Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | C5×SL(2,𝔽5) ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×SL(2,𝔽5) | C4 |
| Fitting, socle | C2×C5 | A5⋊C4 |
| prime radical, cosocle | C5⋊#6732 | C2 |
| LCS | G ▷ C5×SL(2,𝔽5) | |
| UCS | C1 ◁ C2 | |
112 conjugacy classes of subgroups.
Permutation generators:
(1,102,50,53,104,4,28,75,77,26)(2,79,100,101,78,3,51,25,29,52)(5,135,375,390,145,20,515,250,260,505)(6,237,425,443,249,24,543,325,337,531)(7,214,475,491,223,23,566,275,289,557)(8,186,400,419,197,22,594,350,361,583)(9,163,450,467,171,21,617,300,313,609)(10,270,125,130,265,15,380,500,520,385)(11,372,175,183,369,19,408,575,597,411)(12,349,225,231,343,18,431,525,549,437)(13,321,150,159,317,17,459,600,621,463)(14,298,200,207,291,16,482,550,573,489)(27,103)(30,164,427,392,224,120,616,328,263,556)(31,136,477,440,198,124,519,278,335,582)(32,238,402,493,172,123,542,353,287,608)(33,210,452,416,146,122,565,303,364,509)(34,187,377,469,245,121,593,253,311,530)(35,299,177,132,344,115,481,578,523,436)(36,271,227,180,318,119,384,528,595,462)(37,373,152,233,292,118,407,603,547,488)(38,345,202,156,266,117,430,553,624,389)(39,322,127,209,365,116,458,503,571,410)(40,409,552,522,464,110,371,203,133,316)(41,381,602,570,438,114,274,153,205,342)(42,483,527,623,412,113,297,228,157,368)(43,455,577,546,386,112,320,178,234,269)(44,432,502,599,485,111,348,128,181,290)(45,544,302,262,584,105,236,453,393,196)(46,516,352,310,558,109,139,403,465,222)(47,618,277,363,532,108,162,478,417,248)(48,590,327,286,506,107,185,428,494,149)(49,567,252,339,605,106,213,378,441,170)(54,76)(55,188,479,394,173,95,592,276,261,607)(56,160,404,442,147,99,615,351,338,508)(57,137,454,490,246,98,518,301,285,534)(58,239,379,418,220,97,541,251,362,555)(59,211,429,466,199,96,569,326,314,581)(60,323,229,134,293,90,457,526,521,487)(61,295,154,182,267,94,480,601,598,388)(62,272,204,230,366,93,383,551,545,414)(63,374,129,158,340,92,406,501,622,435)(64,346,179,206,319,91,434,576,574,461)(65,433,604,524,413,85,347,151,131,367)(66,405,529,572,387,89,370,226,208,268)(67,382,579,620,486,88,273,176,155,294)(68,484,504,548,460,87,296,126,232,315)(69,456,554,596,439,86,324,201,184,341)(70,568,354,264,533,80,212,401,391,247)(71,540,279,312,507,84,235,476,468,148)(72,517,329,360,606,83,138,426,415,174)(73,619,254,288,580,82,161,376,492,195)(74,591,304,336,559,81,189,451,444,221)(140,510)(141,612,190,563,244,514,168,585,217,536)(142,589,240,611,218,513,191,535,169,562)(143,561,165,539,192,512,219,610,241,588)(144,538,215,587,166,511,242,560,193,614)(167,613)(194,586)(216,564)(243,537)(255,395)(256,497,305,448,359,399,283,470,332,421)(257,474,355,496,333,398,306,420,284,447)(258,446,280,424,307,397,334,495,356,473)(259,423,330,472,281,396,357,445,308,499)(282,498)(309,471)(331,449)(358,422);(1,53,52,4,77,78)(2,101,104,3,29,26)(5,390,385,20,260,