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D8197 #30655869
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1178 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);(2,7)(3,6)(4,5)(9,1178)(10,1177)(11,1176)(12,1175)(13,1174)(14,1173)(15,1172)(16,1171)(17,1170)(18,1169)(19,1168)(20,1167)(21,1166)(22,1165)(23,1164)(24,1163)(25,1162)(26,1161)(27,1160)(28,1159)(29,1158)(30,1157)(31,1156)(32,1155)(33,1154)(34,1153)(35,1152)(36,1151)(37,1150)(38,1149)(39,1148)(40,1147)(41,1146)(42,1145)(43,1144)(44,1143)(45,1142)(46,1141)(47,1140)(48,1139)(49,1138)(50,1137)(51,1136)(52,1135)(53,1134)(54,1133)(55,1132)(56,1131)(57,1130)(58,1129)(59,1128)(60,1127)(61,1126)(62,1125)(63,1124)(64,1123)(65,1122)(66,1121)(67,1120)(68,1119)(69,1118)(70,1117)(71,1116)(72,1115)(73,1114)(74,1113)(75,1112)(76,1111)(77,1110)(78,1109)(79,1108)(80,1107)(81,1106)(82,1105)(83,1104)(84,1103)(85,1102)(86,1101)(87,1100)(88,1099)(89,1098)(90,1097)(91,1096)(92,1095)(93,1094)(94,1093)(95,1092)(96,1091)(97,1090)(98,1089)(99,1088)(100,1087)(101,1086)(102,1085)(103,1084)(104,1083)(105,1082)(106,1081)(107,1080)(108,1079)(109,1078)(110,1077)(111,1076)(112,1075)(113,1074)(114,1073)(115,1072)(116,1071)(117,1070)(118,1069)(119,1068)(120,1067)(121,1066)(122,1065)(123,1064)(124,1063)(125,1062)(126,1061)(127,1060)(128,1059)(129,1058)(130,1057)(131,1056)(132,1055)(133,1054)(134,1053)(135,1052)(136,1051)(137,1050)(138,1049)(139,1048)(140,1047)(141,1046)(142,1045)(143,1044)(144,1043)(145,1042)(146,1041)(147,1040)(148,1039)(149,1038)(150,1037)(151,1036)(152,1035)(153,1034)(154,1033)(155,1032)(156,1031)(157,1030)(158,1029)(159,1028)(160,1027)(161,1026)(162,1025)(163,1024)(164,1023)(165,1022)(166,1021)(167,1020)(168,1019)(169,1018)(170,1017)(171,1016)(172,1015)(173,1014)(174,1013)(175,1012)(176,1011)(177,1010)(178,1009)(179,1008)(180,1007)(181,1006)(182,1005)(183,1004)(184,1003)(185,1002)(186,1001)(187,1000)(188,999)(189,998)(190,997)(191,996)(192,995)(193,994)(194,993)(195,992)(196,991)(197,990)(198,989)(199,988)(200,987)(201,986)(202,985)(203,984)(204,983)(205,982)(206,981)(207,980)(208,979)(209,978)(210,977)(211,976)(212,975)(213,974)(214,973)(215,972)(216,971)(217,970)(218,969)(219,968)(220,967)(221,966)(222,965)(223,964)(224,963)(225,962)(226,961)(227,960)(228,959)(229,958)(230,957)(231,956)(232,955)(233,954)(234,953)(235,952)(236,951)(237,950)(238,949)(239,948)(240,947)(241,946)(242,945)(243,944)(244,943)(245,942)(246,941)(247,940)(248,939)(249,938)(250,937)(251,936)(252,935)(253,934)(254,933)(255,932)(256,931)(257,930)(258,929)(259,928)(260,927)(261,926)(262,925)(263,924)(264,923)(265,922)(266,921)(267,920)(268,919)(269,918)(270,917)(271,916)(272,915)(273,914)(274,913)(275,912)(276,911)(277,910)(278,909)(279,908)(280,907)(281,906)(282,905)(283,904)(284,903)(285,902)(286,901)(287,900)(288,899)(289,898)(290,897)(291,896)(292,895)(293,894)(294,893)(295,892