Polytope of Type {22,8,4} with group SmallGroup(1408,13831)

Overview

Group: SmallGroup(1408,13831)
Rank: 4
Schläfli Type: {22,8,4}
Vertices, edges, …: 22, 88, 16, 4
Order of s₀s₁s₂s₃: 88
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

{22,4,4}*704

4-fold

8-fold

11-fold

{2,8,4}*128b

16-fold

{11,2,2}*88

22-fold

{2,4,4}*64

44-fold

88-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, 89)(  2, 99)(  3, 98)(  4, 97)(  5, 96)(  6, 95)(  7, 94)(  8, 93)(  9, 92)( 10, 91)( 11, 90)( 12,100)( 13,110)( 14,109)( 15,108)( 16,107)( 17,106)( 18,105)( 19,104)( 20,103)( 21,102)( 22,101)( 23,111)( 24,121)( 25,120)( 26,119)( 27,118)( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)( 33,112)( 34,122)( 35,132)( 36,131)( 37,130)( 38,129)( 39,128)( 40,127)( 41,126)( 42,125)( 43,124)( 44,123)( 45,133)( 46,143)( 47,142)( 48,141)( 49,140)( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,134)( 56,144)( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)( 64,147)( 65,146)( 66,145)( 67,155)( 68,165)( 69,164)( 70,163)( 71,162)( 72,161)( 73,160)( 74,159)( 75,158)( 76,157)( 77,156)( 78,166)( 79,176)( 80,175)( 81,174)( 82,173)( 83,172)( 84,171)( 85,170)( 86,169)( 87,168)( 88,167)(177,265)(178,275)(179,274)(180,273)(181,272)(182,271)(183,270)(184,269)(185,268)(186,267)(187,266)(188,276)(189,286)(190,285)(191,284)(192,283)(193,282)(194,281)(195,280)(196,279)(197,278)(198,277)(199,287)(200,297)(201,296)(202,295)(203,294)(204,293)(205,292)(206,291)(207,290)(208,289)(209,288)(210,298)(211,308)(212,307)(213,306)(214,305)(215,304)(216,303)(217,302)(218,301)(219,300)(220,299)(221,309)(222,319)(223,318)(224,317)(225,316)(226,315)(227,314)(228,313)(229,312)(230,311)(231,310)(232,320)(233,330)(234,329)(235,328)(236,327)(237,326)(238,325)(239,324)(240,323)(241,322)(242,321)(243,331)(244,341)(245,340)(246,339)(247,338)(248,337)(249,336)(250,335)(251,334)(252,333)(253,332)(254,342)(255,352)(256,351)(257,350)(258,349)(259,348)(260,347)(261,346)(262,345)(263,344)(264,343)(353,441)(354,451)(355,450)(356,449)(357,448)(358,447)(359,446)(360,445)(361,444)(362,443)(363,442)(364,452)(365,462)(366,461)(367,460)(368,459)(369,458)(370,457)(371,456)(372,455)(373,454)(374,453)(375,463)(376,473)(377,472)(378,471)(379,470)(380,469)(381,468)(382,467)(383,466)(384,465)(385,464)(386,474)(387,484)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)(394,477)(395,476)(396,475)(397,485)(398,495)(399,494)(400,493)(401,492)(402,491)(403,490)(404,489)(405,488)(406,487)(407,486)(408,496)(409,506)(410,505)(411,504)(412,503)(413,502)(414,501)(415,500)(416,499)(417,498)(418,497)(419,507)(420,517)(421,516)(422,515)(423,514)(424,513)(425,512)(426,511)(427,510)(428,509)(429,508)(430,518)(431,528)(432,527)(433,526)(434,525)(435,524)(436,523)(437,522)(438,521)(439,520)(440,519)(529,617)(530,627)(531,626)(532,625)(533,624)(534,623)(535,622)(536,621)(537,620)(538,619)(539,618)(540,628)(541,638)(542,637)(543,636)(544,635)(545,634)(546,633)(547,632)(548,631)(549,630)(550,629)(551,639)(552,649)(553,648)(554,647)(555,646)(556,645)(557,644)(558,643)(559,642)(560,641)(561,640)(562,650)(563,660)(564,659)(565,658)(566,657)(567,656)(568,655)(569,654)(570,653)(571,652)(572,651)(573,661)(574,671)(575,670)(576,669)(577,668)(578,667)(579,666)(580,665)(581,664)(582,663)(583,662)(584,672)(585,682)(586,681)(587,680)(588,679)(589,678)(590,677)(591,676)(592,675)(593,674)(594,673)(595,683)(596,693)(597,692)(598,691)(599,690)(600,689)(601,688)(602,687)(603,686)(604,685)(605,684)(606,694)(607,704)(608,703)(609,702)(610,701)(611,700)(612,699)(613,698)(614,697)(615,696)(616,695);;
