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Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1672 points:
(2,3)(5,6,8)(7,10,15)(9,13,12)(11,17,25)(14,20,22)(16,23,19)(18,27,38)(21,30,35)(24,33,32)(26,36,29)(28,40,54)(31,43,51)(34,46,48)(37,49,45)(39,52,42)(41,56,73)(44,59,70)(47,62,67)(50,65,64)(53,68,61)(55,71,58)(57,75,95)(60,78,92)(63,81,89)(66,84,86)(69,87,83)(72,90,80)(74,93,77)(76,97,120)(79,100,117)(82,103,114)(85,106,111)(88,109,108)(91,112,105)(94,115,102)(96,118,99)(98,122,148)(101,125,145)(104,128,142)(107,131,139)(110,134,136)(113,137,133)(116,140,130)(119,143,127)(121,146,124)(123,150,179)(126,153,176)(129,156,173)(132,159,170)(135,162,167)(138,165,164)(141,168,161)(144,171,158)(147,174,155)(149,177,152)(151,181,213)(154,184,210)(157,187,207)(160,190,204)(163,193,201)(166,196,198)(169,199,195)(172,202,192)(175,205,189)(178,208,186)(180,211,183)(182,215,250)(185,218,247)(188,221,244)(191,224,241)(194,227,238)(197,230,235)(200,233,232)(203,236,229)(206,239,226)(209,242,223)(212,245,220)(214,248,217)(216,252,290)(219,255,287)(222,258,284)(225,261,281)(228,264,278)(231,267,275)(234,270,272)(237,273,269)(240,276,266)(243,279,263)(246,282,260)(249,285,257)(251,288,254)(253,292,333)(256,295,330)(259,298,327)(262,301,324)(265,304,321)(268,307,318)(271,310,315)(274,313,312)(277,316,309)(280,319,306)(283,322,303)(286,325,300)(289,328,297)(291,331,294)(293,335,379)(296,338,376)(299,341,373)(302,344,370)(305,347,367)(308,350,364)(311,353,361)(314,356,358)(317,359,355)(320,362,352)(323,365,349)(326,368,346)(329,371,343)(332,374,340)(334,377,337)(336,381,428)(339,384,425)(342,387,422)(345,390,419)(348,393,416)(351,396,413)(354,399,410)(357,402,407)(360,405,404)(363,408,401)(366,411,398)(369,414,395)(372,417,392)(375,420,389)(378,423,386)(380,426,383)(382,430,480)(385,433,477)(388,436,474)(391,439,471)(394,442,468)(397,445,465)(400,448,462)(403,451,459)(406,454,456)(409,457,453)(412,460,450)(415,463,447)(418,466,444)(421,469,441)(424,472,438)(427,475,435)(429,478,432)(431,482,535)(434,485,532)(437,488,529)(440,491,526)(443,494,523)(446,497,520)(449,500,517)(452,503,514)(455,506,511)(458,509,508)(461,512,505)(464,515,502)(467,518,499)(470,521,496)(473,524,493)(476,527,490)(479,530,487)(481,533,484)(483,537,593)(486,540,590)(489,543,587)(492,546,584)(495,549,581)(498,552,578)(501,555,575)(504,558,572)(507,561,569)(510,564,566)(513,567,563)(516,570,560)(519,573,557)(522,576,554)(525,579,551)(528,582,548)(531,585,545)(534,588,542)(536,591,539)(538,595,654)(541,598,651)(544,601,648)(547,604,645)(550,607,642)(553,610,639)(556,613,636)(559,616,633)(562,619,630)(565,622,627)(568,625,624)(571,628,621)(574,631,618)(577,634,615)(580,637,612)(583,640,609)(586,643,606)(589,646,603)(592,649,600)(594,652,597)(596,656,718)(599,659,715)(602,662,712)(605,665,709)(608,668,706)(611,671,703)(614,674,700)(617,677,697)(620,680,694)(623,683,691)(626,686,688)(629,689,685)(632,692,682)(635,695,679)(638,698,676)(641,701,673)(644,704,670)(647,707,667)(650,710,664)(653,713,661)(655,716,658)(657,720,785)(660,723,782)(663,726,779)(666,729,776)(669,732,773)(672,735,770)(675,738,767)(678,741,764)(681,744,761)(684,747,758)(687,750,755)(690,753,752)(693,756,749)(696,759,746)(699,762,743)(702,765,740)(705,768,737)(708,771,734)(711,774,731)(714,777,728)(717,780,725)(719,783,722)(721,787,855)(724,790,852)(727,793,849)(730,796,846)(733,799,843)(736,802,840)(739,805,837)(742,808,834)(745,811,831)(748,814,828)(751,817,825)(754,820,822)(757,823,819)(760,826,816)(763,829,813)(766,832,810)(769,835,807)(772,838,804)(775,841,801)(778,844,798)(781,847,795)(784,850,792)(786,853,789)(788,857,927)(791,860,924)(794,863,922)(797,866,919)(800,869,916)(803,872,913)(806,875,910)(809,878,907)(812,881,904)(815,884,901)(818,887,898)(821,890,895)(824,893,892)(827,896,889)(830,899,886)(833,902,883)(836,905,880)(839,908,877)(842,911,874)(845,914,871)(848,917,868)(851,920,865)(854,858,862)(856,925,859)(861,930,996)(864,933,994)(867,936,992)(870,939,989)(873,942,986)(876,945,983)(879,948,980)(882,951,977)(885,954,974)(888,957,971)(891,960,968)(894,963,965)(897,966,962)(900,969,959)(903,972,956)(906,975,953)(909,978,950)(912,981,947)(915,984,944)(918,987,941)(921,990,938)(923,931,935)(926,995,932)(928,997,929)(934,1000,1061)(937,1002,1060)(940,1005,1058)(943,1008,1055)(946,1011,1052)(949,1014,1049)(952,1017,1046)(955,1020,1043)(958,1023,1040)(961,1026,1037)(964,1029,1034)(967,1032,1031)(970,1035,1028)(973,1038,1025)(976,1041,1022)(979,1044,1019)(982,1047,1016)(985,1050,1013)(988,1053,1010)(991,1056,1007)(993,1001,1004)(998,1062,999)(1003,1063,1121)(1006,1065,1120)(1009,1068,1118)(1012,1071,1115)(1015,1074,1112)(1018,1077,1109)(1021,1080,1106)(1024,1083,1103)(1027,1086,1100)(1030,1089,1097)(1033,1092,1094)(1036,1095,1091)(1039,1098,1088)(1042,1101,1085)(1045,1104,1082)(1048,1107,1079)(1051,1110,1076)(1054,1113,1073)(1057,1116,1070)(1059,1064,1067)(1066,1122,1177)(1069,1124,1176)(1072,1127,1174)(1075,1130,1171)(1078,1133,1168)(1081,1136,1165)(1084,1139,1162)(1087,1142,1159)(1090,1145,1156)(1093,1148,1153)(1096,1151,1150)(1099,1154,1147)(1102,1157,1144)(1105,1160,1141)(1108,1163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1,1257,1151,1032,893,753,625,509,405,313,233,165,109,65,33,13)
Conjugacy classes & character table
1677 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30042, 10);
Finite Group Databasebeta