Polytope of Type {4,4,4,14} with group SmallGroup(1792,336970)

Overview

Group: SmallGroup(1792,336970)
Rank: 5
Schläfli Type: {4,4,4,14}
Vertices, edges, …: 4, 8, 8, 28, 14
Order of s₀s₁s₂s₃s₄: 28
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 2
Also known as: {{4,4|2},{4,4|2},{4,14|2}}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

4-fold

7-fold

{4,4,4,2}*256

8-fold

14-fold

16-fold

{2,2,2,7}*112

28-fold

56-fold

{2,2,2,2}*32

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (  1,113)(  2,114)(  3,115)(  4,116)(  5,117)(  6,118)(  7,119)(  8,120)(  9,121)( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)( 16,128)( 17,129)( 18,130)( 19,131)( 20,132)( 21,133)( 22,134)( 23,135)( 24,136)( 25,137)( 26,138)( 27,139)( 28,140)( 29,141)( 30,142)( 31,143)( 32,144)( 33,145)( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)( 40,152)( 41,153)( 42,154)( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)( 48,160)( 49,161)( 50,162)( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)( 56,168)( 57,169)( 58,170)( 59,171)( 60,172)( 61,173)( 62,174)( 63,175)( 64,176)( 65,177)( 66,178)( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)( 72,184)( 73,185)( 74,186)( 75,187)( 76,188)( 77,189)( 78,190)( 79,191)( 80,192)( 81,193)( 82,194)( 83,195)( 84,196)( 85,197)( 86,198)( 87,199)( 88,200)( 89,201)( 90,202)( 91,203)( 92,204)( 93,205)( 94,206)( 95,207)( 96,208)( 97,209)( 98,210)( 99,211)(100,212)(101,213)(102,214)(103,215)(104,216)(105,217)(106,218)(107,219)(108,220)(109,221)(110,222)(111,223)(112,224)(225,337)(226,338)(227,339)(228,340)(229,341)(230,342)(231,343)(232,344)(233,345)(234,346)(235,347)(236,348)(237,349)(238,350)(239,351)(240,352)(241,353)(242,354)(243,355)(244,356)(245,357)(246,358)(247,359)(248,360)(249,361)(250,362)(251,363)(252,364)(253,365)(254,366)(255,367)(256,368)(257,369)(258,370)(259,371)(260,372)(261,373)(262,374)(263,375)(264,376)(265,377)(266,378)(267,379)(268,380)(269,381)(270,382)(271,383)(272,384)(273,385)(274,386)(275,387)(276,388)(277,389)(278,390)(279,391)(280,392)(281,393)(282,394)(283,395)(284,396)(285,397)(286,398)(287,399)(288,400)(289,401)(290,402)(291,403)(292,404)(293,405)(294,406)(295,407)(296,408)(297,409)(298,410)(299,411)(300,412)(301,413)(302,414)(303,415)(304,416)(305,417)(306,418)(307,419)(308,420)(309,421)(310,422)(311,423)(312,424)(313,425)(314,426)(315,427)(316,428)(317,429)(318,430)(319,431)(320,432)(321,433)(322,434)(323,435)(324,436)(325,437)(326,438)(327,439)(328,440)(329,441)(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)(336,448)(449,561)(450,562)(451,563)(452,564)(453,565)(454,566)(455,567)(456,568)(457,569)(458,570)(459,571)(460,572)(461,573)(462,574)(463,575)(464,576)(465,577)(466,578)(467,579)(468,580)(469,581)(470,582)(471,583)(472,584)(473,585)(474,586)(475,587)(476,588)(477,589)(478,590)(479,591)(480,592)(481,593)(482,594)(483,595)(484,596)(485,597)(486,598)(487,599)(488,600)(489,601)(490,602)(491,603)(492,604)(493,605)(494,606)(495,607)(496,608)(497,609)(498,610)(499,611)(500,612)(501,613)(502,614)(503,615)(504,616)(505,617)(506,618)(507,619)(508,620)(509,621)(510,622)(511,623)(512,624)(513,625)(514,626)(515,627)(516,628)(517,629)(518,630)(519,631)(520,632)(521,633)(522,634)(523,635)(524,636)(525,637)(526,638)(527,639)(528,640)(529,641)(530,642)(531,643)(532,644)(533,645)(534,646)(535,647)(536,648)(537,649)(538,650)(539,651)(540,652)(541,653)(542,654)(543,655)(544,656)(545,657)(546,658)(547,659)(548,660)(549,661)(550,662)(551,663)(552,664)(553,665)(554,666)(555,667)(556,668)(557,669)(558,670)(559,671)(560,672)(673,785)(674,786)(675,787)(676,788)(677,789)(678,790)(679,791)(680,792)(681,793)(682,794)(683,795)(684,796)(685,797)(686,798)(687,799)(688,800)(689,801)(690,802)(691,803)(692,804)(693,805)(694,806)(695,807)(696,808)(697,809)(698,810)(699,811)(700,812)(701,813)(702,814)(703,815)(704,816)(705,817)(706,818)(707,819)(708,820)(709,821)(710,822)(711,823)(712,824)(713,825)(714,826)(715,827)(716,828)(717,829)(718,830)(719,831)(720,832)(721,833)(722,834)(723,835)(724,836)(725,837)(726,838)(727,839)(728,840)(729,841)(730,842)(731,843)(732,844)(733,845)(734,846)(735,847)(736,848)(737,849)(738,850)(739,851)(740,852)(741,853)(742,854)(743,855)(744,856)(745,857)(746,858)(747,859)(748,860)(749,861)(750,862)(751,863)(752,864)(753,865)(754,866)(755,867)(756,868)(757,869)(758,870)(759,871)(760,872)(761,873)(762,874)(763,875)(764,876)(765,877)(766,878)(767,879)(768,880)(769,881)(770,882)(771,883)(772,884)(773,885)(774,886)(775,887)(776,888)(777,889)(778,890)(779,891)(780,892)(781,893)(782,894)(783,895)(784,896);;