s1 := (  1,442)(  2,441)(  3,451)(  4,450)(  5,449)(  6,448)(  7,447)(  8,446)(  9,445)( 10,444)( 11,443)( 12,453)( 13,452)( 14,462)( 15,461)( 16,460)( 17,459)( 18,458)( 19,457)( 20,456)( 21,455)( 22,454)( 23,475)( 24,474)( 25,484)( 26,483)( 27,482)( 28,481)( 29,480)( 30,479)( 31,478)( 32,477)( 33,476)( 34,464)( 35,463)( 36,473)( 37,472)( 38,471)( 39,470)( 40,469)( 41,468)( 42,467)( 43,466)( 44,465)( 45,497)( 46,496)( 47,506)( 48,505)( 49,504)( 50,503)( 51,502)( 52,501)( 53,500)( 54,499)( 55,498)( 56,486)( 57,485)( 58,495)( 59,494)( 60,493)( 61,492)( 62,491)( 63,490)( 64,489)( 65,488)( 66,487)( 67,508)( 68,507)( 69,517)( 70,516)( 71,515)( 72,514)( 73,513)( 74,512)( 75,511)( 76,510)( 77,509)( 78,519)( 79,518)( 80,528)( 81,527)( 82,526)( 83,525)( 84,524)( 85,523)( 86,522)( 87,521)( 88,520)( 89,354)( 90,353)( 91,363)( 92,362)( 93,361)( 94,360)( 95,359)( 96,358)( 97,357)( 98,356)( 99,355)(100,365)(101,364)(102,374)(103,373)(104,372)(105,371)(106,370)(107,369)(108,368)(109,367)(110,366)(111,387)(112,386)(113,396)(114,395)(115,394)(116,393)(117,392)(118,391)(119,390)(120,389)(121,388)(122,376)(123,375)(124,385)(125,384)(126,383)(127,382)(128,381)(129,380)(130,379)(131,378)(132,377)(133,409)(134,408)(135,418)(136,417)(137,416)(138,415)(139,414)(140,413)(141,412)(142,411)(143,410)(144,398)(145,397)(146,407)(147,406)(148,405)(149,404)(150,403)(151,402)(152,401)(153,400)(154,399)(155,420)(156,419)(157,429)(158,428)(159,427)(160,426)(161,425)(162,424)(163,423)(164,422)(165,421)(166,431)(167,430)(168,440)(169,439)(170,438)(171,437)(172,436)(173,435)(174,434)(175,433)(176,432)(177,618)(178,617)(179,627)(180,626)(181,625)(182,624)(183,623)(184,622)(185,621)(186,620)(187,619)(188,629)(189,628)(190,638)(191,637)(192,636)(193,635)(194,634)(195,633)(196,632)(197,631)(198,630)(199,651)(200,650)(201,660)(202,659)(203,658)(204,657)(205,656)(206,655)(207,654)(208,653)(209,652)(210,640)(211,639)(212,649)(213,648)(214,647)(215,646)(216,645)(217,644)(218,643)(219,642)(220,641)(221,673)(222,672)(223,682)(224,681)(225,680)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)(232,662)(233,661)(234,671)(235,670)(236,669)(237,668)(238,667)(239,666)(240,665)(241,664)(242,663)(243,684)(244,683)(245,693)(246,692)(247,691)(248,690)(249,689)(250,688)(251,687)(252,686)(253,685)(254,695)(255,694)(256,704)(257,703)(258,702)(259,701)(260,700)(261,699)(262,698)(263,697)(264,696)(265,530)(266,529)(267,539)(268,538)(269,537)(270,536)(271,535)(272,534)(273,533)(274,532)(275,531)(276,541)(277,540)(278,550)(279,549)(280,548)(281,547)(282,546)(283,545)(284,544)(285,543)(286,542)(287,563)(288,562)(289,572)(290,571)(291,570)(292,569)(293,568)(294,567)(295,566)(296,565)(297,564)(298,552)(299,551)(300,561)(301,560)(302,559)(303,558)(304,557)(305,556)(306,555)(307,554)(308,553)(309,585)(310,584)(311,594)(312,593)(313,592)(314,591)(315,590)(316,589)(317,588)(318,587)(319,586)(320,574)(321,573)(322,583)(323,582)(324,581)(325,580)(326,579)(327,578)(328,577)(329,576)(330,575)(331,596)(332,595)(333,605)(334,604)(335,603)(336,602)(337,601)(338,600)(339,599)(340,598)(341,597)(342,607)(343,606)(344,616)(345,615)(346,614)(347,613)(348,612)(349,611)(350,610)(351,609)(352,608);;
