Polytope of Type {4,16,14} with group SmallGroup(1792,323449)

Overview

Group: SmallGroup(1792,323449)
Rank: 4
Schläfli Type: {4,16,14}
Vertices, edges, …: 4, 32, 112, 14
Order of s₀s₁s₂s₃: 112
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{4,8,14}*896a

4-fold

7-fold

{4,16,2}*256b

8-fold

14-fold

{4,8,2}*128a

16-fold

28-fold

32-fold

{2,2,7}*56

56-fold

112-fold

{2,2,2}*16

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (  1,225)(  2,226)(  3,227)(  4,228)(  5,229)(  6,230)(  7,231)(  8,232)(  9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)( 16,240)( 17,241)( 18,242)( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)( 24,248)( 25,249)( 26,250)( 27,251)( 28,252)( 29,253)( 30,254)( 31,255)( 32,256)( 33,257)( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)( 40,264)( 41,265)( 42,266)( 43,267)( 44,268)( 45,269)( 46,270)( 47,271)( 48,272)( 49,273)( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)( 56,280)( 57,288)( 58,289)( 59,290)( 60,291)( 61,292)( 62,293)( 63,294)( 64,281)( 65,282)( 66,283)( 67,284)( 68,285)( 69,286)( 70,287)( 71,302)( 72,303)( 73,304)( 74,305)( 75,306)( 76,307)( 77,308)( 78,295)( 79,296)( 80,297)( 81,298)( 82,299)( 83,300)( 84,301)( 85,316)( 86,317)( 87,318)( 88,319)( 89,320)( 90,321)( 91,322)( 92,309)( 93,310)( 94,311)( 95,312)( 96,313)( 97,314)( 98,315)( 99,330)(100,331)(101,332)(102,333)(103,334)(104,335)(105,336)(106,323)(107,324)(108,325)(109,326)(110,327)(111,328)(112,329)(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)(121,345)(122,346)(123,347)(124,348)(125,349)(126,350)(127,351)(128,352)(129,353)(130,354)(131,355)(132,356)(133,357)(134,358)(135,359)(136,360)(137,361)(138,362)(139,363)(140,364)(141,365)(142,366)(143,367)(144,368)(145,369)(146,370)(147,371)(148,372)(149,373)(150,374)(151,375)(152,376)(153,377)(154,378)(155,379)(156,380)(157,381)(158,382)(159,383)(160,384)(161,385)(162,386)(163,387)(164,388)(165,389)(166,390)(167,391)(168,392)(169,400)(170,401)(171,402)(172,403)(173,404)(174,405)(175,406)(176,393)(177,394)(178,395)(179,396)(180,397)(181,398)(182,399)(183,414)(184,415)(185,416)(186,417)(187,418)(188,419)(189,420)(190,407)(191,408)(192,409)(193,410)(194,411)(195,412)(196,413)(197,428)(198,429)(199,430)(200,431)(201,432)(202,433)(203,434)(204,421)(205,422)(206,423)(207,424)(208,425)(209,426)(210,427)(211,442)(212,443)(213,444)(214,445)(215,446)(216,447)(217,448)(218,435)(219,436)(220,437)(221,438)(222,439)(223,440)(224,441)(449,673)(450,674)(451,675)(452,676)(453,677)(454,678)(455,679)(456,680)(457,681)(458,682)(459,683)(460,684)(461,685)(462,686)(463,687)(464,688)(465,689)(466,690)(467,691)(468,692)(469,693)(470,694)(471,695)(472,696)(473,697)(474,698)(475,699)(476,700)(477,701)(478,702)(479,703)(480,704)(481,705)(482,706)(483,707)(484,708)(485,709)(486,710)(487,711)(488,712)(489,713)(490,714)(491,715)(492,716)(493,717)(494,718)(495,719)(496,720)(497,721)(498,722)(499,723)(500,724)(501,725)(502,726)(503,727)(504,728)(505,736)(506,737)(507,738)(508,739)(509,740)(510,741)(511,742)(512,729)(513,730)(514,731)(515,732)(516,733)(517,734)(518,735)(519,750)(520,751)(521,752)(522,753)(523,754)(524,755)(525,756)(526,743)(527,744)(528,745)(529,746)(530,747)(531,748)(532,749)(533,764)(534,765)(535,766)(536,767)(537,768)(538,769)(539,770)(540,757)(541,758)(542,759)(543,760)(544,761)(545,762)(546,763)(547,778)(548,779)(549,780)(550,781)(551,782)(552,783)(553,784)(554,771)(555,772)(556,773)(557,774)(558,775)(559,776)(560,777)(561,785)(562,786)(563,787)(564,788)(565,789)(566,790)(567,791)(568,792)(569,793)(570,794)(571,795)(572,796)(573,797)(574,798)(575,799)(576,800)(577,801)(578,802)(579,803)(580,804)(581,805)(582,806)(583,807)(584,808)(585,809)(586,810)(587,811)(588,812)(589,813)(590,814)(591,815)(592,816)(593,817)(594,818)(595,819)(596,820)(597,821)(598,822)(599,823)(600,824)(601,825)(602,826)(603,827)(604,828)(605,829)(606,830)(607,831)(608,832)(609,833)(610,834)(611,835)(612,836)(613,837)(614,838)(615,839)(616,840)(617,848)(618,849)(619,850)(620,851)(621,852)(622,853)(623,854)(624,841)(625,842)(626,843)(627,844)(628,845)(629,846)(630,847)(631,862)(632,863)(633,864)(634,865)(635,866)(636,867)(637,868)(638,855)(639,856)(640,857)(641,858)(642,859)(643,860)(644,861)(645,876)(646,877)(647,878)(648,879)(649,880)(650,881)(651,882)(652,869)(653,870)(654,871)(655,872)(656,873)(657,874)(658,875)(659,890)(660,891)(661,892)(662,893)(663,894)(664,895)(665,896)(666,883)(667,884)(668,885)(669,886)(670,887)(671,888)(672,889);;
