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Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 955 points:
(2,3,5,9,17,33,65)(4,7,13,25,49,97,186)(6,11,21,41,81,154,126)(8,15,29,57,113,216,382)(10,19,37,73,64,66,127)(12,23,45,89,170,305,332)(14,27,53,105,200,352,234)(16,31,61,120,226,396,618)(18,35,69,132,34,67,129)(20,39,77,147,268,187,179)(22,43,85,162,84,160,235)(24,47,93,178,321,523,600)(26,51,101,192,276,128,236)(28,55,109,208,366,363,535)(30,59,116,220,387,605,403)(32,63,123,230,377,595,119)(36,71,136,249,98,188,334)(38,75,143,260,155,279,238)(40,79,62,121,227,383,100)(42,83,158,284,125,130,239)(44,87,166,298,293,483,322)(46,91,174,313,439,557,404)(48,95,182,327,530,754,825)(50,99,189,335,68,131,241)(52,103,196,344,547,333,324)(54,107,204,358,565,288,405)(56,111,212,374,591,803,810)(58,114,217,384,602,237,406)(60,118,223,392,612,820,756)(70,134,246,82,156,281,243)(72,138,225,96,184,329,532)(74,141,257,140,185,133,244)(76,145,264,443,306,480,537)(78,149,272,456,353,558,407)(80,152,183,328,531,619,642)(86,164,294,203,161,289,408)(88,168,277,330,533,746,191)(90,172,309,502,464,240,409)(92,176,317,516,703,573,525)(94,180,323,526,749,813,625)(102,194,341,543,280,467,410)(104,198,348,499,709,601,195)(106,202,355,561,233,242,411)(108,206,362,571,788,702,527)(110,210,370,583,734,772,626)(112,214,378,536,529,115,218)(117,221,389,609,817,477,627)(122,228,398,603,308,416,636)(124,231,400,606,452,628,151)(135,248,420,171,307,500,538)(137,251,425,201,354,560,413)(139,254,429,450,397,620,827)(142,259,435,269,451,336,375)(144,262,440,291,165,296,414)(146,266,447,412,524,209,368)(148,270,453,339,465,245,415)(150,274,460,685,578,575,757)(153,278,379,580,759,808,229)(157,283,470,422,190,337,540)(159,286,474,437,282,468,417)(163,292,173,311,331,247,418)(167,300,493,511,660,773,629)(169,303,498,608,816,906,839)(175,315,512,681,780,478,630)(177,319,520,621,828,930,338)(181,325,528,752,903,937,748)(193,340,497,256,381,250,423)(197,346,550,767,559,774,631)(199,350,555,729,856,826,840)(205,360,568,784,290,479,632)(207,364,574,747,371,585,343)(211,372,587,798,793,791,751)(213,376,593,806,932,936,829)(215,380,597,761,431,617,395)(219,385,320,521,745,811,347)(222,390,463,690,874,879,753)(224,393,614,822,939,912,830)(232,401,623,818,710,706,836)(252,427,649,367,579,588,758)(253,399,304,388,607,815,633)(255,430,651,764,596,541,326)(258,433,261,438,285,472,432)(263,442,664,490,486,705,592)(265,445,669,509,663,775,634)(267,449,674,657,755,686,869)(271,455,678,548,765,539,594)(273,458,682,566,781,487,635)(275,462,688,695,804,845,581)(287,476,699,666,501,720,760)(295,485,369,357,297,488,637)(299,491,492,712,691,419,638)(301,495,643,342,545,763,481)(302,466,598,796,901,675,831)(310,504,724,762,469,693,639)(312,507,653,441,662,484,361)(314,510,668,776,534,421,640)(316,514,659,475,697,661,482)(318,518,740,883,891,913,832)(345,549,766,542,692,424,644)(349,554,723,888,814,677,833)(351,556,771,894,951,934,402)(356,563,779,658,471,694,646)(359,567,783,506,599,426,647)(365,576,792,902,741,896,942)(373,589,801,907,872,949,546)(386,604,590,802,929,940,943)(391,611,718,886,944,797,552)(394,615,770,616,823,927,905)(428,624,577,613,821,938,908)(434,654,444,667,503,722,719)(436,656,457,680,562,777,652)(446,671,862,737,880,800,805)(448,672,641,750,517,738,834)(454,676,544,744,473,696,655)(459,684,868,789,925,881,807)(461,687,871,794,892,914,835)(489,708,838,513,732,870,922)(494,714,739,865,919,707,837)(496,717,843,569,786,924,564)(505,645,842,553,721,887,812)(508,728,851,683,866,785,923)(515,735,853,704,586,582,570)(519,742,857,725,889,909,701)(522,610,819,935,726,824,622)(551,769,911,782,920,716,841)(572,790,926,882,875,648,844)(584,795,898,915,809,650,846)(665,855,713,733,858,916,848)(670,860,731,867,921,727,849)(673,863,847,904,799,928,931)(679,864,768,910,778,917,850)(689,873,878,933,947,895,941)(698,876,854,711,715,885,900)(700,877,859,730,861,918,852)(736