s2 := ( 45, 56)( 46, 57)( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 67, 78)( 68, 79)( 69, 80)( 70, 81)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)(133,144)(134,145)(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)(142,153)(143,154)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)(161,172)(162,173)(163,174)(164,175)(165,176)(177,199)(178,200)(179,201)(180,202)(181,203)(182,204)(183,205)(184,206)(185,207)(186,208)(187,209)(188,210)(189,211)(190,212)(191,213)(192,214)(193,215)(194,216)(195,217)(196,218)(197,219)(198,220)(221,254)(222,255)(223,256)(224,257)(225,258)(226,259)(227,260)(228,261)(229,262)(230,263)(231,264)(232,243)(233,244)(234,245)(235,246)(236,247)(237,248)(238,249)(239,250)(240,251)(241,252)(242,253)(265,287)(266,288)(267,289)(268,290)(269,291)(270,292)(271,293)(272,294)(273,295)(274,296)(275,297)(276,298)(277,299)(278,300)(279,301)(280,302)(281,303)(282,304)(283,305)(284,306)(285,307)(286,308)(309,342)(310,343)(311,344)(312,345)(313,346)(314,347)(315,348)(316,349)(317,350)(318,351)(319,352)(320,331)(321,332)(322,333)(323,334)(324,335)(325,336)(326,337)(327,338)(328,339)(329,340)(330,341)(353,397)(354,398)(355,399)(356,400)(357,401)(358,402)(359,403)(360,404)(361,405)(362,406)(363,407)(364,408)(365,409)(366,410)(367,411)(368,412)(369,413)(370,414)(371,415)(372,416)(373,417)(374,418)(375,419)(376,420)(377,421)(378,422)(379,423)(380,424)(381,425)(382,426)(383,427)(384,428)(385,429)(386,430)(387,431)(388,432)(389,433)(390,434)(391,435)(392,436)(393,437)(394,438)(395,439)(396,440)(441,485)(442,486)(443,487)(444,488)(445,489)(446,490)(447,491)(448,492)(449,493)(450,494)(451,495)(452,496)(453,497)(454,498)(455,499)(456,500)(457,501)(458,502)(459,503)(460,504)(461,505)(462,506)(463,507)(464,508)(465,509)(466,510)(467,511)(468,512)(469,513)(470,514)(471,515)(472,516)(473,517)(474,518)(475,519)(476,520)(477,521)(478,522)(479,523)(480,524)(481,525)(482,526)(483,527)(484,528)(529,606)(530,607)(531,608)(532,609)(533,610)(534,611)(535,612)(536,613)(537,614)(538,615)(539,616)(540,595)(541,596)(542,597)(543,598)(544,599)(545,600)(546,601)(547,602)(548,603)(549,604)(550,605)(551,584)(552,585)(553,586)(554,587)(555,588)(556,589)(557,590)(558,591)(559,592)(560,593)(561,594)(562,573)(563,574)(564,575)(565,576)(566,577)(567,578)(568,579)(569,580)(570,581)(571,582)(572,583)(617,694)(618,695)(619,696)(620,697)(621,698)(622,699)(623,700)(624,701)(625,702)(626,703)(627,704)(628,683)(629,684)(630,685)(631,686)(632,687)(633,688)(634,689)(635,690)(636,691)(637,692)(638,693)(639,672)(640,673)(641,674)(642,675)(643,676)(644,677)(645,678)(646,679)(647,680)(648,681)(649,682)(650,661)(651,662)(652,663)(653,664)(654,665)(655,666)(656,667)(657,668)(658,669)(659,670)(660,671);;