s1 := ( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 43, 50)( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 57, 71)( 58, 72)( 59, 73)( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)( 66, 80)( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 85, 99)( 86,100)( 87,101)( 88,102)( 89,103)( 90,104)( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)( 97,111)( 98,112)(127,134)(128,135)(129,136)(130,137)(131,138)(132,139)(133,140)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)(161,168)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224)(225,253)(226,254)(227,255)(228,256)(229,257)(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,274)(240,275)(241,276)(242,277)(243,278)(244,279)(245,280)(246,267)(247,268)(248,269)(249,270)(250,271)(251,272)(252,273)(281,323)(282,324)(283,325)(284,326)(285,327)(286,328)(287,329)(288,330)(289,331)(290,332)(291,333)(292,334)(293,335)(294,336)(295,309)(296,310)(297,311)(298,312)(299,313)(300,314)(301,315)(302,316)(303,317)(304,318)(305,319)(306,320)(307,321)(308,322)(337,365)(338,366)(339,367)(340,368)(341,369)(342,370)(343,371)(344,372)(345,373)(346,374)(347,375)(348,376)(349,377)(350,378)(351,386)(352,387)(353,388)(354,389)(355,390)(356,391)(357,392)(358,379)(359,380)(360,381)(361,382)(362,383)(363,384)(364,385)(393,435)(394,436)(395,437)(396,438)(397,439)(398,440)(399,441)(400,442)(401,443)(402,444)(403,445)(404,446)(405,447)(406,448)(407,421)(408,422)(409,423)(410,424)(411,425)(412,426)(413,427)(414,428)(415,429)(416,430)(417,431)(418,432)(419,433)(420,434)(449,505)(450,506)(451,507)(452,508)(453,509)(454,510)(455,511)(456,512)(457,513)(458,514)(459,515)(460,516)(461,517)(462,518)(463,526)(464,527)(465,528)(466,529)(467,530)(468,531)(469,532)(470,519)(471,520)(472,521)(473,522)(474,523)(475,524)(476,525)(477,533)(478,534)(479,535)(480,536)(481,537)(482,538)(483,539)(484,540)(485,541)(486,542)(487,543)(488,544)(489,545)(490,546)(491,554)(492,555)(493,556)(494,557)(495,558)(496,559)(497,560)(498,547)(499,548)(500,549)(501,550)(502,551)(503,552)(504,553)(561,617)(562,618)(563,619)(564,620)(565,621)(566,622)(567,623)(568,624)(569,625)(570,626)(571,627)(572,628)(573,629)(574,630)(575,638)(576,639)(577,640)(578,641)(579,642)(580,643)(581,644)(582,631)(583,632)(584,633)(585,634)(586,635)(587,636)(588,637)(589,645)(590,646)(591,647)(592,648)(593,649)(594,650)(595,651)(596,652)(597,653)(598,654)(599,655)(600,656)(601,657)(602,658)(603,666)(604,667)(605,668)(606,669)(607,670)(608,671)(609,672)(610,659)(611,660)(612,661)(613,662)(614,663)(615,664)(616,665)(673,764)(674,765)(675,766)(676,767)(677,768)(678,769)(679,770)(680,757)(681,758)(682,759)(683,760)(684,761)(685,762)(686,763)(687,771)(688,772)(689,773)(690,774)(691,775)(692,776)(693,777)(694,778)(695,779)(696,780)(697,781)(698,782)(699,783)(700,784)(701,736)(702,737)(703,738)(704,739)(705,740)(706,741)(707,742)(708,729)(709,730)(710,731)(711,732)(712,733)(713,734)(714,735)(715,743)(716,744)(717,745)(718,746)(719,747)(720,748)(721,749)(722,750)(723,751)(724,752)(725,753)(726,754)(727,755)(728,756)(785,876)(786,877)(787,878)(788,879)(789,880)(790,881)(791,882)(792,869)(793,870)(794,871)(795,872)(796,873)(797,874)(798,875)(799,883)(800,884)(801,885)(802,886)(803,887)(804,888)(805,889)(806,890)(807,891)(808,892)(809,893)(810,894)(811,895)(812,896)(813,848)(814,849)(815,850)(816,851)(817,852)(818,853)(819,854)(820,841)(821,842)(822,843)(823,844)(824,845)(825,846)(826,847)(827,855)(828,856)(829,857)(830,858)(831,859)(832,860)(833,861)(834,862)(835,863)(836,864)(837,865)(838,866)(839,867)(840,868);;