265)(6,443,437,24,337,343)(7,491,489,23,289,291)(8,419,411,22,361,369)(9,467,463,21,313,317)(10,130,145,15,520,505)(11,183,197,19,597,583)(12,231,249,18,549,531)(13,159,171,17,621,609)(14,207,223,16,573,557)(25,79,54,100,51,76)(27,50,28,103,75,102)(30,469,439,120,311,341)(31,392,486,124,263,294)(32,440,413,123,335,367)(33,493,460,122,287,315)(34,416,387,121,364,268)(35,209,199,115,571,581)(36,132,246,119,523,534)(37,180,173,118,595,607)(38,233,220,117,547,555)(39,156,147,116,624,508)(40,599,559,110,181,221)(41,522,606,114,133,174)(42,570,533,113,205,247)(43,623,580,112,157,195)(44,546,507,111,234,148)(45,339,319,105,441,461)(46,262,366,109,393,414)(47,310,293,108,465,487)(48,363,340,107,417,435)(49,286,267,106,494,388)(55,418,488,95,362,292)(56,466,410,99,314,365)(57,394,462,98,261,318)(58,442,389,97,338,266)(59,490,436,96,285,344)(60,158,248,90,622,532)(61,206,170,94,574,605)(62,134,222,93,521,558)(63,182,149,92,598,506)(64,230,196,91,545,584)(65,548,608,85,232,172)(66,596,530,89,184,245)(67,524,582,88,131,198)(68,572,509,87,208,146)(69,620,556,86,155,224)(70,288,368,80,492,412)(71,336,290,84,444,485)(72,264,342,83,391,438)(73,312,269,82,468,386)(74,360,316,81,415,464)(125,380,255,500,270,395)(126,433,307,504,347,473)(127,481,359,503,299,421)(128,409,281,502,371,499)(129,457,333,501,323,447)(135,510,375,515,140,250)(136,563,427,519,217,328)(137,611,479,518,169,276)(138,539,401,517,241,354)(139,587,453,516,193,302)(141,303,187,514,452,593)(142,351,239,513,404,541)(143,279,161,512,476,619)(144,327,213,511,428,567)(150,459,309,600,321,471)(151,382,356,604,273,424)(152,430,283,603,345,497)(153,483,330,602,297,445)(154,406,257,601,374,398)(160,589,429,615,191,326)(162,560,403,618,215,352)(163,613,450,617,167,300)(164,536,377,616,244,253)(165,329,189,610,426,591)(166,252,236,614,378,544)(168,353,210,612,402,565)(175,408,358,575,372,422)(176,456,280,579,324,495)(177,384,332,578,271,448)(178,432,259,577,348,396)(179,480,306,576,295,474)(185,538,478,590,242,277)(186,586,400,594,194,350)(188,562,379,592,218,251)(190,278,238,585,477,542)(192,254,212,588,376,568)(200,482,282,550,298,498)(201,405,334,554,370,446)(202,458,256,553,322,399)(203,381,308,552,274,472)(204,434,355,551,346,420)(211,535,454,569,240,301)(214,564,475,566,216,275)(219,304,235,561,451,540)(225,431,331,525,349,449)(226,484,258,529,296,397)(227,407,305,528,373,470)(228,455,357,527,320,423)(229,383,284,526,272,496)(237,537,425,543,243,325);(1,4)(2,3)(5,20)(6,24)(7,23)(8,22)(9,21)(10,15)(11,19)(12,18)(13,17)(14,16)(25,100)(26,104)(27,103)(28,102)(29,101)(30,120)(31,124)(32,123)(33,122)(34,121)(35,115)(36,119)(37,118)(38,117)(39,116)(40,110)(41,114)(42,113)(43,112)(44,111)(45,105)(46,109)(47,108)(48,107)(49,106)(50,75)(51,79)(52,78)(53,77)(54,76)(55,95)(56,99)(57,98)(58,97)(59,96)(60,90)(61,94)(62,93)(63,92)(64,91)(65,85)(66,89)(67,88