Polytope of Type {3,6,12,4} with group SmallGroup(1728,30242)

Overview

Group: SmallGroup(1728,30242)
Rank: 5
Schläfli Type: {3,6,12,4}
Vertices, edges, …: 3, 9, 36, 24, 4
Order of s₀s₁s₂s₃s₄: 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Non-Orientable
Flat

Quotients maximal quotients in bold

2-fold

{3,6,6,4}*864b

3-fold

{3,2,12,4}*576b

4-fold

{3,6,3,4}*432

6-fold

{3,2,6,4}*288c

12-fold

{3,2,3,4}*144

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (  5,  9)(  6, 10)(  7, 11)(  8, 12)( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 69)( 54, 70)( 55, 71)( 56, 72)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89,105)( 90,106)( 91,107)( 92,108)( 93,101)( 94,102)( 95,103)( 96,104)(113,117)(114,118)(115,119)(116,120)(121,133)(122,134)(123,135)(124,136)(125,141)(126,142)(127,143)(128,144)(129,137)(130,138)(131,139)(132,140)(149,153)(150,154)(151,155)(152,156)(157,169)(158,170)(159,171)(160,172)(161,177)(162,178)(163,179)(164,180)(165,173)(166,174)(167,175)(168,176)(185,189)(186,190)(187,191)(188,192)(193,205)(194,206)(195,207)(196,208)(197,213)(198,214)(199,215)(200,216)(201,209)(202,210)(203,211)(204,212)(221,225)(222,226)(223,227)(224,228)(229,241)(230,242)(231,243)(232,244)(233,249)(234,250)(235,251)(236,252)(237,245)(238,246)(239,247)(240,248)(257,261)(258,262)(259,263)(260,264)(265,277)(266,278)(267,279)(268,280)(269,285)(270,286)(271,287)(272,288)(273,281)(274,282)(275,283)(276,284)(293,297)(294,298)(295,299)(296,300)(301,313)(302,314)(303,315)(304,316)(305,321)(306,322)(307,323)(308,324)(309,317)(310,318)(311,319)(312,320)(329,333)(330,334)(331,335)(332,336)(337,349)(338,350)(339,351)(340,352)(341,357)(342,358)(343,359)(344,360)(345,353)(346,354)(347,355)(348,356)(365,369)(366,370)(367,371)(368,372)(373,385)(374,386)(375,387)(376,388)(377,393)(378,394)(379,395)(380,396)(381,389)(382,390)(383,391)(384,392)(401,405)(402,406)(403,407)(404,408)(409,421)(410,422)(411,423)(412,424)(413,429)(414,430)(415,431)(416,432)(417,425)(418,426)(419,427)(420,428);;
s1 := (  1, 13)(  2, 14)(  3, 15)(  4, 16)(  5, 21)(  6, 22)(  7, 23)(  8, 24)(  9, 17)( 10, 18)( 11, 19)( 12, 20)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 37, 49)( 38, 50)( 39, 51)( 40, 52)( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 53)( 46, 54)( 47, 55)( 48, 56)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 85)( 74, 86)( 75, 87)( 76, 88)( 77, 93)( 78, 94)( 79, 95)( 80, 96)( 81, 89)( 82, 90)( 83, 91)( 84, 92)(101,105)(102,106)(103,107)(104,108)(109,121)(110,122)(111,123)(112,124)(113,129)(114,130)(115,131)(116,132)(117,125)(118,126)(119,127)(120,128)(137,141)(138,142)(139,143)(140,144)(145,157)(146,158)(147,159)(148,160)(149,165)(150,166)(151,167)(152,168)(153,161)(154,162)(155,163)(156,164)(173,177)(174,178)(175,179)(176,180)(181,193)(182,194)(183,195)(184,196)(185,201)(186,202)(187,203)(188,204)(189,197)(190,198)(191,199)(192,200)(209,213)(210,214)(211,215)(212,216)(217,229)(218,230)(219,231)(220,232)(221,237)(222,238)(223,239)(224,240)(225,233)(226,234)(227,235)(228,236)(245,249)(246,250)(247,251)(248,252)(253,265)(254,266)(255,267)(256,268