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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 762 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,176)(123,150,173)(126,153,170)(129,156,167)(132,159,164)(135,162,161)(138,165,158)(141,168,155)(144,171,152)(146,174,149)(148,178,210)(151,181,207)(154,184,204)(157,187,201)(160,190,198)(163,193,195)(166,196,192)(169,199,189)(172,202,186)(175,205,183)(177,208,180)(179,212,247)(182,215,244)(185,218,241)(188,221,238)(191,224,235)(194,227,232)(197,230,229)(200,233,226)(203,236,223)(206,239,220)(209,242,217)(211,245,214)(213,249,287)(216,252,284)(219,255,281)(222,258,278)(225,261,275)(228,264,272)(231,267,269)(234,270,266)(237,273,263)(240,276,260)(243,279,257)(246,282,254)(248,285,251)(250,289,330)(253,292,327)(256,295,324)(259,298,321)(262,301,318)(265,304,315)(268,307,312)(271,310,309)(274,313,306)(277,316,303)(280,319,300)(283,322,297)(286,325,294)(288,328,291)(290,332,376)(293,335,373)(296,338,370)(299,341,367)(302,344,364)(305,347,361)(308,350,358)(311,353,355)(314,356,352)(317,359,349)(320,362,346)(323,365,343)(326,368,340)(329,371,337)(331,374,334)(333,378,425)(336,381,422)(339,384,419)(342,387,416)(345,390,413)(348,393,410)(351,396,407)(354,399,404)(357,402,401)(360,405,398)(363,408,395)(366,411,392)(369,414,389)(372,417,386)(375,420,383)(377,423,380)(379,427,439)(382,429,473)(385,432,470)(388,435,467)(391,438,464)(394,441,461)(397,444,458)(400,447,455)(403,450,452)(406,453,449)(409,456,446)(412,459,443)(415,462,440)(418,465,437)(421,468,434)(424,471,431)(426,474,428)(430,478,486)(433,480,519)(436,483,516)(442,488,511)(445,491,508)(448,494,505)(451,497,502)(454,500,499)(457,503,496)(460,506,493)(463,509,490)(466,512,487)(469,514,485)(472,517,482)(475,520,479)(476,489,477)(481,524,529)(484,526,559)(492,532,552)(495,535,549)(498,538,546)(501,541,543)(504,544,540)(507,547,537)(510,550,534)(513,553,531)(515,555,530)(518,557,528)(521,560,525)(522,533,523)(527,564,566)(536,570,587)(539,573,584)(542,576,581)(545,579,578)(548,582,575)(551,585,572)(554,588,569)(556,590,568)(558,592,567)(561,594,565)(562,571,563)(574,602,616)(577,605,613)(580,608,610)(583,611,607)(586,614,604)(589,617,601)(591,619,600)(593,621,599)(595,623,598)(596,603,597)(606,631,642)(609,634,639)(612,637,636)(615,640,633)(618,643,630)(620,645,629)(622,647,628)(624,649,627)(625,632,626)(635,657,665)(638,660,662)(641,663,659)(644,666,656)(646,668,655)(648,670,654)(650,672,653)(651,658,652)(661,680,685)(664,683,682)(667,686,679)(669,688,678)(671,690,677)(673,692,676)(674,681,675)(684,700,702)(687,703,699)(689,705,698)(691,707,697)(693,709,696)(694,701,695)(704,717,716)(706,719,715)(708,721,714)(710,723,713)(711,718,712)(720,730,729)(722,732,728)(724,734,727)(725,731,726)(733,740,739)(735,742,738)(736,741,737)(743,747,746)(744,748,745)(749,751,750)(752,756,760,754,759,755,757,753,758)(761,762);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,333,379,387,295,215,147,177,209,243,280,320,363,409,457,504,545,580,609,635,658,623,557,468,371,285,210,244,281,321,364,410,458,505,546,581,610,636,659,679,698,714,727,737,730,703,663,611,544,453,356,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,334,380,428,477,438,341,255,181,119,146,175,206,240,277,317,360,406,454,501,542,577,606,632,594,517,420,328,247,284,324,367,413,461,508,549,584,613,639,662,682,699,715,728,738,745,740,719,686,640,582,503,405,313,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,431,479,523,488,390,298,218,150,94,118,144,172,203,237,274,314,357,403,451,498,539,574,603,560,471,374,287,327,370,416,464,511,552,587,616,642,665,685,702,716,729,739,746,750,747,732,705,666,614,547,456,359,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,340,386,434,482,525,563,532,441,344,258,184,122,72,93,116,141,169,200,234,271,311,354,400,448,495,536,571,520,423,330,373,419,467,427,476,522,562,596,625,651,674,694,711,725,736,744,749,751,742,721,688,643,585,506,408,316,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,343,389,437,485,528,565,597,570,491,393,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,397,445,492,533,474,376,422,470,516,478,378,426,475,521,561,595,624,650,673,693,710,724,735,743,748,734,707,668,617,550,459,362,276,202,140,90,51,67,86,108,133,161,192,226,263,303,346,392,440,487,530,567,598,626,602,535,444,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,394,442,489,425,473,519,559,524,429,332,377,424,472,518,558,593,622,648,671,691,708,722,733,741,723,690,645,588,509,411,319,239,171,115,70,89,111,136,164,195,229,266,306,349,395,443,490,531,568,599,627,652,631,573,494,396,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,391,439,486,529,566,564,480,381,289,331,375,421,469,515,556,591,620,646,669,689,706,720,731,709,670,619,553,462,365,279,205,143,92,114,139,167,198,232,269,309,352,398,446,493,534,569,600,628,653,675,657,605,538,447,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,388,436,484,527,526,432,335,249,288,329,372,418,466,513,554,589,618,644,667,687,704,718,692,647,590,512,414,322,242,174,117,142,170,201,235,272,312,355,401,449,496,537,572,601,629,654,676,695,680,634,576,497,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,433,481,483,384,292,212,248,286,326,369,415,463,510,551,586,615,641,664,684,701,672,621,555,465,368,282,208,145,173,204,238,275,315,358,404,452,499,540,575,604,630,655,677,696,712,700,660,608,541,450,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,430,435,338,252,178,211,246,283,323,366,412,460,507,548,583,612,638,661,681,649,592,514,417,325,245,176,207,241,278,318,361,407,455,502,543,578,607,633,656,678,697,713,726,717,683,637,579,500,402,310,230,162,106,62,30,10)
Conjugacy classes & character table
1518 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13518, 3);
Finite Group Databasebeta