s3 := (  1,177)(  2,178)(  3,179)(  4,180)(  5,181)(  6,182)(  7,183)(  8,184)(  9,185)( 10,186)( 11,187)( 12,188)( 13,189)( 14,190)( 15,191)( 16,192)( 17,193)( 18,194)( 19,195)( 20,196)( 21,197)( 22,198)( 23,199)( 24,200)( 25,201)( 26,202)( 27,203)( 28,204)( 29,205)( 30,206)( 31,207)( 32,208)( 33,209)( 34,210)( 35,211)( 36,212)( 37,213)( 38,214)( 39,215)( 40,216)( 41,217)( 42,218)( 43,219)( 44,220)( 45,232)( 46,233)( 47,234)( 48,235)( 49,236)( 50,237)( 51,238)( 52,239)( 53,240)( 54,241)( 55,242)( 56,221)( 57,222)( 58,223)( 59,224)( 60,225)( 61,226)( 62,227)( 63,228)( 64,229)( 65,230)( 66,231)( 67,254)( 68,255)( 69,256)( 70,257)( 71,258)( 72,259)( 73,260)( 74,261)( 75,262)( 76,263)( 77,264)( 78,243)( 79,244)( 80,245)( 81,246)( 82,247)( 83,248)( 84,249)( 85,250)( 86,251)( 87,252)( 88,253)( 89,265)( 90,266)( 91,267)( 92,268)( 93,269)( 94,270)( 95,271)( 96,272)( 97,273)( 98,274)( 99,275)(100,276)(101,277)(102,278)(103,279)(104,280)(105,281)(106,282)(107,283)(108,284)(109,285)(110,286)(111,287)(112,288)(113,289)(114,290)(115,291)(116,292)(117,293)(118,294)(119,295)(120,296)(121,297)(122,298)(123,299)(124,300)(125,301)(126,302)(127,303)(128,304)(129,305)(130,306)(131,307)(132,308)(133,320)(134,321)(135,322)(136,323)(137,324)(138,325)(139,326)(140,327)(141,328)(142,329)(143,330)(144,309)(145,310)(146,311)(147,312)(148,313)(149,314)(150,315)(151,316)(152,317)(153,318)(154,319)(155,342)(156,343)(157,344)(158,345)(159,346)(160,347)(161,348)(162,349)(163,350)(164,351)(165,352)(166,331)(167,332)(168,333)(169,334)(170,335)(171,336)(172,337)(173,338)(174,339)(175,340)(176,341)(353,529)(354,530)(355,531)(356,532)(357,533)(358,534)(359,535)(360,536)(361,537)(362,538)(363,539)(364,540)(365,541)(366,542)(367,543)(368,544)(369,545)(370,546)(371,547)(372,548)(373,549)(374,550)(375,551)(376,552)(377,553)(378,554)(379,555)(380,556)(381,557)(382,558)(383,559)(384,560)(385,561)(386,562)(387,563)(388,564)(389,565)(390,566)(391,567)(392,568)(393,569)(394,570)(395,571)(396,572)(397,584)(398,585)(399,586)(400,587)(401,588)(402,589)(403,590)(404,591)(405,592)(406,593)(407,594)(408,573)(409,574)(410,575)(411,576)(412,577)(413,578)(414,579)(415,580)(416,581)(417,582)(418,583)(419,606)(420,607)(421,608)(422,609)(423,610)(424,611)(425,612)(426,613)(427,614)(428,615)(429,616)(430,595)(431,596)(432,597)(433,598)(434,599)(435,600)(436,601)(437,602)(438,603)(439,604)(440,605)(441,617)(442,618)(443,619)(444,620)(445,621)(446,622)(447,623)(448,624)(449,625)(450,626)(451,627)(452,628)(453,629)(454,630)(455,631)(456,632)(457,633)(458,634)(459,635)(460,636)(461,637)(462,638)(463,639)(464,640)(465,641)(466,642)(467,643)(468,644)(469,645)(470,646)(471,647)(472,648)(473,649)(474,650)(475,651)(476,652)(477,653)(478,654)(479,655)(480,656)(481,657)(482,658)(483,659)(484,660)(485,672)(486,673)(487,674)(488,675)(489,676)(490,677)(491,678)(492,679)(493,680)(494,681)(495,682)(496,661)(497,662)(498,663)(499,664)(500,665)(501,666)(502,667)(503,668)(504,669)(505,670)(506,671)(507,694)(508,695)(509,696)(510,697)(511,698)(512,699)(513,700)(514,701)(515,702)(516,703)(517,704)(518,683)(519,684)(520,685)(521,686)(522,687)(523,688)(524,689)(525,690)(526,691)(527,692)(528,693);;
