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Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 5827 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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5635,5667,5696,5722,5745,5765,5782,5796,5807,5785,5746,5695,5632,5557,5461,5341,5197,5029,4838,4623,4384,4121,3834,3539,3255,2983,2723,2475,2239,2015,1803,1603,1415,1239,1075,923,782,849,919,992,1068,1147,1229,1314,1402,1493,1587,1684,1784,1887,1993,2102,2214,2329,2447,2568,2692,2819,2949,3082,3218,3357,3499,3644,3791,3937,4077,4211,4341,4465,4583,4695,4801,4901,4995,5083,5165,5241,5311,5375,5433,5485,5531,5571,5608,5642,5673,5652,5583,5499,5391,5259,5103,4923,4719,4491,4239,3962,3666,3376,3098,2832,2578,2336,2106,1888,1682,1488,1306,1136,978,832,698,576,466,368,282,208,145,173,204,238,275,315,358,404,453,505,560,618,679,743,810,880,953,1029,1108,1190,1275,1363,1454,1548,1645,1745,1848,1954,2063,2175,2290,2408,2529,2653,2780,2910,3043,3179,3318,3460,3605,3752,3899,4041,4177,4307,4431,4549,4661,4767,4868,4807,4590,4349,4084,3795,3500,3216,2944,2684,2436,2200,1976,1764,1564,1376,1200,1036,884,744,616,500,396,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,605,666,730,797,867,940,1016,1095,1177,1262,1350,1441,1535,1632,1732,1835,1941,2050,2162,2277,2395,2516,2640,2767,2897,3030,3166,3305,3447,3592,3739,3886,4028,4164,4205,3924,3627,3337,3059,2793,2539,2297,2067,1849,1643,1449,1267,1097,939,793,659,537,427,478,531,586,644,705,769,836,906,979,1055,1134,1216,1301,1389,1480,1574,1671,1771,1874,1980,2089,2201,2316,2434,2555,2679,2806,2936,3069,3205,3344,3486,3631,3778,3925,4067,4203,4333,4457,4575,4687,4793,4893,4987,5075,5157,5233,5303,5367,5425,5427,5302,5153,4980,4783,4562,4317,4048,3756,3461,3177,2905,2645,2397,2161,1937,1725,1525,1337,1427,1519,1613,1710,1810,1913,2019,2128,2240,2355,2473,2594,2718,2845,2975,3108,3244,3383,3525,3670,3817,3963,4103,4237,4365,4487,4603,4713,4817,4915,5007,5093,4962,4759,4532,4281,4006,3711,3421,3143,2877,2623,2380,2498,2619,2743,2870,3000,3133,3269,3408,3550,3695,3842,3987,4126,4259,4386,4507,4622,4731,4657,4423,4166,3885,3588,3298,3020,2754,2883,3014,3147,3283,3422,3564,3709,3856,4001,4140,4273,4400,4521,4636,4745,4848,4945,5036,5121,5200,5274,5342,5404,5460,5510,5554,5592,5627,5659,5688,5714,5737,5699,5636,5561,5465,5345,5202,5035,4844,4629,4390,4127,3840,3545,3261,2989,2729,2481,2245,2021,1809,1609,1421,1245,1080,1159,1241,1326,1414,1505,1599,1696,1796,1899,2005,2114,2226,2341,2459,2580,2704,2831,2961,3094,3230,3369,3511,3656,3803,3949,4089,4223,4351,4473,4589,4699,4805,4905,4999,5087,5169,5245,5315,5379,5437,5489,5535,5575,5612,5646,5677,5705,5730,5752,5771,5758,5713,5656,5587,5503,5395,5263,5107,4927,4723,4495,4243,3967,3672,3382,3104,2838,2584,2342,2112,1894,1688,1494,1312,1142,984,838,704,582,472,374,287,327,370,416,465,517,572,630,691,755,822,892,965,1041,1120,1202,1287,1375,1466,1560,1657,1757,1860,1966,2075,2187,2302,2420,2541,2665,2792,2922,3055,3191,3330,3472,3617,3764,3911,4053,4189,4319,4443,4561,4673,4779,4879,4973,5061,5143,5220,5175,5006,4813,4596,4355,4090,3801,3506,3222,2950,2690,2442,2206,1982,1770,1570,1382,1206,1042,890,750,622,506,402,310,230,162,106,62,30,10)
Polycyclic presentation:
3,5827|b^a=b^1350
Conjugacy classes & character table
1945 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17481, 1);
Finite Group Databasebeta