s1 := (  1,449)(  2,450)(  3,451)(  4,452)(  5,453)(  6,454)(  7,455)(  8,456)(  9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,463)( 16,464)( 17,465)( 18,466)( 19,467)( 20,468)( 21,469)( 22,470)( 23,471)( 24,472)( 25,473)( 26,474)( 27,475)( 28,476)( 29,477)( 30,478)( 31,479)( 32,480)( 33,481)( 34,482)( 35,483)( 36,484)( 37,485)( 38,486)( 39,487)( 40,488)( 41,489)( 42,490)( 43,491)( 44,492)( 45,493)( 46,494)( 47,495)( 48,496)( 49,497)( 50,498)( 51,499)( 52,500)( 53,501)( 54,502)( 55,503)( 56,504)( 57,505)( 58,506)( 59,507)( 60,508)( 61,509)( 62,510)( 63,511)( 64,512)( 65,513)( 66,514)( 67,515)( 68,516)( 69,517)( 70,518)( 71,519)( 72,520)( 73,521)( 74,522)( 75,523)( 76,524)( 77,525)( 78,526)( 79,527)( 80,528)( 81,529)( 82,530)( 83,531)( 84,532)( 85,533)( 86,534)( 87,535)( 88,536)( 89,537)( 90,538)( 91,539)( 92,540)( 93,541)( 94,542)( 95,543)( 96,544)( 97,545)( 98,546)( 99,547)(100,548)(101,549)(102,550)(103,551)(104,552)(105,553)(106,554)(107,555)(108,556)(109,557)(110,558)(111,559)(112,560)(113,568)(114,569)(115,570)(116,571)(117,572)(118,573)(119,574)(120,561)(121,562)(122,563)(123,564)(124,565)(125,566)(126,567)(127,582)(128,583)(129,584)(130,585)(131,586)(132,587)(133,588)(134,575)(135,576)(136,577)(137,578)(138,579)(139,580)(140,581)(141,596)(142,597)(143,598)(144,599)(145,600)(146,601)(147,602)(148,589)(149,590)(150,591)(151,592)(152,593)(153,594)(154,595)(155,610)(156,611)(157,612)(158,613)(159,614)(160,615)(161,616)(162,603)(163,604)(164,605)(165,606)(166,607)(167,608)(168,609)(169,624)(170,625)(171,626)(172,627)(173,628)(174,629)(175,630)(176,617)(177,618)(178,619)(179,620)(180,621)(181,622)(182,623)(183,638)(184,639)(185,640)(186,641)(187,642)(188,643)(189,644)(190,631)(191,632)(192,633)(193,634)(194,635)(195,636)(196,637)(197,652)(198,653)(199,654)(200,655)(201,656)(202,657)(203,658)(204,645)(205,646)(206,647)(207,648)(208,649)(209,650)(210,651)(211,666)(212,667)(213,668)(214,669)(215,670)(216,671)(217,672)(218,659)(219,660)(220,661)(221,662)(222,663)(223,664)(224,665)(225,680)(226,681)(227,682)(228,683)(229,684)(230,685)(231,686)(232,673)(233,674)(234,675)(235,676)(236,677)(237,678)(238,679)(239,694)(240,695)(241,696)(242,697)(243,698)(244,699)(245,700)(246,687)(247,688)(248,689)(249,690)(250,691)(251,692)(252,693)(253,708)(254,709)(255,710)(256,711)(257,712)(258,713)(259,714)(260,701)(261,702)(262,703)(263,704)(264,705)(265,706)(266,707)(267,722)(268,723)(269,724)(270,725)(271,726)(272,727)(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)(280,721)(281,736)(282,737)(283,738)(284,739)(285,740)(286,741)(287,742)(288,729)(289,730)(290,731)(291,732)(292,733)(293,734)(294,735)(295,750)(296,751)(297,752)(298,753)(299,754)(300,755)(301,756)(302,743)(303,744)(304,745)(305,746)(306,747)(307,748)(308,749)(309,764)(310,765)(311,766)(312,767)(313,768)(314,769)(315,770)(316,757)(317,758)(318,759)(319,760)(320,761)(321,762)(322,763)(323,778)(324,779)(325,780)(326,781)(327,782)(328,783)(329,784)(330,771)(331,772)(332,773)(333,774)(334,775)(335,776)(336,777)(337,785)(338,786)(339,787)(340,788)(341,789)(342,790)(343,791)(344,792)(345,793)(346,794)(347,795)(348,796)(349,797)(350,798)(351,799)(352,800)(353,801)(354,802)(355,803)(356,804)(357,805)(358,806)(359,807)(360,808)(361,809)(362,810)(363,811)(364,812)(365,813)(366,814)(367,815)(368,816)(369,817)(370,818)(371,819)(372,820)(373,821)(374,822)(375,823)(376,824)(377,825)(378,826)(379,827)(380,828)(381,829)(382,830)(383,831)(384,832)(385,833)(386,834)(387,835)(388,836)(389,837)(390,838)(391,839)(392,840)(393,841)(394,842)(395,843)(396,844)(397,845)(398,846)(399,847)(400,848)(401,849)(402,850)(403,851)(404,852)(405,853)(406,854)(407,855)(408,856)(409,857)(410,858)(411,859)(412,860)(413,861)(414,862)(415,863)(416,864)(417,865)(418,866)(419,867)(420,868)(421,869)(422,870)(423,871)(424,872)(425,873)(426,874)(427,875)(428,876)(429,877)(430,878)(431,879)(432,880)(433,881)(434,882)(435,883)(436,884)(437,885)(438,886)(439,887)(440,888)(441,889)(442,890)(443,891)(444,892)(445,893)(446,894)(447,895)(448,896);;
s2 := (225,239)(226,240)(227,241)(228,242)(229,243)(230,244)(231,245)(232,246)(233,247)(234,248)(235,249)(236,250)(237,251)(238,252)(253,267)(254,268)(255,269)(256,270)(257,271)(258,272)(259,273)(260,274)(261,275)(262,276)(263,277)(264,278)(265,279)(266,280)(281,295)(282,296)(283,297)(284,298)(285,299)(286,300)(287,301)(288,302)(289,303)(290,304)(291,305)(292,306)(293,307)(294,308)(309,323)(310,324)(311,325)(312,326)(313,327)(314,328)(315,329)(316,330)(317,331)(318,332)(319,333)(320,334)(321,335)(322,336)(337,351)(338,352)(339,353)(340,354)(341,355)(342,356)(343,357)(344,358)(345,359)(346,360)(347,361)(348,362)(349,363)(350,364)(365,379)(366,380)(367,381)(368,382)(369,383)(370,384)(371,385)(372,386)(373,387)(374,388)(375,389)(376,390)(377,391)(378,392)(393,407)(394,408)(395,409)(396,410)(397,411)(398,412)(399,413)(400,414)(401,415)(402,416)(403,417)(404,418)(405,419)(406,420)(421,435)(422,436)(423,437)(424,438)(425,439)(426,440)(427,441)(428,442)(429,443)(430,444)(431,445)(432,446)(433,447)(434,448)(449,477)(450,478)(451,479)(452,480)(453,481)(454,482)(455,483)(456,484)(457,485)(458,486)(459,487)(460,488)(461,489)(462,490)(463,491)(464,492)(465,493)(466,