)(257,273)(258,274)(259,275)(260,276)(261,269)(262,270)(263,271)(264,272)(281,285)(282,286)(283,287)(284,288)(289,301)(290,302)(291,303)(292,304)(293,309)(294,310)(295,311)(296,312)(297,305)(298,306)(299,307)(300,308)(317,321)(318,322)(319,323)(320,324)(325,337)(326,338)(327,339)(328,340)(329,345)(330,346)(331,347)(332,348)(333,341)(334,342)(335,343)(336,344)(353,357)(354,358)(355,359)(356,360)(361,373)(362,374)(363,375)(364,376)(365,381)(366,382)(367,383)(368,384)(369,377)(370,378)(371,379)(372,380)(389,393)(390,394)(391,395)(392,396)(397,409)(398,410)(399,411)(400,412)(401,417)(402,418)(403,419)(404,420)(405,413)(406,414)(407,415)(408,416)(425,429)(426,430)(427,431)(428,432);;
s2 := (  1, 37)(  2, 40)(  3, 39)(  4, 38)(  5, 45)(  6, 48)(  7, 47)(  8, 46)(  9, 41)( 10, 44)( 11, 43)( 12, 42)( 13, 53)( 14, 56)( 15, 55)( 16, 54)( 17, 49)( 18, 52)( 19, 51)( 20, 50)( 21, 57)( 22, 60)( 23, 59)( 24, 58)( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 65)( 30, 68)( 31, 67)( 32, 66)( 33, 61)( 34, 64)( 35, 63)( 36, 62)( 74, 76)( 77, 81)( 78, 84)( 79, 83)( 80, 82)( 85, 89)( 86, 92)( 87, 91)( 88, 90)( 94, 96)( 97,105)( 98,108)( 99,107)(100,106)(102,104)(109,145)(110,148)(111,147)(112,146)(113,153)(114,156)(115,155)(116,154)(117,149)(118,152)(119,151)(120,150)(121,161)(122,164)(123,163)(124,162)(125,157)(126,160)(127,159)(128,158)(129,165)(130,168)(131,167)(132,166)(133,177)(134,180)(135,179)(136,178)(137,173)(138,176)(139,175)(140,174)(141,169)(142,172)(143,171)(144,170)(182,184)(185,189)(186,192)(187,191)(188,190)(193,197)(194,200)(195,199)(196,198)(202,204)(205,213)(206,216)(207,215)(208,214)(210,212)(217,361)(218,364)(219,363)(220,362)(221,369)(222,372)(223,371)(224,370)(225,365)(226,368)(227,367)(228,366)(229,377)(230,380)(231,379)(232,378)(233,373)(234,376)(235,375)(236,374)(237,381)(238,384)(239,383)(240,382)(241,393)(242,396)(243,395)(244,394)(245,389)(246,392)(247,391)(248,390)(249,385)(250,388)(251,387)(252,386)(253,325)(254,328)(255,327)(256,326)(257,333)(258,336)(259,335)(260,334)(261,329)(262,332)(263,331)(264,330)(265,341)(266,344)(267,343)(268,342)(269,337)(270,340)(271,339)(272,338)(273,345)(274,348)(275,347)(276,346)(277,357)(278,360)(279,359)(280,358)(281,353)(282,356)(283,355)(284,354)(285,349)(286,352)(287,351)(288,350)(289,397)(290,400)(291,399)(292,398)(293,405)(294,408)(295,407)(296,406)(297,401)(298,404)(299,403)(300,402)(301,413)(302,416)(303,415)(304,414)(305,409)(306,412)(307,411)(308,410)(309,417)(310,420)(311,419)(312,418)(313,429)(314,432)(315,431)(316,430)(317,425)(318,428)(319,427)(320,426)(321,421)(322,424)(323,423)(324,422);;
s3 := (  1,217)(  2,218)(  3,220)(  4,219)(  5,225)(  6,226)(  7,228)(  8,227)(  9,221)( 10,222)( 11,224)( 12,223)( 13,229)( 14,230)( 15,232)( 16,231)( 17,237)( 18,238)( 19,240)( 20,239)( 21,233)( 22,234)( 23,236)( 24,235)( 25,241)( 26,242)( 27,244)( 28,243)( 29,249)( 30,250)( 31,252)( 32,251)( 33,245)( 34,246)( 35,248)( 36,247)( 37,289)( 38,290)( 39,292)( 40,291)( 41,297)( 42,298)( 43,300)( 44,299)( 45,293)( 46,294)( 47,296)( 48,295)( 49,301)( 50,302)( 51,304)( 52,303)( 53,309)( 54,310)( 55,312)( 