s2 := (  1,561)(  2,567)(  3,566)(  4,565)(  5,564)(  6,563)(  7,562)(  8,568)(  9,574)( 10,573)( 11,572)( 12,571)( 13,570)( 14,569)( 15,582)( 16,588)( 17,587)( 18,586)( 19,585)( 20,584)( 21,583)( 22,575)( 23,581)( 24,580)( 25,579)( 26,578)( 27,577)( 28,576)( 29,596)( 30,602)( 31,601)( 32,600)( 33,599)( 34,598)( 35,597)( 36,589)( 37,595)( 38,594)( 39,593)( 40,592)( 41,591)( 42,590)( 43,603)( 44,609)( 45,608)( 46,607)( 47,606)( 48,605)( 49,604)( 50,610)( 51,616)( 52,615)( 53,614)( 54,613)( 55,612)( 56,611)( 57,631)( 58,637)( 59,636)( 60,635)( 61,634)( 62,633)( 63,632)( 64,638)( 65,644)( 66,643)( 67,642)( 68,641)( 69,640)( 70,639)( 71,617)( 72,623)( 73,622)( 74,621)( 75,620)( 76,619)( 77,618)( 78,624)( 79,630)( 80,629)( 81,628)( 82,627)( 83,626)( 84,625)( 85,666)( 86,672)( 87,671)( 88,670)( 89,669)( 90,668)( 91,667)( 92,659)( 93,665)( 94,664)( 95,663)( 96,662)( 97,661)( 98,660)( 99,652)(100,658)(101,657)(102,656)(103,655)(104,654)(105,653)(106,645)(107,651)(108,650)(109,649)(110,648)(111,647)(112,646)(113,449)(114,455)(115,454)(116,453)(117,452)(118,451)(119,450)(120,456)(121,462)(122,461)(123,460)(124,459)(125,458)(126,457)(127,470)(128,476)(129,475)(130,474)(131,473)(132,472)(133,471)(134,463)(135,469)(136,468)(137,467)(138,466)(139,465)(140,464)(141,484)(142,490)(143,489)(144,488)(145,487)(146,486)(147,485)(148,477)(149,483)(150,482)(151,481)(152,480)(153,479)(154,478)(155,491)(156,497)(157,496)(158,495)(159,494)(160,493)(161,492)(162,498)(163,504)(164,503)(165,502)(166,501)(167,500)(168,499)(169,519)(170,525)(171,524)(172,523)(173,522)(174,521)(175,520)(176,526)(177,532)(178,531)(179,530)(180,529)(181,528)(182,527)(183,505)(184,511)(185,510)(186,509)(187,508)(188,507)(189,506)(190,512)(191,518)(192,517)(193,516)(194,515)(195,514)(196,513)(197,554)(198,560)(199,559)(200,558)(201,557)(202,556)(203,555)(204,547)(205,553)(206,552)(207,551)(208,550)(209,549)(210,548)(211,540)(212,546)(213,545)(214,544)(215,543)(216,542)(217,541)(218,533)(219,539)(220,538)(221,537)(222,536)(223,535)(224,534)(225,785)(226,791)(227,790)(228,789)(229,788)(230,787)(231,786)(232,792)(233,798)(234,797)(235,796)(236,795)(237,794)(238,793)(239,806)(240,812)(241,811)(242,810)(243,809)(244,808)(245,807)(246,799)(247,805)(248,804)(249,803)(250,802)(251,801)(252,800)(253,820)(254,826)(255,825)(256,824)(257,823)(258,822)(259,821)(260,813)(261,819)(262,818)(263,817)(264,816)(265,815)(266,814)(267,827)(268,833)(269,832)(270,831)(271,830)(272,829)(273,828)(274,834)(275,840)(276,839)(277,838)(278,837)(279,836)(280,835)(281,855)(282,861)(283,860)(284,859)(285,858)(286,857)(287,856)(288,862)(289,868)(290,867)(291,866)(292,865)(293,864)(294,863)(295,841)(296,847)(297,846)(298,845)(299,844)(300,843)(301,842)(302,848)(303,854)(304,853)(305,852)(306,851)(307,850)(308,849)(309,890)(310,896)(311,895)(312,894)(313,893)(314,892)(315,891)(316,883)(317,889)(318,888)(319,887)(320,886)(321,885)(322,884)(323,876)(324,882)(325,881)(326,880)(327,879)(328,878)(329,877)(330,869)(331,875)(332,874)(333,873)(334,872)(335,871)(336,870)(337,673)(338,679)(339,678)(340,677)(341,676)(342,675)(343,674)(344,680)(345,686)(346,685)(347,684)(348,683)(349,682)(350,681)(351,694)(352,700)(353,699)(354,698)(355,697)(356,696)(357,695)(358,687)(359,693)(360,692)(361,691)(362,690)(363,689)(364,688)(365,708)(366,714)(367,713)(368,712)(369,711)(370,710)(371,709)(372,701)(373,707)(374,706)(375,705)(376,704)(377,703)(378,702)(379,715)(380,721)(381,720)(382,719)(383,718)(384,717)(385,716)(386,722)(387,728)(388,727)(389,726)(390,725)(391,724)(392,723)(393,743)(394,749)(395,748)(396,747)(397,746)(398,745)(399,744)(400,750)(401,756)(402,755)(403,754)(404,753)(405,752)(406,751)(407,729)(408,735)(409,734)(410,733)(411,732)(412,731)(413,730)(414,736)(415,742)(416,741)(417,740)(418,739)(419,738)(420,737)(421,778)(422,784)(423,783)(424,782)(425,781)(426,780)(427,779)(428,771)(429,777)(430,776)(431,775)(432,774)(433,773)(434,772)(435,764)(436,770)(437,769)(438,768)(439,767)(440,766)(441,765)(442,757)(443,763)(444,762)(445,761)(446,760)(447,759)(448,758);;