494)(467,495)(468,496)(469,497)(470,498)(471,499)(472,500)(473,501)(474,502)(475,503)(476,504)(505,533)(506,534)(507,535)(508,536)(509,537)(510,538)(511,539)(512,540)(513,541)(514,542)(515,543)(516,544)(517,545)(518,546)(519,547)(520,548)(521,549)(522,550)(523,551)(524,552)(525,553)(526,554)(527,555)(528,556)(529,557)(530,558)(531,559)(532,560)(561,589)(562,590)(563,591)(564,592)(565,593)(566,594)(567,595)(568,596)(569,597)(570,598)(571,599)(572,600)(573,601)(574,602)(575,603)(576,604)(577,605)(578,606)(579,607)(580,608)(581,609)(582,610)(583,611)(584,612)(585,613)(586,614)(587,615)(588,616)(617,645)(618,646)(619,647)(620,648)(621,649)(622,650)(623,651)(624,652)(625,653)(626,654)(627,655)(628,656)(629,657)(630,658)(631,659)(632,660)(633,661)(634,662)(635,663)(636,664)(637,665)(638,666)(639,667)(640,668)(641,669)(642,670)(643,671)(644,672)(673,715)(674,716)(675,717)(676,718)(677,719)(678,720)(679,721)(680,722)(681,723)(682,724)(683,725)(684,726)(685,727)(686,728)(687,701)(688,702)(689,703)(690,704)(691,705)(692,706)(693,707)(694,708)(695,709)(696,710)(697,711)(698,712)(699,713)(700,714)(729,771)(730,772)(731,773)(732,774)(733,775)(734,776)(735,777)(736,778)(737,779)(738,780)(739,781)(740,782)(741,783)(742,784)(743,757)(744,758)(745,759)(746,760)(747,761)(748,762)(749,763)(750,764)(751,765)(752,766)(753,767)(754,768)(755,769)(756,770)(785,827)(786,828)(787,829)(788,830)(789,831)(790,832)(791,833)(792,834)(793,835)(794,836)(795,837)(796,838)(797,839)(798,840)(799,813)(800,814)(801,815)(802,816)(803,817)(804,818)(805,819)(806,820)(807,821)(808,822)(809,823)(810,824)(811,825)(812,826)(841,883)(842,884)(843,885)(844,886)(845,887)(846,888)(847,889)(848,890)(849,891)(850,892)(851,893)(852,894)(853,895)(854,896)(855,869)(856,870)(857,871)(858,872)(859,873)(860,874)(861,875)(862,876)(863,877)(864,878)(865,879)(866,880)(867,881)(868,882);;
s3 := (  1,393)(  2,399)(  3,398)(  4,397)(  5,396)(  6,395)(  7,394)(  8,400)(  9,406)( 10,405)( 11,404)( 12,403)( 13,402)( 14,401)( 15,407)( 16,413)( 17,412)( 18,411)( 19,410)( 20,409)( 21,408)( 22,414)( 23,420)( 24,419)( 25,418)( 26,417)( 27,416)( 28,415)( 29,421)( 30,427)( 31,426)( 32,425)( 33,424)( 34,423)( 35,422)( 36,428)( 37,434)( 38,433)( 39,432)( 40,431)( 41,430)( 42,429)( 43,435)( 44,441)( 45,440)( 46,439)( 47,438)( 48,437)( 49,436)( 50,442)( 51,448)( 52,447)( 53,446)( 54,445)( 55,444)( 56,443)( 57,337)( 58,343)( 59,342)( 60,341)( 61,340)( 62,339)( 63,338)( 64,344)( 65,350)( 66,349)( 67,348)( 68,347)( 69,346)( 70,345)( 71,351)( 72,357)( 73,356)( 74,355)( 75,354)( 76,353)( 77,352)( 78,358)( 79,364)( 80,363)( 81,362)( 82,361)( 83,360)( 84,359)( 85,365)( 86,371)( 87,370)( 88,369)( 89,368)( 90,367)( 91,366)( 92,372)( 93,378)( 94,377)( 95,376)( 96,375)( 97,374)( 98,373)( 99,379)(100,385)(101,384)(102,383)(103,382)(104,381)(105,380)(106,386)(107,392)(108,391)(109,390)(110,389)(111,388)(112,387)(113,281)(114,287)(115,286)(116,285)(117,284)(118,283)(119,282)(120,288)(121,294)(122,293)(123,292)(124,291)(125,290)(126,289)(127,295)(128,301)(129,300)(130,299)(131,298)(132,297)(133,296)(134,302)(135,308)(136,307)(137,306)(138,305)(139,304)(140,303)(141,309)(142,315)(143,314)(144,313)(145,312)(146,311)(147,310)(148,316)(149,322)(150,321)(151,320)(152,319)(153,318)(154,317)(155,323)(156,329)(157,328)(158,327)(159,326)(160,325)(161,324)(162,330)(163,336)(164,335)(165,334)(166,333)(167,332)(168,331)(169,225)(170,231)(171,230)(172,229)(173,228)(174,227)(175,226)(176,232)(177,238)(178,237)(179,236)(180,235)(181,234)(182,233)(183,239)(184,245)(185,244)(186,243)(187,242)(188,241)(189,240)(190,246)(191,252)(192,251)(193,250)(194,249)(195,248)(196,247)(197,253)(198,259)(199,258)(200,257)(201,256)(202,255)(203,254)(204,260)(205,266)(206,265)(207,264)(208,263)(209,262)(210,261)(211,267)(212,273)(213,272)(214,271)(215,270)(216,269)(217,268)(218,274)(219,280)(220,279)(221,278)(222,277)(223,276)(224,275)(449,841)(450,847)(451,846)(452,845)(453,844)(454,843)(455,842)(456,848)(457,854)(458,853)(459,852)(460,851)(461,850)(462,849)(463,855)(464,861)(465,860)(466,859)(467,858)(468,857)(469,856)(470,862)(471,868)(472,867)(473,866)(474,865)(475,864)(476,863)(477,869)(478,875)(479,874)(480,873)(481,872)(482,871)(483,870)(484,876)(485,882)(486,881)(487,880)(488,879)(489,878)(490,877)(491,883)(492,889)(493,888)(494,887)(495,886)(496,885)(497,884)(498,890)(499,896)(500,895)(501,894)(502,893)(503,892)(504,891)(505,785)(506,791)(507,790)(508,789)(509,788)(510,787)(511,786)(512,792)(513,798)(514,797)(515,796)(516,795)(517,794)(518,793)(519,799)(520,805)(521,804)(522,803)(523,802)(524,801)(525,800)(526,806)(527,812)(528,811)(529,810)(530,809)(531,808)(532,807)(533,813)(534,819)(535,818)(536,817)(537,816)(538,815)(539,814)(540,820)(541,826)(542,825)(543,824)(544,823)(545,822)(546,821)(547,827)(548,833)(549,832)(550,831)(551,830)(552,829)(553,828)(554,834)(555,840)(556,839)(557,838)(558,837)(559,836)(560,835