Polytope of Type {4,38,4} with group SmallGroup(1216,1181)

Overview

Group: SmallGroup(1216,1181)
Rank: 4
Schläfli Type: {4,38,4}
Vertices, edges, …: 4, 76, 76, 4
Order of s₀s₁s₂s₃: 76
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{4,38|2},{38,4|2}}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat
Self-Dual

Quotients maximal quotients in bold

2-fold

4-fold

{2,38,2}*304

8-fold

{2,19,2}*152

19-fold

{4,2,4}*64

38-fold

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

Permutation Representation (Magma)

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

References