s3 := (  1,114)(  2,113)(  3,119)(  4,118)(  5,117)(  6,116)(  7,115)(  8,121)(  9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,128)( 16,127)( 17,133)( 18,132)( 19,131)( 20,130)( 21,129)( 22,135)( 23,134)( 24,140)( 25,139)( 26,138)( 27,137)( 28,136)( 29,142)( 30,141)( 31,147)( 32,146)( 33,145)( 34,144)( 35,143)( 36,149)( 37,148)( 38,154)( 39,153)( 40,152)( 41,151)( 42,150)( 43,156)( 44,155)( 45,161)( 46,160)( 47,159)( 48,158)( 49,157)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)( 56,164)( 57,170)( 58,169)( 59,175)( 60,174)( 61,173)( 62,172)( 63,171)( 64,177)( 65,176)( 66,182)( 67,181)( 68,180)( 69,179)( 70,178)( 71,184)( 72,183)( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,191)( 79,190)( 80,196)( 81,195)( 82,194)( 83,193)( 84,192)( 85,198)( 86,197)( 87,203)( 88,202)( 89,201)( 90,200)( 91,199)( 92,205)( 93,204)( 94,210)( 95,209)( 96,208)( 97,207)( 98,206)( 99,212)(100,211)(101,217)(102,216)(103,215)(104,214)(105,213)(106,219)(107,218)(108,224)(109,223)(110,222)(111,221)(112,220)(225,338)(226,337)(227,343)(228,342)(229,341)(230,340)(231,339)(232,345)(233,344)(234,350)(235,349)(236,348)(237,347)(238,346)(239,352)(240,351)(241,357)(242,356)(243,355)(244,354)(245,353)(246,359)(247,358)(248,364)(249,363)(250,362)(251,361)(252,360)(253,366)(254,365)(255,371)(256,370)(257,369)(258,368)(259,367)(260,373)(261,372)(262,378)(263,377)(264,376)(265,375)(266,374)(267,380)(268,379)(269,385)(270,384)(271,383)(272,382)(273,381)(274,387)(275,386)(276,392)(277,391)(278,390)(279,389)(280,388)(281,394)(282,393)(283,399)(284,398)(285,397)(286,396)(287,395)(288,401)(289,400)(290,406)(291,405)(292,404)(293,403)(294,402)(295,408)(296,407)(297,413)(298,412)(299,411)(300,410)(301,409)(302,415)(303,414)(304,420)(305,419)(306,418)(307,417)(308,416)(309,422)(310,421)(311,427)(312,426)(313,425)(314,424)(315,423)(316,429)(317,428)(318,434)(319,433)(320,432)(321,431)(322,430)(323,436)(324,435)(325,441)(326,440)(327,439)(328,438)(329,437)(330,443)(331,442)(332,448)(333,447)(334,446)(335,445)(336,444)(449,562)(450,561)(451,567)(452,566)(453,565)(454,564)(455,563)(456,569)(457,568)(458,574)(459,573)(460,572)(461,571)(462,570)(463,576)(464,575)(465,581)(466,580)(467,579)(468,578)(469,577)(470,583)(471,582)(472,588)(473,587)(474,586)(475,585)(476,584)(477,590)(478,589)(479,595)(480,594)(481,593)(482,592)(483,591)(484,597)(485,596)(486,602)(487,601)(488,600)(489,599)(490,598)(491,604)(492,603)(493,609)(494,608)(495,607)(496,606)(497,605)(498,611)(499,610)(500,616)(501,615)(502,614)(503,613)(504,612)(505,618)(506,617)(507,623)(508,622)(509,621)(510,620)(511,619)(512,625)(513,624)(514,630)(515,629)(516,628)(517,627)(518,626)(519,632)(520,631)(521,637)(522,636)(523,635)(524,634)(525,633)(526,639)(527,638)(528,644)(529,643)(530,642)(531,641)(532,640)(533,646)(534,645)(535,651)(536,650)(537,649)(538,648)(539,647)(540,653)(541,652)(542,658)(543,657)(544,656)(545,655)(546,654)(547,660)(548,659)(549,665)(550,664)(551,663)(552,662)(553,661)(554,667)(555,666)(556,672)(557,671)(558,670)(559,669)(560,668)(673,786)(674,785)(675,791)(676,790)(677,789)(678,788)(679,787)(680,793)(681,792)(682,798)(683,797)(684,796)(685,795)(686,794)(687,800)(688,799)(689,805)(690,804)(691,803)(692,802)(693,801)(694,807)(695,806)(696,812)(697,811)(698,810)(699,809)(700,808)(701,814)(702,813)(703,819)(704,818)(705,817)(706,816)(707,815)(708,821)(709,820)(710,826)(711,825)(712,824)(713,823)(714,822)(715,828)(716,827)(717,833)(718,832)(719,831)(720,830)(721,829)(722,835)(723,834)(724,840)(725,839)(726,838)(727,837)(728,836)(729,842)(730,841)(731,847)(732,846)(733,845)(734,844)(735,843)(736,849)(737,848)(738,854)(739,853)(740,852)(741,851)(742,850)(743,856)(744,855)(745,861)(746,860)(747,859)(748,858)(749,857)(750,863)(751,862)(752,868)(753,867)(754,866)(755,865)(756,864)(757,870)(758,869)(759,875)(760,874)(761,873)(762,872)(763,871)(764,877)(765,876)(766,882)(767,881)(768,880)(769,879)(770,878)(771,884)(772,883)(773,889)(774,888)(775,887)(776,886)(777,885)(778,891)(779,890)(780,896)(781,895)(782,894)(783,893)(784,892);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(896)!