)(561,729)(562,735)(563,734)(564,733)(565,732)(566,731)(567,730)(568,736)(569,742)(570,741)(571,740)(572,739)(573,738)(574,737)(575,743)(576,749)(577,748)(578,747)(579,746)(580,745)(581,744)(582,750)(583,756)(584,755)(585,754)(586,753)(587,752)(588,751)(589,757)(590,763)(591,762)(592,761)(593,760)(594,759)(595,758)(596,764)(597,770)(598,769)(599,768)(600,767)(601,766)(602,765)(603,771)(604,777)(605,776)(606,775)(607,774)(608,773)(609,772)(610,778)(611,784)(612,783)(613,782)(614,781)(615,780)(616,779)(617,673)(618,679)(619,678)(620,677)(621,676)(622,675)(623,674)(624,680)(625,686)(626,685)(627,684)(628,683)(629,682)(630,681)(631,687)(632,693)(633,692)(634,691)(635,690)(636,689)(637,688)(638,694)(639,700)(640,699)(641,698)(642,697)(643,696)(644,695)(645,701)(646,707)(647,706)(648,705)(649,704)(650,703)(651,702)(652,708)(653,714)(654,713)(655,712)(656,711)(657,710)(658,709)(659,715)(660,721)(661,720)(662,719)(663,718)(664,717)(665,716)(666,722)(667,728)(668,727)(669,726)(670,725)(671,724)(672,723);;
s4 := (  1, 58)(  2, 57)(  3, 63)(  4, 62)(  5, 61)(  6, 60)(  7, 59)(  8, 65)(  9, 64)( 10, 70)( 11, 69)( 12, 68)( 13, 67)( 14, 66)( 15, 72)( 16, 71)( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 79)( 23, 78)( 24, 84)( 25, 83)( 26, 82)( 27, 81)( 28, 80)( 29, 86)( 30, 85)( 31, 91)( 32, 90)( 33, 89)( 34, 88)( 35, 87)( 36, 93)( 37, 92)( 38, 98)( 39, 97)( 40, 96)( 41, 95)( 42, 94)( 43,100)( 44, 99)( 45,105)( 46,104)( 47,103)( 48,102)( 49,101)( 50,107)( 51,106)( 52,112)( 53,111)( 54,110)( 55,109)( 56,108)(113,170)(114,169)(115,175)(116,174)(117,173)(118,172)(119,171)(120,177)(121,176)(122,182)(123,181)(124,180)(125,179)(126,178)(127,184)(128,183)(129,189)(130,188)(131,187)(132,186)(133,185)(134,191)(135,190)(136,196)(137,195)(138,194)(139,193)(140,192)(141,198)(142,197)(143,203)(144,202)(145,201)(146,200)(147,199)(148,205)(149,204)(150,210)(151,209)(152,208)(153,207)(154,206)(155,212)(156,211)(157,217)(158,216)(159,215)(160,214)(161,213)(162,219)(163,218)(164,224)(165,223)(166,222)(167,221)(168,220)(225,282)(226,281)(227,287)(228,286)(229,285)(230,284)(231,283)(232,289)(233,288)(234,294)(235,293)(236,292)(237,291)(238,290)(239,296)(240,295)(241,301)(242,300)(243,299)(244,298)(245,297)(246,303)(247,302)(248,308)(249,307)(250,306)(251,305)(252,304)(253,310)(254,309)(255,315)(256,314)(257,313)(258,312)(259,311)(260,317)(261,316)(262,322)(263,321)(264,320)(265,319)(266,318)(267,324)(268,323)(269,329)(270,328)(271,327)(272,326)(273,325)(274,331)(275,330)(276,336)(277,335)(278,334)(279,333)(280,332)(337,394)(338,393)(339,399)(340,398)(341,397)(342,396)(343,395)(344,401)(345,400)(346,406)(347,405)(348,404)(349,403)(350,402)(351,408)(352,407)(353,413)(354,412)(355,411)(356,410)(357,409)(358,415)(359,414)(360,420)(361,419)(362,418)(363,417)(364,416)(365,422)(366,421)(367,427)(368,426)(369,425)(370,424)(371,423)(372,429)(373,428)(374,434)(375,433)(376,432)(377,431)(378,430)(379,436)(380,435)(381,441)(382,440)(383,439)(384,438)(385,437)(386,443)(387,442)(388,448)(389,447)(390,446)(391,445)(392,444)(449,506)(450,505)(451,511)(452,510)(453,509)(454,508)(455,507)(456,513)(457,512)(458,518)(459,517)(460,516)(461,515)(462,514)(463,520)(464,519)(465,525)(466,524)(467,523)(468,522)(469,521)(470,527)(471,526)(472,532)(473,531)(474,530)(475,529)(476,528)(477,534)(478,533)(479,539)(480,538)(481,537)(482,536)(483,535)(484,541)(485,540)(486,546)(487,545)(488,544)(489,543)(490,542)(491,548)(492,547)(493,553)(494,552)(495,551)(496,550)(497,549)(498,555)(499,554)(500,560)(501,559)(502,558)(503,557)(504,556)(561,618)(562,617)(563,623)(564,622)(565,621)(566,620)(567,619)(568,625)(569,624)(570,630)(571,629)(572,628)(573,627)(574,626)(575,632)(576,631)(577,637)(578,636)(579,635)(580,634)(581,633)(582,639)(583,638)(584,644)(585,643)(586,642)(587,641)(588,640)(589,646)(590,645)(591,651)(592,650)(593,649)(594,648)(595,647)(596,653)(597,652)(598,658)(599,657)(600,656)(601,655)(602,654)(603,660)(604,659)(605,665)(606,664)(607,663)(608,662)(609,661)(610,667)(611,666)(612,672)(613,671)(614,670)(615,669)(616,668)(673,730)(674,729)(675,735)(676,734)(677,733)(678,732)(679,731)(680,737)(681,736)(682,742)(683,741)(684,740)(685,739)(686,738)(687,744)(688,743)(689,749)(690,748)(691,747)(692,746)(693,745)(694,751)(695,750)(696,756)(697,755)(698,754)(699,753)(700,752)(701,758)(702,757)(703,763)(704,762)(705,761)(706,760)(707,759)(708,765)(709,764)(710,770)(711,769)(712,768)(713,767)(714,766)(715,772)(716,771)(717,777)(718,776)(719,775)(720,774)(721,773)(722,779)(723,778)(724,784)(725,783)(726,782)(727,781)(728,780)(785,842)(786,841)(787,847)(788,846)(789,845)(790,844)(791,843)(792,849)(793,848)(794,854)(795,853)(796,852)(797,851)(798,850)(799,856)(800,855)(801,861)(802,860)(803,859)(804,858)(805,857)(806,863)(807,862)(808,868)(809,867)(810,866)(811,865)(812,864)(813,870)(814,869)(815,875)(816,874)(817,873)(818,872)(819,871)(820,877)(821,876)(822,882)(823,881)(824,880)(825,879)(826,878)(827,884)(828,883)(829,889)(830,888)(831,887)(832,886)(833,885)(834,891)(835,890)(836,896)(837,895)(838,894)(839,893)(840,892);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(896)!