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*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(704)!(  1, 89)(  2, 99)(  3, 98)(  4, 97)(  5, 96)(  6, 95)(  7, 94)(  8, 93)(  9, 92)( 10, 91)( 11, 90)( 12,100)( 13,110)( 14,109)( 15,108)( 16,107)( 17,106)( 18,105)( 19,104)( 20,103)( 21,102)( 22,101)( 23,111)( 24,121)( 25,120)( 26,119)( 27,118)( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)( 33,112)( 34,122)( 35,132)( 36,131)( 37,130)( 38,129)( 39,128)( 40,127)( 41,126)( 42,125)( 43,124)( 44,123)( 45,133)( 46,143)( 47,142)( 48,141)( 49,140)( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,134)( 56,144)( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)( 64,147)( 65,146)( 66,145)( 67,155)( 68,165)( 69,164)( 70,163)( 71,162)( 72,161)( 73,160)( 74,159)( 75,158)( 76,157)( 77,156)( 78,166)( 79,176)( 80,175)( 81,174)( 82,173)( 83,172)( 84,171)( 85,170)( 86,169)( 87,168)( 88,167)(177,265)(178,275)(179,274)(180,273)(181,272)(182,271)(183,270)(184,269)(185,268)(186,267)(187,266)(188,276)(189,286)(190,285)(191,284)(192,283)(193,282)(194,281)(195,280)(196,279)(197,278)(198,277)(199,287)(200,297)(201,296)(202,295)(203,294)(204,293)(205,292)(206,291)(207,290)(208,289)(209,288)(210,298)(211,308)(212,307)(213,306)(214,305)(215,304)(216,303)(217,302)(218,301)(219,300)(220,299)(221,309)(222,319)(223,318)(224,317)(225,316)(226,315)(227,314)(228,313)(229,312)(230,311)(231,310)(232,320)(233,330)(234,329)(235,328)(236,327)(237,326)(238,325)(239,324)(240,323)(241,322)(242,321)(243,331)(244,341)(245,340)(246,339)(247,338)(248,337)(249,336)(250,335)(251,334)(252,333)(253,332)(254,342)(255,352)(256,351)(257,350)(258,349)(259,348)(260,347)(261,346)(262,345)(263,344)(264,343)(353,441)(354,451)(355,450)(356,449)(357,448)(358,447)(359,446)(360,445)(361,444)(362,443)(363,442)(364,452)(365,462)(366,461)(367,460)(368,459)(369,458)(370,457)(371,456)(372,455)(373,454)(374,453)(375,463)(376,473)(377,472)(378,471)(379,470)(380,469)(381,468)(382,467)(383,466)(384,465)(385,464)(386,474)(387,484)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)(394,477)(395,476)(396,475)(397,485)(398,495)(399,494)(400,493)(401,492)(402,491)(403,490)(404,489)(405,488)(406,487)(407,486)(408,496)(409,506)(410,505)(411,504)(412,503)(413,502)(414,501)(415,500)(416,499)(417,498)(418,497)(419,507)(420,517)(421,516)(422,515)(423,514)(424,513)(425,512)(426,511)(427,510)(428,509)(429,508)(430,518)(431,528)(432,527)(433,526)(434,525)(435,524)(436,523)(437,522)(438,521)(439,520)(440,519)(529,617)(530,627)(531,626)(532,625)(533,624)(534,623)(535,622)(536,621)(537,620)(538,619)(539,618)(540,628)(541,638)(542,637)(543,636)(544,635)(545,634)(546,633)(547,632)(548,631)(549,630)(550,629)(551,639)(552,649)(553,648)(554,647)(555,646)(556,645)(557,644)(558,643)(559,642)(560,641)(561,640)(562,650)(563,660)(564,659)(565,658)(566,657)(567,656)(568,655)(569,654)(570,653)(571,652)(572,651)(573,661)(574,671)(575,670)(576,669)(577,668)(578,667)(579,666)(580,665)(581,664)(582,663)(583,662)(584,672)(585,682)(586,681)(587,680)(588,679)(589,678)(590,677)(591,676)(592,675)(593,674)(594,673)(595,683)(596,693)(597,692)(598,691)(599,690)(600,689)(601,688)(602,687)(603,686)(604,685)(605,684)(606,694)(607,704)(608,703)(609,702)(610,701)(611,700)(612,699)(613,698)(614,697)(615,696)(616,695);