(  1,225)(  2,226)(  3,227)(  4,228)(  5,229)(  6,230)(  7,231)(  8,232)(  9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)( 16,240)( 17,241)( 18,242)( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)( 24,248)( 25,249)( 26,250)( 27,251)( 28,252)( 29,253)( 30,254)( 31,255)( 32,256)( 33,257)( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)( 40,264)( 41,265)( 42,266)( 43,267)( 44,268)( 45,269)( 46,270)( 47,271)( 48,272)( 49,273)( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)( 56,280)( 57,288)( 58,289)( 59,290)( 60,291)( 61,292)( 62,293)( 63,294)( 64,281)( 65,282)( 66,283)( 67,284)( 68,285)( 69,286)( 70,287)( 71,302)( 72,303)( 73,304)( 74,305)( 75,306)( 76,307)( 77,308)( 78,295)( 79,296)( 80,297)( 81,298)( 82,299)( 83,300)( 84,301)( 85,316)( 86,317)( 87,318)( 88,319)( 89,320)( 90,321)( 91,322)( 92,309)( 93,310)( 94,311)( 95,312)( 96,313)( 97,314)( 98,315)( 99,330)(100,331)(101,332)(102,333)(103,334)(104,335)(105,336)(106,323)(107,324)(108,325)(109,326)(110,327)(111,328)(112,329)(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)(121,345)(122,346)(123,347)(124,348)(125,349)(126,350)(127,351)(128,352)(129,353)(130,354)(131,355)(132,356)(133,357)(134,358)(135,359)(136,360)(137,361)(138,362)(139,363)(140,364)(141,365)(142,366)(143,367)(144,368)(145,369)(146,370)(147,371)(148,372)(149,373)(150,374)(151,375)(152,376)(153,377)(154,378)(155,379)(156,380)(157,381)(158,382)(159,383)(160,384)(161,385)(162,386)(163,387)(164,388)(165,389)(166,390)(167,391)(168,392)(169,400)(170,401)(171,402)(172,403)(173,404)(174,405)(175,406)(176,393)(177,394)(178,395)(179,396)(180,397)(181,398)(182,399)(183,414)(184,415)(185,416)(186,417)(187,418)(188,419)(189,420)(190,407)(191,408)(192,409)(193,410)(194,411)(195,412)(196,413)(197,428)(198,429)(199,430)(200,431)(201,432)(202,433)(203,434)(204,421)(205,422)(206,423)(207,424)(208,425)(209,426)(210,427)(211,442)(212,443)(213,444)(214,445)(215,446)(216,447)(217,448)(218,435)(219,436)(220,437)(221,438)(222,439)(223,440)(224,441)(449,673)(450,674)(451,675)(452,676)(453,677)(454,678)(455,679)(456,680)(457,681)(458,682)(459,683)(460,684)(461,685)(462,686)(463,687)(464,688)(465,689)(466,690)(467,691)(468,692)(469,693)(470,694)(471,695)(472,696)(473,697)(474,698)(475,699)(476,700)(477,701)(478,702)(479,703)(480,704)(481,705)(482,706)(483,707)(484,708)(485,709)(486,710)(487,711)(488,712)(489,713)(490,714)(491,715)(492,716)(493,717)(494,718)(495,719)(496,720)(497,721)(498,722)(499,723)(500,724)(501,725)(502,726)(503,727)(504,728)(505,736)(506,737)(507,738)(508,739)(509,740)(510,741)(511,742)(512,729)(513,730)(514,731)(515,732)(516,733)(517,734)(518,735)(519,750)(520,751)(521,752)(522,753)(523,754)(524,755)(525,756)(526,743)(527,744)(528,745)(529,746)(530,747)(531,748)(532,749)(533,764)(534,765)(535,766)(536,767)(537,768)(538,769)(539,770)(540,757)(541,758)(542,759)(543,760)(544,761)(545,762)(546,763)(547,778)(548,779)(549,780)(550,781)(551,782)(552,783)(553,784)(554,771)(555,772)(556,773)(557,774)(558,775)(559,776)(560,777)(561,785)(562,786)(563,787)(564,788)(565,789)(566,790)(567,791)(568,792)(569,793)(570,794)(571,795)(572,796)(573,797)(574,798)(575,799)(576,800)(577,801)(578,802)(579,803)(580,804)(581,805)(582,806)(583,807)(584,808)(585,809)(586,810)(587,811)(588,812)(589,813)(590,814)(591,815)(592,816)(593,817)(594,818)(595,819)(596,820)(597,821)(598,822)(599,823)(600,824)(601,825)(602,826)(603,827)(604,828)(605,829)(606,830)(607,831)(608,832)(609,833)(610,834)(611,835)(612,836)(613,837)(614,838)(615,839)(616,840)(617,848)(618,849)(619,850)(620,851)(621,852)(622,853)(623,854)(624,841)(625,842)(626,843)(627,844)(628,845)(629,846)(630,847)(631,862)(632,863)(633,864)(634,865)(635,866)(636,867)(637,868)(638,855)(639,856)(640,857)(641,858)(642,859)(643,860)(644,861)(645,876)(646,877)(647,878)(648,879)(649,880)(650,881)(651,882)(652,869)(653,870)(654,871)(655,872)(656,873)(657,874)(658,875)(659,890)(660,891)(661,892)(662,893)(663,894)(664,895)(665,896)(666,883)(667,884)(668,885)(669,886)(670,887)(671,888)(672,889);