(  1,113)(  2,114)(  3,115)(  4,116)(  5,117)(  6,118)(  7,119)(  8,120)(  9,121)( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)( 16,128)( 17,129)( 18,130)( 19,131)( 20,132)( 21,133)( 22,134)( 23,135)( 24,136)( 25,137)( 26,138)( 27,139)( 28,140)( 29,141)( 30,142)( 31,143)( 32,144)( 33,145)( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)( 40,152)( 41,153)( 42,154)( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)( 48,160)( 49,161)( 50,162)( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)( 56,168)( 57,169)( 58,170)( 59,171)( 60,172)( 61,173)( 62,174)( 63,175)( 64,176)( 65,177)( 66,178)( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)( 72,184)( 73,185)( 74,186)( 75,187)( 76,188)( 77,189)( 78,190)( 79,191)( 80,192)( 81,193)( 82,194)( 83,195)( 84,196)( 85,197)( 86,198)( 87,199)( 88,200)( 89,201)( 90,202)( 91,203)( 92,204)( 93,205)( 94,206)( 95,207)( 96,208)( 97,209)( 98,210)( 99,211)(100,212)(101,213)(102,214)(103,215)(104,216)(105,217)(106,218)(107,219)(108,220)(109,221)(110,222)(111,223)(112,224)(225,337)(226,338)(227,339)(228,340)(229,341)(230,342)(231,343)(232,344)(233,345)(234,346)(235,347)(236,348)(237,349)(238,350)(239,351)(240,352)(241,353)(242,354)(243,355)(244,356)(245,357)(246,358)(247,359)(248,360)(249,361)(250,362)(251,363)(252,364)(253,365)(254,366)(255,367)(256,368)(257,369)(258,370)(259,371)(260,372)(261,373)(262,374)(263,375)(264,376)(265,377)(266,378)(267,379)(268,380)(269,381)(270,382)(271,383)(272,384)(273,385)(274,386)(275,387)(276,388)(277,389)(278,390)(279,391)(280,392)(281,393)(282,394)(283,395)(284,396)(285,397)(286,398)(287,399)(288,400)(289,401)(290,402)(291,403)(292,404)(293,405)(294,406)(295,407)(296,408)(297,409)(298,410)(299,411)(300,412)(301,413)(302,414)(303,415)(304,416)(305,417)(306,418)(307,419)(308,420)(309,421)(310,422)(311,423)(312,424)(313,425)(314,426)(315,427)(316,428)(317,429)(318,430)(319,431)(320,432)(321,433)(322,434)(323,435)(324,436)(325,437)(326,438)(327,439)(328,440)(329,441)(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)(336,448)(449,561)(450,562)(451,563)(452,564)(453,565)(454,566)(455,567)(456,568)(457,569)(458,570)(459,571)(460,572)(461,573)(462,574)(463,575)(464,576)(465,577)(466,578)(467,579)(468,580)(469,581)(470,582)(471,583)(472,584)(473,585)(474,586)(475,587)(476,588)(477,589)(478,590)(479,591)(480,592)(481,593)(482,594)(483,595)(484,596)(485,597)(486,598)(487,599)(488,600)(489,601)(490,602)(491,603)(492,604)(493,605)(494,606)(495,607)(496,608)(497,609)(498,610)(499,611)(500,612)(501,613)(502,614)(503,615)(504,616)(505,617)(506,618)(507,619)(508,620)(509,621)(510,622)(511,623)(512,624)(513,625)(514,626)(515,627)(516,628)(517,629)(518,630)(519,631)(520,632)(521,633)(522,634)(523,635)(524,636)(525,637)(526,638)(527,639)(528,640)(529,641)(530,642)(531,643)(532,644)(533,645)(534,646)(535,647)(536,648)(537,649)(538,650)(539,651)(540,652)(541,653)(542,654)(543,655)(544,656)(545,657)(546,658)(547,659)(548,660)(549,661)(550,662)(551,663)(552,664)(553,665)(554,666)(555,667)(556,668)(557,669)(558,670)(559,671)(560,672)(673,785)(674,786)(675,787)(676,788)(677,789)(678,790)(679,791)(680,792)(681,793)(682,794)(683,795)(684,796)(685,797)(686,798)(687,799)(688,800)(689,801)(690,802)(691,803)(692,804)(693,805)(694,806)(695,807)(696,808)(697,809)(698,810)(699,811)(700,812)(701,813)(702,814)(703,815)(704,816)(705,817)(706,818)(707,819)(708,820)(709,821)(710,822)(711,823)(712,824)(713,825)(714,826)(715,827)(716,828)(717,829)(718,830)(719,831)(720,832)(721,833)(722,834)(723,835)(724,836)(725,837)(726,838)(727,839)(728,840)(729,841)(730,842)(731,843)(732,844)(733,845)(734,846)(735,847)(736,848)(737,849)(738,850)(739,851)(740,852)(741,853)(742,854)(743,855)(744,856)(745,857)(746,858)(747,859)(748,860)(749,861)(750,862)(751,863)(752,864)(753,865)(754,866)(755,867)(756,868)(757,869)(758,870)(759,871)(760,872)(761,873)(762,874)(763,875)(764,876)(765,877)(766,878)(767,879)(768,880)(769,881)(770,882)(771,883)(772,884)(773,885)(774,886)(775,887)(776,888)(777,889)(778,890)(779,891)(780,892)(781,893)(782,894)(783,895)(784,896);