)(68,87)(69,86)(70,80)(71,84)(72,83)(73,82)(74,81)(125,500)(126,504)(127,503)(128,502)(129,501)(130,520)(131,524)(132,523)(133,522)(134,521)(135,515)(136,519)(137,518)(138,517)(139,516)(140,510)(141,514)(142,513)(143,512)(144,511)(145,505)(146,509)(147,508)(148,507)(149,506)(150,600)(151,604)(152,603)(153,602)(154,601)(155,620)(156,624)(157,623)(158,622)(159,621)(160,615)(161,619)(162,618)(163,617)(164,616)(165,610)(166,614)(167,613)(168,612)(169,611)(170,605)(171,609)(172,608)(173,607)(174,606)(175,575)(176,579)(177,578)(178,577)(179,576)(180,595)(181,599)(182,598)(183,597)(184,596)(185,590)(186,594)(187,593)(188,592)(189,591)(190,585)(191,589)(192,588)(193,587)(194,586)(195,580)(196,584)(197,583)(198,582)(199,581)(200,550)(201,554)(202,553)(203,552)(204,551)(205,570)(206,574)(207,573)(208,572)(209,571)(210,565)(211,569)(212,568)(213,567)(214,566)(215,560)(216,564)(217,563)(218,562)(219,561)(220,555)(221,559)(222,558)(223,557)(224,556)(225,525)(226,529)(227,528)(228,527)(229,526)(230,545)(231,549)(232,548)(233,547)(234,546)(235,540)(236,544)(237,543)(238,542)(239,541)(240,535)(241,539)(242,538)(243,537)(244,536)(245,530)(246,534)(247,533)(248,532)(249,531)(250,375)(251,379)(252,378)(253,377)(254,376)(255,395)(256,399)(257,398)(258,397)(259,396)(260,390)(261,394)(262,393)(263,392)(264,391)(265,385)(266,389)(267,388)(268,387)(269,386)(270,380)(271,384)(272,383)(273,382)(274,381)(275,475)(276,479)(277,478)(278,477)(279,476)(280,495)(281,499)(282,498)(283,497)(284,496)(285,490)(286,494)(287,493)(288,492)(289,491)(290,485)(291,489)(292,488)(293,487)(294,486)(295,480)(296,484)(297,483)(298,482)(299,481)(300,450)(301,454)(302,453)(303,452)(304,451)(305,470)(306,474)(307,473)(308,472)(309,471)(310,465)(311,469)(312,468)(313,467)(314,466)(315,460)(316,464)(317,463)(318,462)(319,461)(320,455)(321,459)(322,458)(323,457)(324,456)(325,425)(326,429)(327,428)(328,427)(329,426)(330,445)(331,449)(332,448)(333,447)(334,446)(335,440)(336,444)(337,443)(338,442)(339,441)(340,435)(341,439)(342,438)(343,437)(344,436)(345,430)(346,434)(347,433)(348,432)(349,431)(350,400)(351,404)(352,403)(353,402)(354,401)(355,420)(356,424)(357,423)(358,422)(359,421)(360,415)(361,419)(362,418)(363,417)(364,416)(365,410)(366,414)(367,413)(368,412)(369,411)(370,405)(371,409)(372,408)(373,407)(374,406);(1,6,11,16,21)(2,12,22,7,17)(3,18,8,23,13)(4,24,19,14,9)(25,525,400,275,150)(26,531,411,291,171)(27,537,422,282,167)(28,543,408,298,163)(29,549,419,289,159)(30,530,405,280,155)(31,536,416,296,151)(32,542,402,287,172)(33,548,413,278,168)(34,529,424,294,164)(35,535,410,285,160)(36,541,421,276,156)(37,547,407,292,152)(38,528,418,283,173)(39,534,404,299,169)(40,540,415,290,165)(41,546,401,281,161)(42,527,412,297,157)(43,533,423,288,153)(44,539,409,279,174)(45,545,420,295,170)(46,526,406,286,166)(47,532,417,277,162)(48,538,403,293,158