s1 := Sym(896)!( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 43, 50)( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 57, 71)( 58, 72)( 59, 73)( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)( 66, 80)( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 85, 99)( 86,100)( 87,101)( 88,102)( 89,103)( 90,104)( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)( 97,111)( 98,112)(127,134)(128,135)(129,136)(130,137)(131,138)(132,139)(133,140)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)(161,168)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224)(225,253)(226,254)(227,255)(228,256)(229,257)(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,274)(240,275)(241,276)(242,277)(243,278)(244,279)(245,280)(246,267)(247,268)(248,269)(249,270)(250,271)(251,272)(252,273)(281,323)(282,324)(283,325)(284,326)(285,327)(286,328)(287,329)(288,330)(289,331)(290,332)(291,333)(292,334)(293,335)(294,336)(295,309)(296,310)(297,311)(298,312)(299,313)(300,314)(301,315)(302,316)(303,317)(304,318)(305,319)(306,320)(307,321)(308,322)(337,365)(338,366)(339,367)(340,368)(341,369)(342,370)(343,371)(344,372)(345,373)(346,374)(347,375)(348,376)(349,377)(350,378)(351,386)(352,387)(353,388)(354,389)(355,390)(356,391)(357,392)(358,379)(359,380)(360,381)(361,382)(362,383)(363,384)(364,385)(393,435)(394,436)(395,437)(396,438)(397,439)(398,440)(399,441)(400,442)(401,443)(402,444)(403,445)(404,446)(405,447)(406,448)(407,421)(408,422)(409,423)(410,424)(411,425)(412,426)(413,427)(414,428)(415,429)(416,430)(417,431)(418,432)(419,433)(420,434)(449,505)(450,506)(451,507)(452,508)(453,509)(454,510)(455,511)(456,512)(457,513)(458,514)(459,515)(460,516)(461,517)(462,518)(463,526)(464,527)(465,528)(466,529)(467,530)(468,531)(469,532)(470,519)(471,520)(472,521)(473,522)(474,523)(475,524)(476,525)(477,533)(478,534)(479,535)(480,536)(481,537)(482,538)(483,539)(484,540)(485,541)(486,542)(487,543)(488,544)(489,545)(490,546)(491,554)(492,555)(493,556)(494,557)(495,558)(496,559)(497,560)(498,547)(499,548)(500,549)(501,550)(502,551)(503,552)(504,553)(561,617)(562,618)(563,619)(564,620)(565,621)(566,622)(567,623)(568,624)(569,625)(570,626)(571,627)(572,628)(573,629)(574,630)(575,638)(576,639)(577,640)(578,641)(579,642)(580,643)(581,644)(582,631)(583,632)(584,633)(585,634)(586,635)(587,636)(588,637)(589,645)(590,646)(591,647)(592,648)(593,649)(594,650)(595,651)(596,652)(597,653)(598,654)(599,655)(600,656)(601,657)(602,658)(603,666)(604,667)(605,668)(606,669)(607,670)(608,671)(609,672)(610,659)(611,660)(612,661)(613,662)(614,663)(615,664)(616,665)(673,764)(674,765)(675,766)(676,767)(677,768)(678,769)(679,770)(680,757)(681,758)(682,759)(683,760)(684,761)(685,762)(686,763)(687,771)(688,772)(689,773)(690,774)(691,775)(692,776)(693,777)(694,778)(695,779)(696,780)(697,781)(698,782)(699,783)(700,784)(701,736)(702,737)(703,738)(704,739)(705,740)(706,741)(707,742)(708,729)(709,730)(710,731)(711,732)(712,733)(713,734)(714,735)(715,743)(716,744)(717,745)(718,746)(719,747)(720,748)(721,749)(722,750)(723,751)(724,752)(725,753)(726,754)(727,755)(728,756)(785,876)(786,877)(787,878)(788,879)(789,880)(790,881)(791,882)(792,869)(793,870)(794,871)(795,872)(796,873)(797,874)(798,875)(799,883)(800,884)(801,885)(802,886)(803,887)(804,888)(805,889)(806,890)(807,891)(808,892)(809,893)(810,894)(811,895)(812,896)(813,848)(814,849)(815,850)(816,851)(817,852)(818,853)(819,854)(820,841)(821,842)(822,843)(823,844)(824,845)(825,846)(826,847)(827,855)(828,856)(829,857)(830,858)(831,859)(832,860)(833,861)(834,862)(835,863)(836,864)(837,865)(838,866)(839,867)(840,868);