s1 := Sym(896)!(  1,449)(  2,450)(  3,451)(  4,452)(  5,453)(  6,454)(  7,455)(  8,456)(  9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,463)( 16,464)( 17,465)( 18,466)( 19,467)( 20,468)( 21,469)( 22,470)( 23,471)( 24,472)( 25,473)( 26,474)( 27,475)( 28,476)( 29,477)( 30,478)( 31,479)( 32,480)( 33,481)( 34,482)( 35,483)( 36,484)( 37,485)( 38,486)( 39,487)( 40,488)( 41,489)( 42,490)( 43,491)( 44,492)( 45,493)( 46,494)( 47,495)( 48,496)( 49,497)( 50,498)( 51,499)( 52,500)( 53,501)( 54,502)( 55,503)( 56,504)( 57,505)( 58,506)( 59,507)( 60,508)( 61,509)( 62,510)( 63,511)( 64,512)( 65,513)( 66,514)( 67,515)( 68,516)( 69,517)( 70,518)( 71,519)( 72,520)( 73,521)( 74,522)( 75,523)( 76,524)( 77,525)( 78,526)( 79,527)( 80,528)( 81,529)( 82,530)( 83,531)( 84,532)( 85,533)( 86,534)( 87,535)( 88,536)( 89,537)( 90,538)( 91,539)( 92,540)( 93,541)( 94,542)( 95,543)( 96,544)( 97,545)( 98,546)( 99,547)(100,548)(101,549)(102,550)(103,551)(104,552)(105,553)(106,554)(107,555)(108,556)(109,557)(110,558)(111,559)(112,560)(113,568)(114,569)(115,570)(116,571)(117,572)(118,573)(119,574)(120,561)(121,562)(122,563)(123,564)(124,565)(125,566)(126,567)(127,582)(128,583)(129,584)(130,585)(131,586)(132,587)(133,588)(134,575)(135,576)(136,577)(137,578)(138,579)(139,580)(140,581)(141,596)(142,597)(143,598)(144,599)(145,600)(146,601)(147,602)(148,589)(149,590)(150,591)(151,592)(152,593)(153,594)(154,595)(155,610)(156,611)(157,612)(158,613)(159,614)(160,615)(161,616)(162,603)(163,604)(164,605)(165,606)(166,607)(167,608)(168,609)(169,624)(170,625)(171,626)(172,627)(173,628)(174,629)(175,630)(176,617)(177,618)(178,619)(179,620)(180,621)(181,622)(182,623)(183,638)(184,639)(185,640)(186,641)(187,642)(188,643)(189,644)(190,631)(191,632)(192,633)(193,634)(194,635)(195,636)(196,637)(197,652)(198,653)(199,654)(200,655)(201,656)(202,657)(203,658)(204,645)(205,646)(206,647)(207,648)(208,649)(209,650)(210,651)(211,666)(212,667)(213,668)(214,669)(215,670)(216,671)(217,672)(218,659)(219,660)(220,661)(221,662)(222,663)(223,664)(224,665)(225,680)(226,681)(227,682)(228,683)(229,684)(230,685)(231,686)(232,673)(233,674)(234,675)(235,676)(236,677)(237,678)(238,679)(239,694)(240,695)(241,696)(242,697)(243,698)(244,699)(245,700)(246,687)(247,688)(248,689)(249,690)(250,691)(251,692)(252,693)(253,708)(254,709)(255,710)(256,711)(257,712)(258,713)(259,714)(260,701)(261,702)(262,703)(263,704)(264,705)(265,706)(266,707)(267,722)(268,723)(269,724)(270,725)(271,726)(272,727)(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)(280,721)(281,736)(282,737)(283,738)(284,739)(285,740)(286,741)(287,742)(288,729)(289,730)(290,731)(291,732)(292,733)(293,734)(294,735)(295,750)(296,751)(297,752)(298,753)(299,754)(300,755)(301,756)(302,743)(303,744)(304,745)(305,746)(306,747)(307,748)(308,749)(309,764)(310,765)(311,766)(312,767)(313,768)(314,769)(315,770)(316,757)(317,758)(318,759)(319,760)(320,761)(321,762)(322,763)(323,778)(324,779)(325,780)(326,781)(327,782)(328,783)(329,784)(330,771)(331,772)(332,773)(333,774)(334,775)(335,776)(336,777)(337,785)(338,786)(339,787)(340,788)(341,789)(342,790)(343,791)(344,792)(345,793)(346,794)(347,795)(348,796)(349,797)(350,798)(351,799)(352,800)(353,801)(354,802)(355,803)(356,804)(357,805)(358,806)(359,807)(360,808)(361,809)(362,810)(363,811)(364,812)(365,813)(366,814)(367,815)(368,816)(369,817)(370,818)(371,819)(372,820)(373,821)(374,822)(375,823)(376,824)(377,825)(378,826)(379,827)(380,828)(381,829)(382,830)(383,831)(384,832)(385,833)(386,834)(387,835)(388,836)(389,837)(390,838)(391,839)(392,840)(393,841)(394,842)(395,843)(396,844)(397,845)(398,846)(399,847)(400,848)(401,849)(402,850)(403,851)(404,852)(405,853)(406,854)(407,855)(408,856)(409,857)(410,858)(411,859)(412,860)(413,861)(414,862)(415,863)(416,864)(417,865)(418,866)(419,867)(420,868)(421,869)(422,870)(423,871)(424,872)(425,873)(426,874)(427,875)(428,876)(429,877)(430,878)(431,879)(432,880)(433,881)(434,882)(435,883)(436,884)(437,885)(438,886)(439,887)(440,888)(441,889)(442,890)(443,891)(444,892)(445,893)(446,894)(447,895)(448,896);
s2 := Sym(896)!(225,239)(226,240)(227,241)(228,242)(229,243)(230,244)(231,245)(232,246)(233,247)(234,248)(235,249)(236,250)(237,251)(238,252)(253,267)(254,268)(255,269)(256,270)(257,271)(258,272)(259,273)(260,274)(261,275)(262,276)(263,277)(264,278)(265,279)(266,280)(281,295)(282,296)(283,297)(284,298)(285,299)(286,300)(287,301)(288,302)(289,303)(290,304)(291,305)(292,306)(293,307)(294,308)(309,323)(310,324)(311,325)(312,326)(313,327)(314,328)(315,329)(316,330)(317,331)(318,332)(319,333)(320,334)(321,335)(322,336)(337,351)(338,352)(339,353)(340,354)(341,355)(342,356)(343,357)(344,358)(345,359)(346,360)(347,361)(348,362)(349,363)(350,364)(365,379)(366,380)(367,381)(368,382)(369,383)(370,384)(371,385)(372,386)(373,387)(374,388)(375,389)(376,390)(377,391)(378,392)(393,407)(394,408)(395,409)(396,410)(397,411)(398,412)(399,413)(400,414)(401,415)(402,416)(403,417)(404,418)(405,419)(406,420)(421,435)(422,436)(423,437)(424,438)(425,439)(426,440)(427,441)(428,442)(429,443)(430,444)(431,445)(432,446)(433,447)(434,448)(449,477)(450,478)(451,479)(452,480)(453,481)(454,482)(455,483)(456,484)(457,485)(458,486)(459,487)(460,488)(461,489)(462,490)(463,491)(464,492)(465,493)(466,494)(467,495)(468,496)(469,497)(470,498)(471,499)(472,500)(473,501)(474,502)(475,503)(476,504)(505,533)(506,534)(507,535)(508,536)(509,537)(510,538)(511,539)(512,540)(513,541)(514,542)(515,543)(516,544)(517,545)(518,546)(519,547)(520,548)(521,549)(522,550)(523,551)(524