56,311)( 57,305)( 58,306)( 59,308)( 60,307)( 61,313)( 62,314)( 63,316)( 64,315)( 65,321)( 66,322)( 67,324)( 68,323)( 69,317)( 70,318)( 71,320)( 72,319)( 73,253)( 74,254)( 75,256)( 76,255)( 77,261)( 78,262)( 79,264)( 80,263)( 81,257)( 82,258)( 83,260)( 84,259)( 85,265)( 86,266)( 87,268)( 88,267)( 89,273)( 90,274)( 91,276)( 92,275)( 93,269)( 94,270)( 95,272)( 96,271)( 97,277)( 98,278)( 99,280)(100,279)(101,285)(102,286)(103,288)(104,287)(105,281)(106,282)(107,284)(108,283)(109,325)(110,326)(111,328)(112,327)(113,333)(114,334)(115,336)(116,335)(117,329)(118,330)(119,332)(120,331)(121,337)(122,338)(123,340)(124,339)(125,345)(126,346)(127,348)(128,347)(129,341)(130,342)(131,344)(132,343)(133,349)(134,350)(135,352)(136,351)(137,357)(138,358)(139,360)(140,359)(141,353)(142,354)(143,356)(144,355)(145,397)(146,398)(147,400)(148,399)(149,405)(150,406)(151,408)(152,407)(153,401)(154,402)(155,404)(156,403)(157,409)(158,410)(159,412)(160,411)(161,417)(162,418)(163,420)(164,419)(165,413)(166,414)(167,416)(168,415)(169,421)(170,422)(171,424)(172,423)(173,429)(174,430)(175,432)(176,431)(177,425)(178,426)(179,428)(180,427)(181,361)(182,362)(183,364)(184,363)(185,369)(186,370)(187,372)(188,371)(189,365)(190,366)(191,368)(192,367)(193,373)(194,374)(195,376)(196,375)(197,381)(198,382)(199,384)(200,383)(201,377)(202,378)(203,380)(204,379)(205,385)(206,386)(207,388)(208,387)(209,393)(210,394)(211,396)(212,395)(213,389)(214,390)(215,392)(216,391);;
s4 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432);;
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, 
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s1*s2*s3*s1*s2*s1*s2*s3*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 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(432)!(  5,  9)(  6, 10)(  7, 11)(  8, 12)( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 69)( 54, 70)( 55, 71)( 56, 72)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89,105)( 90,106)( 91,107)( 92,108)( 93,101)( 94,102)( 95,103)( 96,104)(113,117)(114,118)(115,119)(116,120)(121,133)(122,134)(123,135)(124,136)(125,141)(126,142)(127,143)(128,144)(129,137)(130,138)(131,139)(132,140)(149,153)(150,154)(151,155)(152,156)(157,169)(158,170)(159,171)(160,172)(161,177)(162,178)(163,179)(164,180)(165,173)(166,174)(167,175)(168,176)(185,189)(186,190)(187,191)(188,192)(193,205)(194,206)(195,207)(196,208)(197,213)(198,214)(199,215)(200,216)(201,209)(202,210)(203,211)(204,212)(221,225)(222,226)(223,227)(224,228)(229,241)(230,242)(231,243)(232,244)(233,249)(234,250)(235,251)(236,252)(237,245)(238,246)(239,247)(240,248)(257,261)(258,262)(259,263)(260,264)(265,277)(266,278)(267,279)(268,280)(269,285)(270,286)(271,287)(272,288)(273,281)(274,282)(275,283)(276,284)(293,297)(294,298)(295,299)(296,300)(301,313)(302,314)(303,315)(304,316)(305,321)(306,322)(307,323)(308,324)(309,317)(310,318)(311,319)(312,320)(329,333)(330,334)(331,335)(332,336)(337,349)(338,350)(339,351)(340,352)(341,357)(342,358)(343,359)(344,360)(345,353)(346,354)(347,355)(348,356)(365,369)(366,370)(367,371)(368,372)(373,385)(374,386)(375,387)(376,388)(377,393)(378,394)(379,395)(380,396)(381,389)(382,390)(383,391)(384,392)(401,405)(402,406)(403,407)(404,408)(409,421)(410,422)(411,423)(412,424)(413,429)(414,430)(415,431)(416,432)(417,425)(418,426)(419,427)(420,428);