s2 := Sym(896)!(  1,561)(  2,567)(  3,566)(  4,565)(  5,564)(  6,563)(  7,562)(  8,568)(  9,574)( 10,573)( 11,572)( 12,571)( 13,570)( 14,569)( 15,582)( 16,588)( 17,587)( 18,586)( 19,585)( 20,584)( 21,583)( 22,575)( 23,581)( 24,580)( 25,579)( 26,578)( 27,577)( 28,576)( 29,596)( 30,602)( 31,601)( 32,600)( 33,599)( 34,598)( 35,597)( 36,589)( 37,595)( 38,594)( 39,593)( 40,592)( 41,591)( 42,590)( 43,603)( 44,609)( 45,608)( 46,607)( 47,606)( 48,605)( 49,604)( 50,610)( 51,616)( 52,615)( 53,614)( 54,613)( 55,612)( 56,611)( 57,631)( 58,637)( 59,636)( 60,635)( 61,634)( 62,633)( 63,632)( 64,638)( 65,644)( 66,643)( 67,642)( 68,641)( 69,640)( 70,639)( 71,617)( 72,623)( 73,622)( 74,621)( 75,620)( 76,619)( 77,618)( 78,624)( 79,630)( 80,629)( 81,628)( 82,627)( 83,626)( 84,625)( 85,666)( 86,672)( 87,671)( 88,670)( 89,669)( 90,668)( 91,667)( 92,659)( 93,665)( 94,664)( 95,663)( 96,662)( 97,661)( 98,660)( 99,652)(100,658)(101,657)(102,656)(103,655)(104,654)(105,653)(106,645)(107,651)(108,650)(109,649)(110,648)(111,647)(112,646)(113,449)(114,455)(115,454)(116,453)(117,452)(118,451)(119,450)(120,456)(121,462)(122,461)(123,460)(124,459)(125,458)(126,457)(127,470)(128,476)(129,475)(130,474)(131,473)(132,472)(133,471)(134,463)(135,469)(136,468)(137,467)(138,466)(139,465)(140,464)(141,484)(142,490)(143,489)(144,488)(145,487)(146,486)(147,485)(148,477)(149,483)(150,482)(151,481)(152,480)(153,479)(154,478)(155,491)(156,497)(157,496)(158,495)(159,494)(160,493)(161,492)(162,498)(163,504)(164,503)(165,502)(166,501)(167,500)(168,499)(169,519)(170,525)(171,524)(172,523)(173,522)(174,521)(175,520)(176,526)(177,532)(178,531)(179,530)(180,529)(181,528)(182,527)(183,505)(184,511)(185,510)(186,509)(187,508)(188,507)(189,506)(190,512)(191,518)(192,517)(193,516)(194,515)(195,514)(196,513)(197,554)(198,560)(199,559)(200,558)(201,557)(202,556)(203,555)(204,547)(205,553)(206,552)(207,551)(208,550)(209,549)(210,548)(211,540)(212,546)(213,545)(214,544)(215,543)(216,542)(217,541)(218,533)(219,539)(220,538)(221,537)(222,536)(223,535)(224,534)(225,785)(226,791)(227,790)(228,789)(229,788)(230,787)(231,786)(232,792)(233,798)(234,797)(235,796)(236,795)(237,794)(238,793)(239,806)(240,812)(241,811)(242,810)(243,809)(244,808)(245,807)(246,799)(247,805)(248,804)(249,803)(250,802)(251,801)(252,800)(253,820)(254,826)(255,825)(256,824)(257,823)(258,822)(259,821)(260,813)(261,819)(262,818)(263,817)(264,816)(265,815)(266,814)(267,827)(268,833)(269,832)(270,831)(271,830)(272,829)(273,828)(274,834)(275,840)(276,839)(277,838)(278,837)(279,836)(280,835)(281,855)(282,861)(283,860)(284,859)(285,858)(286,857)(287,856)(288,862)(289,868)(290,867)(291,866)(292,865)(293,864)(294,863)(295,841)(296,847)(297,846)(298,845)(299,844)(300,843)(301,842)(302,848)(303,854)(304,853)(305,852)(306,851)(307,850)(308,849)(309,890)(310,896)(311,895)(312,894)(313,893)(314,892)(315,891)(316,883)(317,889)(318,888)(319,887)(320,886)(321,885)(322,884)(323,876)(324,882)(325,881)(326,880)(327,879)(328,878)(329,877)(330,869)(331,875)(332,874)(333,873)(334,872)(335,871)(336,870)(337,673)(338,679)(339,678)(340,677)(341,676)(342,675)(343,674)(344,680)(345,686)(346,685)(347,684)(348,683)(349,682)(350,681)(351,694)(352,700)(353,699)(354,698)(355,697)(356,696)(357,695)(358,687)(359,693)(360,692)(361,691)(362,690)(363,689)(364,688)(365,708)(366,714)(367,713)(368,712)(369,711)(370,710)(371,709)(372,701)(373,707)(374,706)(375,705)(376,704)(377,703)(378,702)(379,715)(380,721)(381,720)(382,719)(383,718)(384,717)(385,716)(386,722)(387,728)(388,727)(389,726)(390,725)(391,724)(392,723)(393,743)(394,749)(395,748)(396,747)(397,746)(398,745)(399,744)(400,750)(401,756)(402,755)(403,754)(404,753)(405,752)(406,751)(407,729)(408,735)(409,734)(410,733)(411,732)(412,731)(413,730)(414,736)(415,742)(416,741)(417,740)(418,739)(419,738)(420,737)(421,778)(422,784)(423,783)(424,782)(425,781)(426,780)(427,779)(428,771)(429,777)(430,776)(431,775)(432,774)(433,773)(434,772)(435,764)(436,770)(437,769)(438,768)(439,767)(440,766)(441,765)(442,757)(443,763)(444,762)(445,761)(446,760)(447,759)(448,758);