,552)(525,553)(526,554)(527,555)(528,556)(529,557)(530,558)(531,559)(532,560)(561,589)(562,590)(563,591)(564,592)(565,593)(566,594)(567,595)(568,596)(569,597)(570,598)(571,599)(572,600)(573,601)(574,602)(575,603)(576,604)(577,605)(578,606)(579,607)(580,608)(581,609)(582,610)(583,611)(584,612)(585,613)(586,614)(587,615)(588,616)(617,645)(618,646)(619,647)(620,648)(621,649)(622,650)(623,651)(624,652)(625,653)(626,654)(627,655)(628,656)(629,657)(630,658)(631,659)(632,660)(633,661)(634,662)(635,663)(636,664)(637,665)(638,666)(639,667)(640,668)(641,669)(642,670)(643,671)(644,672)(673,715)(674,716)(675,717)(676,718)(677,719)(678,720)(679,721)(680,722)(681,723)(682,724)(683,725)(684,726)(685,727)(686,728)(687,701)(688,702)(689,703)(690,704)(691,705)(692,706)(693,707)(694,708)(695,709)(696,710)(697,711)(698,712)(699,713)(700,714)(729,771)(730,772)(731,773)(732,774)(733,775)(734,776)(735,777)(736,778)(737,779)(738,780)(739,781)(740,782)(741,783)(742,784)(743,757)(744,758)(745,759)(746,760)(747,761)(748,762)(749,763)(750,764)(751,765)(752,766)(753,767)(754,768)(755,769)(756,770)(785,827)(786,828)(787,829)(788,830)(789,831)(790,832)(791,833)(792,834)(793,835)(794,836)(795,837)(796,838)(797,839)(798,840)(799,813)(800,814)(801,815)(802,816)(803,817)(804,818)(805,819)(806,820)(807,821)(808,822)(809,823)(810,824)(811,825)(812,826)(841,883)(842,884)(843,885)(844,886)(845,887)(846,888)(847,889)(848,890)(849,891)(850,892)(851,893)(852,894)(853,895)(854,896)(855,869)(856,870)(857,871)(858,872)(859,873)(860,874)(861,875)(862,876)(863,877)(864,878)(865,879)(866,880)(867,881)(868,882);
s3 := Sym(896)!(  1,393)(  2,399)(  3,398)(  4,397)(  5,396)(  6,395)(  7,394)(  8,400)(  9,406)( 10,405)( 11,404)( 12,403)( 13,402)( 14,401)( 15,407)( 16,413)( 17,412)( 18,411)( 19,410)( 20,409)( 21,408)( 22,414)( 23,420)( 24,419)( 25,418)( 26,417)( 27,416)( 28,415)( 29,421)( 30,427)( 31,426)( 32,425)( 33,424)( 34,423)( 35,422)( 36,428)( 37,434)( 38,433)( 39,432)( 40,431)( 41,430)( 42,429)( 43,435)( 44,441)( 45,440)( 46,439)( 47,438)( 48,437)( 49,436)( 50,442)( 51,448)( 52,447)( 53,446)( 54,445)( 55,444)( 56,443)( 57,337)( 58,343)( 59,342)( 60,341)( 61,340)( 62,339)( 63,338)( 64,344)( 65,350)( 66,349)( 67,348)( 68,347)( 69,346)( 70,345)( 71,351)( 72,357)( 73,356)( 74,355)( 75,354)( 76,353)( 77,352)( 78,358)( 79,364)( 80,363)( 81,362)( 82,361)( 83,360)( 84,359)( 85,365)( 86,371)( 87,370)( 88,369)( 89,368)( 90,367)( 91,366)( 92,372)( 93,378)( 94,377)( 95,376)( 96,375)( 97,374)( 98,373)( 99,379)(100,385)(101,384)(102,383)(103,382)(104,381)(105,380)(106,386)(107,392)(108,391)(109,390)(110,389)(111,388)(112,387)(113,281)(114,287)(115,286)(116,285)(117,284)(118,283)(119,282)(120,288)(121,294)(122,293)(123,292)(124,291)(125,290)(126,289)(127,295)(128,301)(129,300)(130,299)(131,298)(132,297)(133,296)(134,302)(135,308)(136,307)(137,306)(138,305)(139,304)(140,303)(141,309)(142,315)(143,314)(144,313)(145,312)(146,311)(147,310)(148,316)(149,322)(150,321)(151,320)(152,319)(153,318)(154,317)(155,323)(156,329)(157,328)(158,327)(159,326)(160,325)(161,324)(162,330)(163,336)(164,335)(165,334)(166,333)(167,332)(168,331)(169,225)(170,231)(171,230)(172,229)(173,228)(174,227)(175,226)(176,232)(177,238)(178,237)(179,236)(180,235)(181,234)(182,233)(183,239)(184,245)(185,244)(186,243)(187,242)(188,241)(189,240)(190,246)(191,252)(192,251)(193,250)(194,249)(195,248)(196,247)(197,253)(198,259)(199,258)(200,257)(201,256)(202,255)(203,254)(204,260)(205,266)(206,265)(207,264)(208,263)(209,262)(210,261)(211,267)(212,273)(213,272)(214,271)(215,270)(216,269)(217,268)(218,274)(219,280)(220,279)(221,278)(222,277)(223,276)(224,275)(449,841)(450,847)(451,846)(452,845)(453,844)(454,843)(455,842)(456,848)(457,854)(458,853)(459,852)(460,851)(461,850)(462,849)(463,855)(464,861)(465,860)(466,859)(467,858)(468,857)(469,856)(470,862)(471,868)(472,867)(473,866)(474,865)(475,864)(476,863)(477,869)(478,875)(479,874)(480,873)(481,872)(482,871)(483,870)(484,876)(485,882)(486,881)(487,880)(488,879)(489,878)(490,877)(491,883)(492,889)(493,888)(494,887)(495,886)(496,885)(497,884)(498,890)(499,896)(500,895)(501,894)(502,893)(503,892)(504,891)(505,785)(506,791)(507,790)(508,789)(509,788)(510,787)(511,786)(512,792)(513,798)(514,797)(515,796)(516,795)(517,794)(518,793)(519,799)(520,805)(521,804)(522,803)(523,802)(524,801)(525,800)(526,806)(527,812)(528,811)(529,810)(530,809)(531,808)(532,807)(533,813)(534,819)(535,818)(536,817)(537,816)(538,815)(539,814)(540,820)(541,826)(542,825)(543,824)(544,823)(545,822)(546,821)(547,827)(548,833)(549,832)(550,831)(551,830)(552,829)(553,828)(554,834)(555,840)(556,839)(557,838)(558,837)(559,836)(560,835)(561,729)(562,735)(563,734)(564,733)(565,732)(566,731)(567,730)(568,736)(569,742)(570,741)(571,740)(572,739)(573,738)(574,737)(575,743)(576,749)(577,748)(578,747)(579,746)(580,745)(581,744)(582,750)(583,756)(584,755)(585,754)(586,753)(587,752)(588,751)(589,757