,893,945,884,897,948,952)(743,899,946,890,950,953,787)(954,955);(1,2,4,8,16,32,64,125,233,279,289,478,547,418,637,781,919,576,745,516,737,894,790,593,136,250,424,645,93,179,322,525,748,89,171,308,270,454,677,685,221,145,265,446,241,410,631,833,319,387,606,814,620,568,785,903,423,643,840,942,604,430,554,97,187,333,536,143,261,439,660,109,209,369,582,793,889,862,947,118,224,394,616,154,160,288,477,246,417,565,780,364,575,763,909,874,571,789,217,380,598,504,725,186,332,535,756,636,836,602,147,269,452,675,116,75,144,263,248,421,641,676,176,318,519,743,396,619,826,940,249,422,642,839,385,254,348,553,409,630,832,220,388,608,510,730,523,746,585,797,724,885,932,59,117,222,391,120,83,159,287,259,436,657,680,206,363,573,791,927,779,918,939,214,379,309,503,723,563,362,572,415,635,835,941,556,605,813,936,37,74,142,134,247,419,453,91,175,316,515,736,887,855,945,806,933,618,825,218,138,253,428,239,408,629,831,303,498,313,509,729,567,370,584,796,714,884,29,58,115,219,386,41,82,157,141,258,434,456,107,205,361,570,787,888,860,946,111,213,377,596,651,355,562,778,244,414,634,834,350,520,744,900,873,917,374,69,133,245,416,45,90,173,312,508,720,664,854,926,877,899,822,114,71,137,252,129,238,407,628,168,302,497,719,674,358,566,782,597,493,713,883,769,528,346,551,406,627,830,73,140,256,431,53,106,203,357,564,722,669,859,55,110,211,373,590,530,755,907,132,243,413,633,198,349,543,762,688,777,916,113,184,330,307,501,721,531,360,569,500,705,881,951,699,742,898,57,35,70,135,131,242,412,451,87,167,301,496,718,560,775,914,384,603,812,935,550,768,196,345,236,405,626,829,278,466,692,875,863,532,368,581,502,712,882,27,54,108,207,365,577,656,851,591,804,886,821,103,197,347,552,770,561,776,915,95,183,170,306,499,354,204,359,533,485,704,880,623,518,741,897,17,34,68,67,130,240,268,43,86,165,297,489,709,662,853,925,876,893,929,752,904,938,928,127,235,404,625,152,277,465,691,672,774,208,367,580,491,711,13,26,52,104,199,351,435,655,850,694,717,612,51,102,195,343,546,764,667,857,47,94,181,326,429,200,353,559,329,294,484,703,545,317,517,739,687,872,950,33,66,128,237,21,42,84,161,290,480,440,661,788,697,735,892,911,846,944,798,65,126,234,403,79,151,276,464,447,558,773,913,378,298,490,710,549,323,194,342,401,476,700,878,470,495,716,25,50,100,191,338,541,443,666,23,46,92,177,320,522,654,849,216,383,601,811,341,544,749,901,460,686,870,948,63,124,232,402,624,327,202,356,305,483,702,879,474,514,734,891,649,845,924,953,823,690,771,39,78,150,275,463,352,557,772,912,540,760,817,344,548,101,193,231,286,475,698,398,300,494,715,671,382,600,810,595,808,934,11,22,44,88,169,304,433,653,848,693,708,792,526,750,902,795,614,754,906,896,31,62,122,229,399,622,105,201,328,292,482,701,400,315,513,733,684,803,930,949,615,462,689,19,38,76,146,267,450,438,659,852,696,728,801,910,844,820,937,123,158,285,473,337,166,299,492,445,670,861,868,376,594,807,5,10,20,40,80,153,257,432,652,468,488,707,766,640,838,583,794,802,819,740,15,30,60,119,225,395,617,824,182,162,291,481,340,174,314,511,458,683,867,871,393,274,461,9,18,36,72,139,255,260,437,658,472,507,727,767,647,843,923,952,226,397,621,189,336,539,759,264,444,668,858,212,375,592,805,931,178,99,190,228,283,471,695,281,296,487,706,420,639,783,921,589,609,818,7,14,28,56,112,215,381,599,809,334,537,757,192,339,542,761,272,457,681,865,223,149,273,459,427,650,847,864,325,529,753,905,284,311,506,726,425,646,784,922,611,449,555,321,524,747,579,389,610,816,732,890,335,538,758,908,842,49,98,121,156,282,469,227,164,295,486,442,665,856,866,372,588,800,3,6,12,24,48,96,185,331,534,467,479,574,765,638,837,920,392,613,815,738,895,77,148,271,251,426,648,678,180,324,527,751,230,172,310,505,455,679,827,869,390,266,448,673,411,632,366,578,521,607,512,731,828,786,587,799,644,841,943,61,81,155,280,188,85,163,293,262,441,663,682,210,371,586)
Conjugacy classes & character table
286 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13342, 2);
Finite Group Databasebeta