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Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 650 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)(290,332,375)(293,335,372)(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)(329,333,337)(331,373,334)(336,378,417)(339,381,415)(342,384,413)(345,387,410)(348,390,407)(351,393,404)(354,396,401)(357,399,398)(360,402,395)(363,405,392)(366,408,389)(369,411,386)(371,379,383)(374,416,380)(376,418,377)(382,421,455)(385,423,454)(388,426,452)(391,429,449)(394,432,446)(397,435,443)(400,438,440)(403,441,437)(406,444,434)(409,447,431)(412,450,428)(414,422,425)(419,456,420)(424,457,488)(427,459,487)(430,462,485)(433,465,482)(436,468,479)(439,471,476)(442,474,473)(445,477,470)(448,480,467)(451,483,464)(453,458,461)(460,489,517)(463,491,516)(466,494,514)(469,497,511)(472,500,508)(475,503,505)(478,506,502)(481,509,499)(484,512,496)(486,490,493)(492,518,543)(495,520,542)(498,523,540)(501,526,537)(504,529,534)(507,532,531)(510,535,528)(513,538,525)(515,519,522)(521,544,566)(524,546,565)(527,549,563)(530,552,560)(533,555,557)(536,558,554)(539,561,551)(541,545,548)(547,567,586)(550,569,585)(553,572,583)(556,575,580)(559,578,577)(562,581,574)(564,568,571)(570,587,603)(573,589,602)(576,592,600)(579,595,597)(582,598,594)(584,588,591)(590,604,617)(593,606,616)(596,609,614)(599,612,611)(601,605,608)(607,618,628)(610,620,627)(613,623,625)(615,619,622)(621,629,636)(624,631,635)(626,630,633)(632,637,641)(634,638,640)(639,642,643)(644,645,646,647,648,649,650);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,333,285,210,244,281,321,364,407,446,479,508,534,557,577,594,608,587,546,494,429,344,258,184,122,72,93,116,141,169,200,234,271,311,354,397,436,469,498,524,547,568,538,480,405,316,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,343,386,425,378,289,331,374,375,417,455,488,517,543,566,586,603,617,628,636,641,643,637,620,592,552,500,435,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,385,424,458,411,322,242,174,117,142,170,201,235,272,312,355,398,437,470,499,525,548,518,459,384,295,215,147,177,209,243,280,320,363,406,445,478,507,533,556,576,593,607,619,598,558,506,441,356,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,334,377,416,328,247,284,324,367,410,449,482,511,537,560,580,597,611,622,604,569,523,465,390,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,394,433,466,495,521,545,512,447,362,276,202,140,90,51,67,86,108,133,161,192,226,263,303,346,389,428,461,421,335,249,288,329,371,414,453,486,515,541,564,584,601,615,626,634,639,642,631,609,575,529,471,396,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,382,422,368,282,208,145,173,204,238,275,315,358,401,440,473,502,528,551,571,544,491,426,341,255,181,119,146,175,206,240,277,317,360,403,442,475,504,530,553,573,590,605,581,535,477,402,313,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,337,380,420,456,373,287,327,370,413,452,485,514,540,563,583,600,614,625,633,618,589,549,497,432,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,391,430,463,492,519,483,408,319,239,171,115,70,89,111,136,164,195,229,266,306,349,392,431,464,493,457,381,292,212,248,286,326,369,412,451,484,513,539,562,582,599,613,624,632,638,623,595,555,503,438,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,379,325,245,176,207,241,278,318,361,404,443,476,505,531,554,574,591,567,520,462,387,298,218,150,94,118,144,172,203,237,274,314,357,400,439,472,501,527,550,570,588,561,509,444,359,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,340,383,332,376,419,418,330,372,415,454,487,516,542,565,585,602,616,627,635,640,629,606,572,526,468,393,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,388,427,460,490,450,365,279,205,143,92,114,139,167,198,232,269,309,352,395,434,467,496,522,489,423,338,252,178,211,246,283,323,366,409,448,481,510,536,559,579,596,610,621,630,612,578,532,474,399,310,230,162,106,62,30,10)
Conjugacy classes & character table
1519 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13503, 2);
Finite Group Databasebeta