)(590,763)(591,762)(592,761)(593,760)(594,759)(595,758)(596,764)(597,770)(598,769)(599,768)(600,767)(601,766)(602,765)(603,771)(604,777)(605,776)(606,775)(607,774)(608,773)(609,772)(610,778)(611,784)(612,783)(613,782)(614,781)(615,780)(616,779)(617,673)(618,679)(619,678)(620,677)(621,676)(622,675)(623,674)(624,680)(625,686)(626,685)(627,684)(628,683)(629,682)(630,681)(631,687)(632,693)(633,692)(634,691)(635,690)(636,689)(637,688)(638,694)(639,700)(640,699)(641,698)(642,697)(643,696)(644,695)(645,701)(646,707)(647,706)(648,705)(649,704)(650,703)(651,702)(652,708)(653,714)(654,713)(655,712)(656,711)(657,710)(658,709)(659,715)(660,721)(661,720)(662,719)(663,718)(664,717)(665,716)(666,722)(667,728)(668,727)(669,726)(670,725)(671,724)(672,723);
s4 := Sym(896)!(  1, 58)(  2, 57)(  3, 63)(  4, 62)(  5, 61)(  6, 60)(  7, 59)(  8, 65)(  9, 64)( 10, 70)( 11, 69)( 12, 68)( 13, 67)( 14, 66)( 15, 72)( 16, 71)( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 79)( 23, 78)( 24, 84)( 25, 83)( 26, 82)( 27, 81)( 28, 80)( 29, 86)( 30, 85)( 31, 91)( 32, 90)( 33, 89)( 34, 88)( 35, 87)( 36, 93)( 37, 92)( 38, 98)( 39, 97)( 40, 96)( 41, 95)( 42, 94)( 43,100)( 44, 99)( 45,105)( 46,104)( 47,103)( 48,102)( 49,101)( 50,107)( 51,106)( 52,112)( 53,111)( 54,110)( 55,109)( 56,108)(113,170)(114,169)(115,175)(116,174)(117,173)(118,172)(119,171)(120,177)(121,176)(122,182)(123,181)(124,180)(125,179)(126,178)(127,184)(128,183)(129,189)(130,188)(131,187)(132,186)(133,185)(134,191)(135,190)(136,196)(137,195)(138,194)(139,193)(140,192)(141,198)(142,197)(143,203)(144,202)(145,201)(146,200)(147,199)(148,205)(149,204)(150,210)(151,209)(152,208)(153,207)(154,206)(155,212)(156,211)(157,217)(158,216)(159,215)(160,214)(161,213)(162,219)(163,218)(164,224)(165,223)(166,222)(167,221)(168,220)(225,282)(226,281)(227,287)(228,286)(229,285)(230,284)(231,283)(232,289)(233,288)(234,294)(235,293)(236,292)(237,291)(238,290)(239,296)(240,295)(241,301)(242,300)(243,299)(244,298)(245,297)(246,303)(247,302)(248,308)(249,307)(250,306)(251,305)(252,304)(253,310)(254,309)(255,315)(256,314)(257,313)(258,312)(259,311)(260,317)(261,316)(262,322)(263,321)(264,320)(265,319)(266,318)(267,324)(268,323)(269,329)(270,328)(271,327)(272,326)(273,325)(274,331)(275,330)(276,336)(277,335)(278,334)(279,333)(280,332)(337,394)(338,393)(339,399)(340,398)(341,397)(342,396)(343,395)(344,401)(345,400)(346,406)(347,405)(348,404)(349,403)(350,402)(351,408)(352,407)(353,413)(354,412)(355,411)(356,410)(357,409)(358,415)(359,414)(360,420)(361,419)(362,418)(363,417)(364,416)(365,422)(366,421)(367,427)(368,426)(369,425)(370,424)(371,423)(372,429)(373,428)(374,434)(375,433)(376,432)(377,431)(378,430)(379,436)(380,435)(381,441)(382,440)(383,439)(384,438)(385,437)(386,443)(387,442)(388,448)(389,447)(390,446)(391,445)(392,444)(449,506)(450,505)(451,511)(452,510)(453,509)(454,508)(455,507)(456,513)(457,512)(458,518)(459,517)(460,516)(461,515)(462,514)(463,520)(464,519)(465,525)(466,524)(467,523)(468,522)(469,521)(470,527)(471,526)(472,532)(473,531)(474,530)(475,529)(476,528)(477,534)(478,533)(479,539)(480,538)(481,537)(482,536)(483,535)(484,541)(485,540)(486,546)(487,545)(488,544)(489,543)(490,542)(491,548)(492,547)(493,553)(494,552)(495,551)(496,550)(497,549)(498,555)(499,554)(500,560)(501,559)(502,558)(503,557)(504,556)(561,618)(562,617)(563,623)(564,622)(565,621)(566,620)(567,619)(568,625)(569,624)(570,630)(571,629)(572,628)(573,627)(574,626)(575,632)(576,631)(577,637)(578,636)(579,635)(580,634)(581,633)(582,639)(583,638)(584,644)(585,643)(586,642)(587,641)(588,640)(589,646)(590,645)(591,651)(592,650)(593,649)(594,648)(595,647)(596,653)(597,652)(598,658)(599,657)(600,656)(601,655)(602,654)(603,660)(604,659)(605,665)(606,664)(607,663)(608,662)(609,661)(610,667)(611,666)(612,672)(613,671)(614,670)(615,669)(616,668)(673,730)(674,729)(675,735)(676,734)(677,733)(678,732)(679,731)(680,737)(681,736)(682,742)(683,741)(684,740)(685,739)(686,738)(687,744)(688,743)(689,749)(690,748)(691,747)(692,746)(693,745)(694,751)(695,750)(696,756)(697,755)(698,754)(699,753)(700,752)(701,758)(702,757)(703,763)(704,762)(705,761)(706,760)(707,759)(708,765)(709,764)(710,770)(711,769)(712,768)(713,767)(714,766)(715,772)(716,771)(717,777)(718,776)(719,775)(720,774)(721,773)(722,779)(723,778)(724,784)(725,783)(726,782)(727,781)(728,780)(785,842)(786,841)(787,847)(788,846)(789,845)(790,844)(791,843)(792,849)(793,848)(794,854)(795,853)(796,852)(797,851)(798,850)(799,856)(800,855)(801,861)(802,860)(803,859)(804,858)(805,857)(806,863)(807,862)(808,868)(809,867)(810,866)(811,865)(812,864)(813,870)(814,869)(815,875)(816,874)(817,873)(818,872)(819,871)(820,877)(821,876)(822,882)(823,881)(824,880)(825,879)(826,878)(827,884)(828,883)(829,889)(830,888)(831,887)(832,886)(833,885)(834,891)(835,890)(836,896)(837,895)(838,894)(839,893)(840,892);
poly := sub<Sym(896)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

References