s1 := Sym(432)!(  1, 13)(  2, 14)(  3, 15)(  4, 16)(  5, 21)(  6, 22)(  7, 23)(  8, 24)(  9, 17)( 10, 18)( 11, 19)( 12, 20)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 37, 49)( 38, 50)( 39, 51)( 40, 52)( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 53)( 46, 54)( 47, 55)( 48, 56)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 85)( 74, 86)( 75, 87)( 76, 88)( 77, 93)( 78, 94)( 79, 95)( 80, 96)( 81, 89)( 82, 90)( 83, 91)( 84, 92)(101,105)(102,106)(103,107)(104,108)(109,121)(110,122)(111,123)(112,124)(113,129)(114,130)(115,131)(116,132)(117,125)(118,126)(119,127)(120,128)(137,141)(138,142)(139,143)(140,144)(145,157)(146,158)(147,159)(148,160)(149,165)(150,166)(151,167)(152,168)(153,161)(154,162)(155,163)(156,164)(173,177)(174,178)(175,179)(176,180)(181,193)(182,194)(183,195)(184,196)(185,201)(186,202)(187,203)(188,204)(189,197)(190,198)(191,199)(192,200)(209,213)(210,214)(211,215)(212,216)(217,229)(218,230)(219,231)(220,232)(221,237)(222,238)(223,239)(224,240)(225,233)(226,234)(227,235)(228,236)(245,249)(246,250)(247,251)(248,252)(253,265)(254,266)(255,267)(256,268)(257,273)(258,274)(259,275)(260,276)(261,269)(262,270)(263,271)(264,272)(281,285)(282,286)(283,287)(284,288)(289,301)(290,302)(291,303)(292,304)(293,309)(294,310)(295,311)(296,312)(297,305)(298,306)(299,307)(300,308)(317,321)(318,322)(319,323)(320,324)(325,337)(326,338)(327,339)(328,340)(329,345)(330,346)(331,347)(332,348)(333,341)(334,342)(335,343)(336,344)(353,357)(354,358)(355,359)(356,360)(361,373)(362,374)(363,375)(364,376)(365,381)(366,382)(367,383)(368,384)(369,377)(370,378)(371,379)(372,380)(389,393)(390,394)(391,395)(392,396)(397,409)(398,410)(399,411)(400,412)(401,417)(402,418)(403,419)(404,420)(405,413)(406,414)(407,415)(408,416)(425,429)(426,430)(427,431)(428,432);
s2 := Sym(432)!(  1, 37)(  2, 40)(  3, 39)(  4, 38)(  5, 45)(  6, 48)(  7, 47)(  8, 46)(  9, 41)( 10, 44)( 11, 43)( 12, 42)( 13, 53)( 14, 56)( 15, 55)( 16, 54)( 17, 49)( 18, 52)( 19, 51)( 20, 50)( 21, 57)( 22, 60)( 23, 59)( 24, 58)( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 65)( 30, 68)( 31, 67)( 32, 66)( 33, 61)( 34, 64)( 35, 63)( 36, 62)( 74, 76)( 77, 81)( 78, 84)( 79, 83)( 80, 82)( 85, 89)( 86, 92)( 87, 91)( 88, 90)( 94, 96)( 97,105)( 98,108)( 99,107)(100,106)(102,104)(109,145)(110,148)(111,147)(112,146)(113,153)(114,156)(115,155)(116,154)(117,149)(118,152)(119,151)(120,150)(121,161)(122,164)(123,163)(124,162)(125,157)(126,160)(127,159)(128,158)(129,165)(130,168)(131,167)(132,166)(133,177)(134,180)(135,179)(136,178)(137,173)(138,176)(139,175)(140,174)(141,169)(142,172)(143,171)(144,170)(182,184)(185,189)(186,192)(187,191)(188,190)(193,197)(194,200)(195,199)(196,198)(202,204)(205,213)(206,216)(207,215)(208,214)(210,212)(217,361)(218,364)(219,363)(220,362)(221,369)(222,372)(223,371)(224,370)(225,365)(226,368)(227,367)(228,366)(229,377)(230,380)(231,379)(232,378)(233,373)(234,376)(235,375)(236,374)(237,381)