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