s3 := Sym(896)!(  1,114)(  2,113)(  3,119)(  4,118)(  5,117)(  6,116)(  7,115)(  8,121)(  9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,128)( 16,127)( 17,133)( 18,132)( 19,131)( 20,130)( 21,129)( 22,135)( 23,134)( 24,140)( 25,139)( 26,138)( 27,137)( 28,136)( 29,142)( 30,141)( 31,147)( 32,146)( 33,145)( 34,144)( 35,143)( 36,149)( 37,148)( 38,154)( 39,153)( 40,152)( 41,151)( 42,150)( 43,156)( 44,155)( 45,161)( 46,160)( 47,159)( 48,158)( 49,157)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)( 56,164)( 57,170)( 58,169)( 59,175)( 60,174)( 61,173)( 62,172)( 63,171)( 64,177)( 65,176)( 66,182)( 67,181)( 68,180)( 69,179)( 70,178)( 71,184)( 72,183)( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,191)( 79,190)( 80,196)( 81,195)( 82,194)( 83,193)( 84,192)( 85,198)( 86,197)( 87,203)( 88,202)( 89,201)( 90,200)( 91,199)( 92,205)( 93,204)( 94,210)( 95,209)( 96,208)( 97,207)( 98,206)( 99,212)(100,211)(101,217)(102,216)(103,215)(104,214)(105,213)(106,219)(107,218)(108,224)(109,223)(110,222)(111,221)(112,220)(225,338)(226,337)(227,343)(228,342)(229,341)(230,340)(231,339)(232,345)(233,344)(234,350)(235,349)(236,348)(237,347)(238,346)(239,352)(240,351)(241,357)(242,356)(243,355)(244,354)(245,353)(246,359)(247,358)(248,364)(249,363)(250,362)(251,361)(252,360)(253,366)(254,365)(255,371)(256,370)(257,369)(258,368)(259,367)(260,373)(261,372)(262,378)(263,377)(264,376)(265,375)(266,374)(267,380)(268,379)(269,385)(270,384)(271,383)(272,382)(273,381)(274,387)(275,386)(276,392)(277,391)(278,390)(279,389)(280,388)(281,394)(282,393)(283,399)(284,398)(285,397)(286,396)(287,395)(288,401)(289,400)(290,406)(291,405)(292,404)(293,403)(294,402)(295,408)(296,407)(297,413)(298,412)(299,411)(300,410)(301,409)(302,415)(303,414)(304,420)(305,419)(306,418)(307,417)(308,416)(309,422)(310,421)(311,427)(312,426)(313,425)(314,424)(315,423)(316,429)(317,428)(318,434)(319,433)(320,432)(321,431)(322,430)(323,436)(324,435)(325,441)(326,440)(327,439)(328,438)(329,437)(330,443)(331,442)(332,448)(333,447)(334,446)(335,445)(336,444)(449,562)(450,561)(451,567)(452,566)(453,565)(454,564)(455,563)(456,569)(457,568)(458,574)(459,573)(460,572)(461,571)(462,570)(463,576)(464,575)(465,581)(466,580)(467,579)(468,578)(469,577)(470,583)(471,582)(472,588)(473,587)(474,586)(475,585)(476,584)(477,590)(478,589)(479,595)(480,594)(481,593)(482,592)(483,591)(484,597)(485,596)(486,602)(487,601)(488,600)(489,599)(490,598)(491,604)(492,603)(493,609)(494,608)(495,607)(496,606)(497,605)(498,611)(499,610)(500,616)(501,615)(502,614)(503,613)(504,612)(505,618)(506,617)(507,623)(508,622)(509,621)(510,620)(511,619)(512,625)(513,624)(514,630)(515,629)(516,628)(517,627)(518,626)(519,632)(520,631)(521,637)(522,636)(523,635)(524,634)(525,633)(526,639)(527,638)(528,644)(529,643)(530,642)(531,641)(532,640)(533,646)(534,645)(535,651)(536,650)(537,649)(538,648)(539,647)(540,653)(541,652)(542,658)(543,657)(544,656)(545,655)(546,654)(547,660)(548,659)(549,665)(550,664)(551,663)(552,662)(553,661)(554,667)(555,666)(556,672)(557,671)(558,670)(559,669)(560,668)(673,786)(674,785)(675,791)(676,790)(677,789)(678,788)(679,787)(680,793)(681,792)(682,798)(683,797)(684,796)(685,795)(686,794)(687,800)(688,799)(689,805)(690,804)(691,803)(692,802)(693,801)(694,807)(695,806)(696,812)(697,811)(698,810)(699,809)(700,808)(701,814)(702,813)(703,819)(704,818)(705,817)(706,816)(707,815)(708,821)(709,820)(710,826)(711,825)(712,824)(713,823)(714,822)(715,828)(716,827)(717,833)(718,832)(719,831)(720,830)(721,829)(722,835)(723,834)(724,840)(725,839)(726,838)(727,837)(728,836)(729,842)(730,841)(731,847)(732,846)(733,845)(734,844)(735,843)(736,849)(737,848)(738,854)(739,853)(740,852)(741,851)(742,850)(743,856)(744,855)(745,861)(746,860)(747,859)(748,858)(749,857)(750,863)(751,862)(752,868)(753,867)(754,866)(755,865)(756,864)(757,870)(758,869)(759,875)(760,874)(761,873)(762,872)(763,871)(764,877)(765,876)(766,882)(767,881)(768,880)(769,879)(770,878)(771,884)(772,883)(773,889)(774,888)(775,887)(776,886)(777,885)(778,891)(779,890)(780,896)(781,895)(782,894)(783,893)(784,892);
poly := sub<Sym(896)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

References