s1 := Sym(704)!(  1,442)(  2,441)(  3,451)(  4,450)(  5,449)(  6,448)(  7,447)(  8,446)(  9,445)( 10,444)( 11,443)( 12,453)( 13,452)( 14,462)( 15,461)( 16,460)( 17,459)( 18,458)( 19,457)( 20,456)( 21,455)( 22,454)( 23,475)( 24,474)( 25,484)( 26,483)( 27,482)( 28,481)( 29,480)( 30,479)( 31,478)( 32,477)( 33,476)( 34,464)( 35,463)( 36,473)( 37,472)( 38,471)( 39,470)( 40,469)( 41,468)( 42,467)( 43,466)( 44,465)( 45,497)( 46,496)( 47,506)( 48,505)( 49,504)( 50,503)( 51,502)( 52,501)( 53,500)( 54,499)( 55,498)( 56,486)( 57,485)( 58,495)( 59,494)( 60,493)( 61,492)( 62,491)( 63,490)( 64,489)( 65,488)( 66,487)( 67,508)( 68,507)( 69,517)( 70,516)( 71,515)( 72,514)( 73,513)( 74,512)( 75,511)( 76,510)( 77,509)( 78,519)( 79,518)( 80,528)( 81,527)( 82,526)( 83,525)( 84,524)( 85,523)( 86,522)( 87,521)( 88,520)( 89,354)( 90,353)( 91,363)( 92,362)( 93,361)( 94,360)( 95,359)( 96,358)( 97,357)( 98,356)( 99,355)(100,365)(101,364)(102,374)(103,373)(104,372)(105,371)(106,370)(107,369)(108,368)(109,367)(110,366)(111,387)(112,386)(113,396)(114,395)(115,394)(116,393)(117,392)(118,391)(119,390)(120,389)(121,388)(122,376)(123,375)(124,385)(125,384)(126,383)(127,382)(128,381)(129,380)(130,379)(131,378)(132,377)(133,409)(134,408)(135,418)(136,417)(137,416)(138,415)(139,414)(140,413)(141,412)(142,411)(143,410)(144,398)(145,397)(146,407)(147,406)(148,405)(149,404)(150,403)(151,402)(152,401)(153,400)(154,399)(155,420)(156,419)(157,429)(158,428)(159,427)(160,426)(161,425)(162,424)(163,423)(164,422)(165,421)(166,431)(167,430)(168,440)(169,439)(170,438)(171,437)(172,436)(173,435)(174,434)(175,433)(176,432)(177,618)(178,617)(179,627)(180,626)(181,625)(182,624)(183,623)(184,622)(185,621)(186,620)(187,619)(188,629)(189,628)(190,638)(191,637)(192,636)(193,635)(194,634)(195,633)(196,632)(197,631)(198,630)(199,651)(200,650)(201,660)(202,659)(203,658)(204,657)(205,656)(206,655)(207,654)(208,653)(209,652)(210,640)(211,639)(212,649)(213,648)(214,647)(215,646)(216,645)(217,644)(218,643)(219,642)(220,641)(221,673)(222,672)(223,682)(224,681)(225,680)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)(232,662)(233,661)(234,671)(235,670)(236,669)(237,668)(238,667)(239,666)(240,665)(241,664)(242,663)(243,684)(244,683)(245,693)(246,692)(247,691)(248,690)(249,689)(250,688)(251,687)(252,686)(253,685)(254,695)(255,694)(256,704)(257,703)(258,702)(259,701)(260,700)(261,699)(262,698)(263,697)(264,696)(265,530)(266,529)(267,539)(268,538)(269,537)(270,536)(271,535)(272,534)(273,533)(274,532)(275,531)(276,541)(277,540)(278,550)(279,549)(280,548)(281,547)(282,546)(283,545)(284,544)(285,543)(286,542)(287,563)(288,562)(289,572)(290,571)(291,570)(292,569)(293,568)(294,567)(295,566)(296,565)(297,564)(298,552)(299,551)(300,561)(301,560)(302,559)(303,558)(304,557)(305,556)(306,555)(307,554)(308,553)(309,585)(310,584)(311,594)(312,593)(313,592)(314,591)(315,590)(316,589)(317,588)(318,587)(319,586)(320,574)(321,573)(322,583)(323,582)(324,581)(325,580)(326,579)(327,578)(328,577)(329,576)(330,575)(331,596)(332,595)(333,605)(334,604)(335,603)(336,602)(337,601)(338,600)(339,599)(340,598)(341,597)(342,607)(343,606)(344,616)(345,615)(346,614)(347,613)(348,612)(349,611)(350,610)(351,609)(352,608);
