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D9608 #34063509
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1209 points:
(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209);(2,8)(3,7)(4,6)(10,1209)(11,1208)(12,1207)(13,1206)(14,1205)(15,1204)(16,1203)(17,1202)(18,1201)(19,1200)(20,1199)(21,1198)(22,1197)(23,1196)(24,1195)(25,1194)(26,1193)(27,1192)(28,1191)(29,1190)(30,1189)(31,1188)(32,1187)(33,1186)(34,1185)(35,1184)(36,1183)(37,1182)(38,1181)(39,1180)(40,1179)(41,1178)(42,1177)(43,1176)(44,1175)(45,1174)(46,1173)(47,1172)(48,1171)(49,1170)(50,1169)(51,1168)(52,1167)(53,1166)(54,1165)(55,1164)(56,1163)(57,1162)(58,1161)(59,1160)(60,1159)(61,1158)(62,1157)(63,1156)(64,1155)(65,1154)(66,1153)(67,1152)(68,1151)(69,1150)(70,1149)(71,1148)(72,1147)(73,1146)(74,1145)(75,1144)(76,1143)(77,1142)(78,1141)(79,1140)(80,1139)(81,1138)(82,1137)(83,1136)(84,1135)(85,1134)(86,1133)(87,1132)(88,1131)(89,1130)(90,1129)(91,1128)(92,1127)(93,1126)(94,1125)(95,1124)(96,1123)(97,1122)(98,1121)(99,1120)(100,1119)(101,1118)(102,1117)(103,1116)(104,1115)(105,1114)(106,1113)(107,1112)(108,1111)(109,1110)(110,1109)(111,1108)(112,1107)(113,1106)(114,1105)(115,1104)(116,1103)(117,1102)(118,1101)(119,1100)(120,1099)(121,1098)(122,1097)(123,1096)(124,1095)(125,1094)(126,1093)(127,1092)(128,1091)(129,1090)(130,1089)(131,1088)(132,1087)(133,1086)(134,1085)(135,1084)(136,1083)(137,1082)(138,1081)(139,1080)(140,1079)(141,1078)(142,1077)(143,1076)(144,1075)(145,1074)(146,1073)(147,1072)(148,1071)(149,1070)(150,1069)(151,1068)(152,1067)(153,1066)(154,1065)(155,1064)(156,1063)(157,1062)(158,1061)(159,1060)(160,1059)(161,1058)(162,1057)(163,1056)(164,1055)(165,1054)(166,1053)(167,1052)(168,1051)(169,1050)(170,1049)(171,1048)(172,1047)(173,1046)(174,1045)(175,1044)(176,1043)(177,1042)(178,1041)(179,1040)(180,1039)(181,1038)(182,1037)(183,1036)(184,1035)(185,1034)(186,1033)(187,1032)(188,1031)(189,1030)(190,1029)(191,1028)(192,1027)(193,1026)(194,1025)(195,1024)(196,1023)(197,1022)(198,1021)(199,1020)(200,1019)(201,1018)(202,1017)(203,1016)(204,1015)(205,1014)(206,1013)(207,1012)(208,1011)(209,1010)(210,1009)(211,1008)(212,1007)(213,1006)(214,1005)(215,1004)(216,1003)(217,1002)(218,1001)(219,1000)(220,999)(221,998)(222,997)(223,996)(224,995)(225,994)(226,993)(227,992)(228,991)(229,990)(230,989)(231,988)(232,987)(233,986)(234,985)(235,984)(236,983)(237,982)(238,981)(239,980)(240,979)(241,978)(242,977)(243,976)(244,975)(245,974)(246,973)(247,972)(248,971)(249,970)(250,969)(251,968)(252,967)(253,966)(254,965)(255,964)(256,963)(257,962)(258,961)(259,960)(260,959)(261,958)(262,957)(263,956)(264,955)(265,954)(266,953)(267,952)(268,951)(269,950)(270,949)(271,948)(272,947)(273,946)(274,945)(275,944)(276,943)(277,942)(278,941)(279,940)(280,939)(281,938)(282,937)(283,936)(284,935)(285,934)(286,933)(287,932)(288,931)(289,930)(290,929)(291,928)(292,927)(293,926)(294,925)(295,924)(296,923)(297,922)(298,921)(299,920)(300,919)(301,918)(302,917)(303,916