)(296,891)(297,890)(298,889)(299,888)(300,887)(301,886)(302,885)(303,884)(304,883)(305,882)(306,881)(307,880)(308,879)(309,878)(310,877)(311,876)(312,875)(313,874)(314,873)(315,872)(316,871)(317,870)(318,869)(319,868)(320,867)(321,866)(322,865)(323,864)(324,863)(325,862)(326,861)(327,860)(328,859)(329,858)(330,857)(331,856)(332,855)(333,854)(334,853)(335,852)(336,851)(337,850)(338,849)(339,848)(340,847)(341,846)(342,845)(343,844)(344,843)(345,842)(346,841)(347,840)(348,839)(349,838)(350,837)(351,836)(352,835)(353,834)(354,833)(355,832)(356,831)(357,830)(358,829)(359,828)(360,827)(361,826)(362,825)(363,824)(364,823)(365,822)(366,821)(367,820)(368,819)(369,818)(370,817)(371,816)(372,815)(373,814)(374,813)(375,812)(376,811)(377,810)(378,809)(379,808)(380,807)(381,806)(382,805)(383,804)(384,803)(385,802)(386,801)(387,800)(388,799)(389,798)(390,797)(391,796)(392,795)(393,794)(394,793)(395,792)(396,791)(397,790)(398,789)(399,788)(400,787)(401,786)(402,785)(403,784)(404,783)(405,782)(406,781)(407,780)(408,779)(409,778)(410,777)(411,776)(412,775)(413,774)(414,773)(415,772)(416,771)(417,770)(418,769)(419,768)(420,767)(421,766)(422,765)(423,764)(424,763)(425,762)(426,761)(427,760)(428,759)(429,758)(430,757)(431,756)(432,755)(433,754)(434,753)(435,752)(436,751)(437,750)(438,749)(439,748)(440,747)(441,746)(442,745)(443,744)(444,743)(445,742)(446,741)(447,740)(448,739)(449,738)(450,737)(451,736)(452,735)(453,734)(454,733)(455,732)(456,731)(457,730)(458,729)(459,728)(460,727)(461,726)(462,725)(463,724)(464,723)(465,722)(466,721)(467,720)(468,719)(469,718)(470,717)(471,716)(472,715)(473,714)(474,713)(475,712)(476,711)(477,710)(478,709)(479,708)(480,707)(481,706)(482,705)(483,704)(484,703)(485,702)(486,701)(487,700)(488,699)(489,698)(490,697)(491,696)(492,695)(493,694)(494,693)(495,692)(496,691)(497,690)(498,689)(499,688)(500,687)(501,686)(502,685)(503,684)(504,683)(505,682)(506,681)(507,680)(508,679)(509,678)(510,677)(511,676)(512,675)(513,674)(514,673)(515,672)(516,671)(517,670)(518,669)(519,668)(520,667)(521,666)(522,665)(523,664)(524,663)(525,662)(526,661)(527,660)(528,659)(529,658)(530,657)(531,656)(532,655)(533,654)(534,653)(535,652)(536,651)(537,650)(538,649)(539,648)(540,647)(541,646)(542,645)(543,644)(544,643)(545,642)(546,641)(547,640)(548,639)(549,638)(550,637)(551,636)(552,635)(553,634)(554,633)(555,632)(556,631)(557,630)(558,629)(559,628)(560,627)(561,626)(562,625)(563,624)(564,623)(565,622)(566,621)(567,620)(568,619)(569,618)(570,617)(571,616)(572,615)(573,614)(574,613)(575,612)(576,611)(577,610)(578,609)(579,608)(580,607)(581,606)(582,605)(583,604)(584,603)(585,602)(586,601)(587,600)(588,599)(589,598)(590,597)(591,596)(592,595)(593,594)
Polycyclic presentation:
2,7,1171|b^a=b^6,c^a=c^1170
Conjugacy classes & character table
4100 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16394, 3);
Finite Group Databasebeta