s2 := Sym(704)!( 45, 56)( 46, 57)( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 67, 78)( 68, 79)( 69, 80)( 70, 81)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)(133,144)(134,145)(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)(142,153)(143,154)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)(161,172)(162,173)(163,174)(164,175)(165,176)(177,199)(178,200)(179,201)(180,202)(181,203)(182,204)(183,205)(184,206)(185,207)(186,208)(187,209)(188,210)(189,211)(190,212)(191,213)(192,214)(193,215)(194,216)(195,217)(196,218)(197,219)(198,220)(221,254)(222,255)(223,256)(224,257)(225,258)(226,259)(227,260)(228,261)(229,262)(230,263)(231,264)(232,243)(233,244)(234,245)(235,246)(236,247)(237,248)(238,249)(239,250)(240,251)(241,252)(242,253)(265,287)(266,288)(267,289)(268,290)(269,291)(270,292)(271,293)(272,294)(273,295)(274,296)(275,297)(276,298)(277,299)(278,300)(279,301)(280,302)(281,303)(282,304)(283,305)(284,306)(285,307)(286,308)(309,342)(310,343)(311,344)(312,345)(313,346)(314,347)(315,348)(316,349)(317,350)(318,351)(319,352)(320,331)(321,332)(322,333)(323,334)(324,335)(325,336)(326,337)(327,338)(328,339)(329,340)(330,341)(353,397)(354,398)(355,399)(356,400)(357,401)(358,402)(359,403)(360,404)(361,405)(362,406)(363,407)(364,408)(365,409)(366,410)(367,411)(368,412)(369,413)(370,414)(371,415)(372,416)(373,417)(374,418)(375,419)(376,420)(377,421)(378,422)(379,423)(380,424)(381,425)(382,426)(383,427)(384,428)(385,429)(386,430)(387,431)(388,432)(389,433)(390,434)(391,435)(392,436)(393,437)(394,438)(395,439)(396,440)(441,485)(442,486)(443,487)(444,488)(445,489)(446,490)(447,491)(448,492)(449,493)(450,494)(451,495)(452,496)(453,497)(454,498)(455,499)(456,500)(457,501)(458,502)(459,503)(460,504)(461,505)(462,506)(463,507)(464,508)(465,509)(466,510)(467,511)(468,512)(469,513)(470,514)(471,515)(472,516)(473,517)(474,518)(475,519)(476,520)(477,521)(478,522)(479,523)(480,524)(481,525)(482,526)(483,527)(484,528)(529,606)(530,607)(531,608)(532,609)(533,610)(534,611)(535,612)(536,613)(537,614)(538,615)(539,616)(540,595)(541,596)(542,597)(543,598)(544,599)(545,600)(546,601)(547,602)(548,603)(549,604)(550,605)(551,584)(552,585)(553,586)(554,587)(555,588)(556,589)(557,590)(558,591)(559,592)(560,593)(561,594)(562,573)(563,574)(564,575)(565,576)(566,577)(567,578)(568,579)(569,580)(570,581)(571,582)(572,583)(617,694)(618,695)(619,696)(620,697)(621,698)(622,699)(623,700)(624,701)(625,702)(626,703)(627,704)(628,683)(629,684)(630,685)(631,686)(632,687)(633,688)(634,689)(635,690)(636,691)(637,692)(638,693)(639,672)(640,673)(641,674)(642,675)(643,676)(644,677)(645,678)(646,679)(647,680)(648,681)(649,682)(650,661)(651,662)(652,663)(653,664)(654,665)(655,666)(656,667)(657,668)(658,669)(659,670)(660,671);
