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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 696 points:
(2,3)(4,5)(7,8,10,14,22)(9,12,18,30,53)(11,16,26,45,38)(13,20,34,61,60)(15,24,41,23,39)(17,28,49,87,95)(19,32,57,102,69)(21,36,65,116,199)(25,43,76,54,96)(27,47,83,80,70)(29,51,91,158,108)(31,55,98,40,71)(33,59,106,184,166)(35,63,112,192,124)(37,67,120,206,329)(42,74,46,81,73)(44,78,136,109,115)(48,85,147,151,167)(50,89,154,177,125)(52,93,162,163,267)(56,100,173,97,168)(58,104,180,140,126)(62,110,157,72,127)(64,114,196,317,273)(66,118,203,325,214)(68,122,210,336,307)(75,131,88,152,170)(77,134,103,178,129)(79,138,231,200,320)(82,142,133,99,171)(84,145,144,141,130)(86,149,246,259,198)(90,156,256,298,274)(92,160,262,310,215)(94,164,269,380,473)(101,175,285,188,205)(105,182,294,250,275)(107,186,301,288,216)(111,190,304,169,276)(113,194,313,235,217)(117,201,321,128,218)(119,204,327,471,410)(121,208,333,479,344)(123,212,340,489,525)(132,223,159,260,258)(135,227,185,299,278)(137,229,193,311,220)(139,233,362,330,474)(143,238,228,189,265)(146,241,243,251,279)(148,244,253,289,221)(150,248,379,268,401)(153,176,282,172,280)(155,254,291,236,222)(161,264,397,462,411)(165,271,406,541,450)(174,283,179,290,225)(181,292,240,237,226)(183,296,436,391,328)(187,303,445,439,412)(191,308,451,305,335)(195,315,458,383,413)(197,213,342,428,345)(202,323,466,277,414)(207,331,475,219,346)(209,334,481,603,549)(211,338,486,467,495)(224,352,266,270,404)(230,358,318,463,416)(232,360,326,470,348)(234,364,508,483,452)(239,369,359,322,465)(242,372,376,392,399)(245,375,388,440,417)(247,377,394,453,349)(249,381,520,519,596)(252,297,424,306,402)(255,309,433,384,418)(257,389,442,429,350)(261,385,447,281,419)(263,395,455,366,351)(272,408,545,643,631)(284,423,300,441,421)(286,425,312,454,354)(287,422,293,432,374)(295,434,386,430,355)(302,443,431,367,356)(314,456,371,368,357)(316,460,589,528,482)(319,409,547,573,550)(324,468,593,448,488)(332,477,599,415,551)(337,484,459,347,496)(339,487,608,600,648)(341,490,610,544,615)(343,493,566,511,503)(353,499,403,521,597)(361,504,472,595,553)(363,506,480,602,497)(365,510,622,609,632)(370,512,505,476,598)(373,514,518,405,539)(378,517,533,591,554)(382,522,629,639,584)(387,461,569,529,537)(390,469,578,574,555)(393,526,583,449,540)(396,530,587,524,556)(398,534,492,564,498)(400,407,543,420,557)(426,563,464,592,559)(427,561,444,577,567)(435,568,527,575,560)(437,570,531,585,501)(438,562,457,586,516)(446,579,576,565,502)(478,601,669,581,612)(485,606,548,552,649)(491,611,674,683,689)(494,613,657,572,656)(500,617,542,640,588)(507,618,604,671,650)(509,620,607,594,616)(513,624,619,605,590)(515,625,627,628,667)(523,614,675,687,684)(532,634,664,633,638)(535,636,646,659,651)(536,546,644,582,642)(538,630,668,558,652)(571,658,635,666,654)(580,662,661,660,655)(621,678,672,670,690)(623,679,673,645,677)(626,681,682,685,665)(637,676,692,663,688)(641,686,647,653,691)(680,695,693,694,696);(1,2,4,5,3)(6,7,9,13,21,37,68,123,213,343,494,614,676,694,695,414,147,243,374,516,114,197,319,451,583,78,137,230,311,453,201,322,419,556,651,598,667,118,87,151,250,383,85,148,245,313,455,203,326,423,561,655,599,668,120,207,332,478,346,89,155,255,387,526,632,684,425,562,640,685,675,290,430,565,479,352,91,159,261,393,530,55,99,172,281,420,558,653,292,22,38,69,124,214,344,495,615,534,57,103,179,122,211,339,488,294,433,567,657,358,503,606,593,644,238,368,511,470,164,270,405,540,638,460,590,665,360,184,298,439,573,241,8,11,17,29,52,94,165,272,409,548,647,362,505,608,672,551,244,10,15,25,44,79,139,234,365,138,232,361,454,585,323,467,557,246,376,489,609,204,152,251,384,524,149,247,378,456,53,95,166,273,410,549,648,689,208,154,253,386,496,156,257,390,458,587,327,472,563,656,686,669,692,210,337,485,602,499,160,263,396,532,634,100,174,284,317,462,206,330,432,39,70,125,215,162,266,400,536,636,104,181,293,212,341,491,612,434,41,73,129,220,348,497,616,677,369,106,185,300,271,407,544,642,436,569,643,687,504,299,440,574,659,372,12,19,33,60,108,61,109,188,305,448,581,506,301,442,576,649,375,16,27,48,86,150,249,382,523,233,363,507,508,619,468,594,652,377,18,31,56,101,176,287,427,471,248,380,519,586,96,167,274,411,379,518,610,673,334,254,14,23,40,72,128,219,347,98,170,278,416,553,650,690,696,338,256,388,527,617,264,398,535,589,664,175,286,426,463,591,331,476,340,71,126,216,199,267,158,259,391,528,182,295,435,342,492,333,480,568,74,130,221,349,269,403,538,637,512,186,302,444,408,546,645,688,570,76,133,225,354,441,575,660,603,514,20,35,64,115,198,110,189,306,449,582,663,618,443,45,80,140,235,28,50,90,157,258,112,193,312,364,509,621,620,445,578,661,691,517,32,58,105,183,297,438,572,595,381,521,628,622,168,275,412,329,473,34,62,111,191,309,24,42,75,132,224,353,500,171,279,417,554,520,627,674,693,487,389,26,46,82,143,239,370,513,173,282,421,559,592,666,477,600,490,127,217,345,320,401,260,392,529,633,296,437,571,493,102,177,288,428,131,222,350,321,404,262,394,531,624,303,446,580,547,646,481,604,658,134,226,355,501,406,542,641,671,625,36,66,119,205,328,190,307,450,136,228,336,483,577,81,141,236,366,51,92,161,265,399,194,314,457,510,623,680,678,579,83,144,240,371,59,107,187,304,447,196,318,464,522,630,683,679,276,413,550,474,596,63,113,195,316,461,43,77,135,192,310,116,200,280,418,555,475,597,65,117,202,324,469,47,84,146,242,373,515,626,283,422,560,654,629,682,601,670,611,218,49,88,153,252,385,525,631,285,424,541,639,613,178,289,429,564,223,351,498,465,539,395,30,54,97,169,277,415,552,180,291,431,566,227,356,502,466,543,397,533,635,681,67,121,209,335,482,308,452,584,229,357,484,605,545,142,237,367,325,93,163,268,402,537,315,459,588,231,359,486,607,662,145)
Conjugacy classes & character table
572 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34550, 10);
Finite Group Databasebeta