165,2280,2398,2519,2643,2770,2900,3033,3169,3308,3450,3595,3743,3894,4045,4193,4335,4471,4601,4394,4101,3796,3500,3216,2944,2684,2436,2200,1976,1764,1564,1376,1200,1036,884,744,616,500,396,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,605,666,730,797,867,940,1016,1095,1177,1262,1350,1441,1535,1632,1732,1835,1941,2050,2162,2277,2395,2516,2640,2767,2897,3030,3166,3305,3447,3592,3740,3891,4042,4190,4332,4468,4252,3950,3648,3358,3080,2814,2560,2318,2088,1870,1664,1470,1288,1118,960,814,680,558,448,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,544,602,663,727,794,864,937,1013,1092,1174,1259,1347,1438,1532,1629,1729,1832,1938,2047,2159,2274,2392,2513,2637,2764,2894,3027,3163,3302,3444,3589,3737,3888,4039,4187,4329,4104,3799,3503,3219,2947,2687,2439,2203,1979,1767,1567,1379,1203,1039,887,747,619,503,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,660,724,791,861,934,1010,1089,1171,1256,1344,1435,1529,1626,1726,1829,1935,2044,2156,2271,2389,2510,2634,2761,2891,3024,3160,3299,3441,3586,3734,3885,4036,4184,3953,3651,3361,3083,2817,2563,2321,2091,1873,1667,1473,1291,1121,963,817,683,561,451,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,657,721,788,858,931,1007,1086,1168,1253,1341,1432,1526,1623,1723,1826,1932,2041,2153,2268,2386,2507,2631,2758,2888,3021,3157,3296,3438,3583,3731,3882,4033,3802,3506,3222,2950,2690,2442,2206,1982,1770,1570,1382,1206,1042,890,750,622,506,402,310,230,162,106,62,30,10)
Polycyclic presentation:
3,6007|b^a=b^5929
Conjugacy classes & character table
2005 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18021, 1);
Finite Group Databasebeta