s3 := Sym(704)!(  1,177)(  2,178)(  3,179)(  4,180)(  5,181)(  6,182)(  7,183)(  8,184)(  9,185)( 10,186)( 11,187)( 12,188)( 13,189)( 14,190)( 15,191)( 16,192)( 17,193)( 18,194)( 19,195)( 20,196)( 21,197)( 22,198)( 23,199)( 24,200)( 25,201)( 26,202)( 27,203)( 28,204)( 29,205)( 30,206)( 31,207)( 32,208)( 33,209)( 34,210)( 35,211)( 36,212)( 37,213)( 38,214)( 39,215)( 40,216)( 41,217)( 42,218)( 43,219)( 44,220)( 45,232)( 46,233)( 47,234)( 48,235)( 49,236)( 50,237)( 51,238)( 52,239)( 53,240)( 54,241)( 55,242)( 56,221)( 57,222)( 58,223)( 59,224)( 60,225)( 61,226)( 62,227)( 63,228)( 64,229)( 65,230)( 66,231)( 67,254)( 68,255)( 69,256)( 70,257)( 71,258)( 72,259)( 73,260)( 74,261)( 75,262)( 76,263)( 77,264)( 78,243)( 79,244)( 80,245)( 81,246)( 82,247)( 83,248)( 84,249)( 85,250)( 86,251)( 87,252)( 88,253)( 89,265)( 90,266)( 91,267)( 92,268)( 93,269)( 94,270)( 95,271)( 96,272)( 97,273)( 98,274)( 99,275)(100,276)(101,277)(102,278)(103,279)(104,280)(105,281)(106,282)(107,283)(108,284)(109,285)(110,286)(111,287)(112,288)(113,289)(114,290)(115,291)(116,292)(117,293)(118,294)(119,295)(120,296)(121,297)(122,298)(123,299)(124,300)(125,301)(126,302)(127,303)(128,304)(129,305)(130,306)(131,307)(132,308)(133,320)(134,321)(135,322)(136,323)(137,324)(138,325)(139,326)(140,327)(141,328)(142,329)(143,330)(144,309)(145,310)(146,311)(147,312)(148,313)(149,314)(150,315)(151,316)(152,317)(153,318)(154,319)(155,342)(156,343)(157,344)(158,345)(159,346)(160,347)(161,348)(162,349)(163,350)(164,351)(165,352)(166,331)(167,332)(168,333)(169,334)(170,335)(171,336)(172,337)(173,338)(174,339)(175,340)(176,341)(353,529)(354,530)(355,531)(356,532)(357,533)(358,534)(359,535)(360,536)(361,537)(362,538)(363,539)(364,540)(365,541)(366,542)(367,543)(368,544)(369,545)(370,546)(371,547)(372,548)(373,549)(374,550)(375,551)(376,552)(377,553)(378,554)(379,555)(380,556)(381,557)(382,558)(383,559)(384,560)(385,561)(386,562)(387,563)(388,564)(389,565)(390,566)(391,567)(392,568)(393,569)(394,570)(395,571)(396,572)(397,584)(398,585)(399,586)(400,587)(401,588)(402,589)(403,590)(404,591)(405,592)(406,593)(407,594)(408,573)(409,574)(410,575)(411,576)(412,577)(413,578)(414,579)(415,580)(416,581)(417,582)(418,583)(419,606)(420,607)(421,608)(422,609)(423,610)(424,611)(425,612)(426,613)(427,614)(428,615)(429,616)(430,595)(431,596)(432,597)(433,598)(434,599)(435,600)(436,601)(437,602)(438,603)(439,604)(440,605)(441,617)(442,618)(443,619)(444,620)(445,621)(446,622)(447,623)(448,624)(449,625)(450,626)(451,627)(452,628)(453,629)(454,630)(455,631)(456,632)(457,633)(458,634)(459,635)(460,636)(461,637)(462,638)(463,639)(464,640)(465,641)(466,642)(467,643)(468,644)(469,645)(470,646)(471,647)(472,648)(473,649)(474,650)(475,651)(476,652)(477,653)(478,654)(479,655)(480,656)(481,657)(482,658)(483,659)(484,660)(485,672)(486,673)(487,674)(488,675)(489,676)(490,677)(491,678)(492,679)(493,680)(494,681)(495,682)(496,661)(497,662)(498,663)(499,664)(500,665)(501,666)(502,667)(503,668)(504,669)(505,670)(506,671)(507,694)(508,695)(509,696)(510,697)(511,698)(512,699)(513,700)(514,701)(515,702)(516,703)(517,704)(518,683)(519,684)(520,685)(521,686)(522,687)(523,688)(524,689)(525,690)(526,691)(527,692)(528,693);
poly := sub<Sym(704)|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*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References