)(304,915)(305,914)(306,913)(307,912)(308,911)(309,910)(310,909)(311,908)(312,907)(313,906)(314,905)(315,904)(316,903)(317,902)(318,901)(319,900)(320,899)(321,898)(322,897)(323,896)(324,895)(325,894)(326,893)(327,892)(328,891)(329,890)(330,889)(331,888)(332,887)(333,886)(334,885)(335,884)(336,883)(337,882)(338,881)(339,880)(340,879)(341,878)(342,877)(343,876)(344,875)(345,874)(346,873)(347,872)(348,871)(349,870)(350,869)(351,868)(352,867)(353,866)(354,865)(355,864)(356,863)(357,862)(358,861)(359,860)(360,859)(361,858)(362,857)(363,856)(364,855)(365,854)(366,853)(367,852)(368,851)(369,850)(370,849)(371,848)(372,847)(373,846)(374,845)(375,844)(376,843)(377,842)(378,841)(379,840)(380,839)(381,838)(382,837)(383,836)(384,835)(385,834)(386,833)(387,832)(388,831)(389,830)(390,829)(391,828)(392,827)(393,826)(394,825)(395,824)(396,823)(397,822)(398,821)(399,820)(400,819)(401,818)(402,817)(403,816)(404,815)(405,814)(406,813)(407,812)(408,811)(409,810)(410,809)(411,808)(412,807)(413,806)(414,805)(415,804)(416,803)(417,802)(418,801)(419,800)(420,799)(421,798)(422,797)(423,796)(424,795)(425,794)(426,793)(427,792)(428,791)(429,790)(430,789)(431,788)(432,787)(433,786)(434,785)(435,784)(436,783)(437,782)(438,781)(439,780)(440,779)(441,778)(442,777)(443,776)(444,775)(445,774)(446,773)(447,772)(448,771)(449,770)(450,769)(451,768)(452,767)(453,766)(454,765)(455,764)(456,763)(457,762)(458,761)(459,760)(460,759)(461,758)(462,757)(463,756)(464,755)(465,754)(466,753)(467,752)(468,751)(469,750)(470,749)(471,748)(472,747)(473,746)(474,745)(475,744)(476,743)(477,742)(478,741)(479,740)(480,739)(481,738)(482,737)(483,736)(484,735)(485,734)(486,733)(487,732)(488,731)(489,730)(490,729)(491,728)(492,727)(493,726)(494,725)(495,724)(496,723)(497,722)(498,721)(499,720)(500,719)(501,718)(502,717)(503,716)(504,715)(505,714)(506,713)(507,712)(508,711)(509,710)(510,709)(511,708)(512,707)(513,706)(514,705)(515,704)(516,703)(517,702)(518,701)(519,700)(520,699)(521,698)(522,697)(523,696)(524,695)(525,694)(526,693)(527,692)(528,691)(529,690)(530,689)(531,688)(532,687)(533,686)(534,685)(535,684)(536,683)(537,682)(538,681)(539,680)(540,679)(541,678)(542,677)(543,676)(544,675)(545,674)(546,673)(547,672)(548,671)(549,670)(550,669)(551,668)(552,667)(553,666)(554,665)(555,664)(556,663)(557,662)(558,661)(559,660)(560,659)(561,658)(562,657)(563,656)(564,655)(565,654)(566,653)(567,652)(568,651)(569,650)(570,649)(571,648)(572,647)(573,646)(574,645)(575,644)(576,643)(577,642)(578,641)(579,640)(580,639)(581,638)(582,637)(583,636)(584,635)(585,634)(586,633)(587,632)(588,631)(589,630)(590,629)(591,628)(592,627)(593,626)(594,625)(595,624)(596,623)(597,622)(598,621)(599,620)(600,619)(601,618)(602,617)(603,616)(604,615)(605,614)(606,613)(607,612)(608,611)(609,610)
Polycyclic presentation:
2^4,1201|c^2=d,b^a=bc,c^a=cd,e^a=e^1200,c^b=cd,e^b=e^1200
Conjugacy classes & character table
4807 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19216, 26);
Finite Group Databasebeta