(238,384)(239,383)(240,382)(241,393)(242,396)(243,395)(244,394)(245,389)(246,392)(247,391)(248,390)(249,385)(250,388)(251,387)(252,386)(253,325)(254,328)(255,327)(256,326)(257,333)(258,336)(259,335)(260,334)(261,329)(262,332)(263,331)(264,330)(265,341)(266,344)(267,343)(268,342)(269,337)(270,340)(271,339)(272,338)(273,345)(274,348)(275,347)(276,346)(277,357)(278,360)(279,359)(280,358)(281,353)(282,356)(283,355)(284,354)(285,349)(286,352)(287,351)(288,350)(289,397)(290,400)(291,399)(292,398)(293,405)(294,408)(295,407)(296,406)(297,401)(298,404)(299,403)(300,402)(301,413)(302,416)(303,415)(304,414)(305,409)(306,412)(307,411)(308,410)(309,417)(310,420)(311,419)(312,418)(313,429)(314,432)(315,431)(316,430)(317,425)(318,428)(319,427)(320,426)(321,421)(322,424)(323,423)(324,422);
s3 := Sym(432)!(  1,217)(  2,218)(  3,220)(  4,219)(  5,225)(  6,226)(  7,228)(  8,227)(  9,221)( 10,222)( 11,224)( 12,223)( 13,229)( 14,230)( 15,232)( 16,231)( 17,237)( 18,238)( 19,240)( 20,239)( 21,233)( 22,234)( 23,236)( 24,235)( 25,241)( 26,242)( 27,244)( 28,243)( 29,249)( 30,250)( 31,252)( 32,251)( 33,245)( 34,246)( 35,248)( 36,247)( 37,289)( 38,290)( 39,292)( 40,291)( 41,297)( 42,298)( 43,300)( 44,299)( 45,293)( 46,294)( 47,296)( 48,295)( 49,301)( 50,302)( 51,304)( 52,303)( 53,309)( 54,310)( 55,312)( 56,311)( 57,305)( 58,306)( 59,308)( 60,307)( 61,313)( 62,314)( 63,316)( 64,315)( 65,321)( 66,322)( 67,324)( 68,323)( 69,317)( 70,318)( 71,320)( 72,319)( 73,253)( 74,254)( 75,256)( 76,255)( 77,261)( 78,262)( 79,264)( 80,263)( 81,257)( 82,258)( 83,260)( 84,259)( 85,265)( 86,266)( 87,268)( 88,267)( 89,273)( 90,274)( 91,276)( 92,275)( 93,269)( 94,270)( 95,272)( 96,271)( 97,277)( 98,278)( 99,280)(100,279)(101,285)(102,286)(103,288)(104,287)(105,281)(106,282)(107,284)(108,283)(109,325)(110,326)(111,328)(112,327)(113,333)(114,334)(115,336)(116,335)(117,329)(118,330)(119,332)(120,331)(121,337)(122,338)(123,340)(124,339)(125,345)(126,346)(127,348)(128,347)(129,341)(130,342)(131,344)(132,343)(133,349)(134,350)(135,352)(136,351)(137,357)(138,358)(139,360)(140,359)(141,353)(142,354)(143,356)(144,355)(145,397)(146,398)(147,400)(148,399)(149,405)(150,406)(151,408)(152,407)(153,401)(154,402)(155,404)(156,403)(157,409)(158,410)(159,412)(160,411)(161,417)(162,418)(163,420)(164,419)(165,413)(166,414)(167,416)(168,415)(169,421)(170,422)(171,424)(172,423)(173,429)(174,430)(175,432)(176,431)(177,425)(178,426)(179,428)(180,427)(181,361)(182,362)(183,364)(184,363)(185,369)(186,370)(187,372)(188,371)(189,365)(190,366)(191,368)(192,367)(193,373)(194,374)(195,376)(196,375)(197,381)(198,382)(199,384)(200,383)(201,377)(202,378)(203,380)(204,379)(205,385)(206,386)(207,388)(208,387)(209,393)(210,394)(211,396)(212,395)(213,389)(214,390)(215,392)(216,391);
s4 := Sym(432)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432);
poly := sub<Sym(432)|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, s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s3*s2*s4*s3*s4*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s1*s2*s3*s1*s2*s1*s2*s3*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 >;

References