)(49,544,414,284,154)(50,425,175,550,300)(51,431,186,566,321)(52,437,197,557,317)(53,443,183,573,313)(54,449,194,564,309)(55,430,180,555,305)(56,436,191,571,301)(57,442,177,562,322)(58,448,188,553,318)(59,429,199,569,314)(60,435,185,560,310)(61,441,196,551,306)(62,447,182,567,302)(63,428,193,558,323)(64,434,179,574,319)(65,440,190,565,315)(66,446,176,556,311)(67,427,187,572,307)(68,433,198,563,303)(69,439,184,554,324)(70,445,195,570,320)(71,426,181,561,316)(72,432,192,552,312)(73,438,178,568,308)(74,444,189,559,304)(75,325,575,200,450)(76,331,586,216,471)(77,337,597,207,467)(78,343,583,223,463)(79,349,594,214,459)(80,330,580,205,455)(81,336,591,221,451)(82,342,577,212,472)(83,348,588,203,468)(84,329,599,219,464)(85,335,585,210,460)(86,341,596,201,456)(87,347,582,217,452)(88,328,593,208,473)(89,334,579,224,469)(90,340,590,215,465)(91,346,576,206,461)(92,327,587,222,457)(93,333,598,213,453)(94,339,584,204,474)(95,345,595,220,470)(96,326,581,211,466)(97,332,592,202,462)(98,338,578,218,458)(99,344,589,209,454)(100,225,350,475,600)(101,231,361,491,621)(102,237,372,482,617)(103,243,358,498,613)(104,249,369,489,609)(105,230,355,480,605)(106,236,366,496,601)(107,242,352,487,622)(108,248,363,478,618)(109,229,374,494,614)(110,235,360,485,610)(111,241,371,476,606)(112,247,357,492,602)(113,228,368,483,623)(114,234,354,499,619)(115,240,365,490,615)(116,246,351,481,611)(117,227,362,497,607)(118,233,373,488,603)(119,239,359,479,624)(120,245,370,495,620)(121,226,356,486,616)(122,232,367,477,612)(123,238,353,493,608)(124,244,364,484,604)(126,131,136,141,146)(127,137,147,132,142)(128,143,133,148,138)(129,149,144,139,134)(251,256,261,266,271)(252,262,272,257,267)(253,268,258,273,263)(254,274,269,264,259)(376,381,386,391,396)(377,387,397,382,392)(378,393,383,398,388)(379,399,394,389,384)(501,506,511,516,521)(502,512,522,507,517)(503,518,508,523,513)(504,524,519,514,509);(1,6)(2,12)(3,18)(4,24)(5,20)(8,13)(9,19)(10,15)(11,21)(17,22)(25,237)(26,243)(27,249)(28,225)(29,231)(30,232)(31,238)(32,244)(33,245)(34,226)(35,227)(36,233)(37,239)(38,240)(39,246)(40,247)(41,228)(42,234)(43,235)(44,241)(45,242)(46,248)(47,229)(48,230)(49,236)(50,349)(51,325)(52,331)(53,337)(54,343)(55,344)(56,345)(57,326)(58,332)(59,338)(60,339)(61,340)(62,346)(63,327)(64,333)(65,334)(66,335)(67,341)(68,347)(69,328)(70,329)(71,330)(72,336)(73,342)(74,348)(75,431)(76,437)(77,443)(78,449)(79,425)(80,426)(81,432)(82,438)(83,444)(84,445)(85,446)(86,427)(87,433)(88,439)(89,440)(90,441)(91,447)(92,428)(93,434)(94,435)(95,436)(96,442)(97,448)(98,429)(99,430)(100,543)(101,549)(102,525)(103,531)(104,537)(105,538)(106,544)(107,545)(108,526)(109,532)(110,533)(111,539)(112,540)(113,546)(114,527)(115,528)(116,534)(117,535)(118,541)(119,547)(120,548)(121,529)(122,530)(123,536)(124,542)(125,135)(126,141)(127,147)(129,134)(131,136)(132,142)(133,148)(138,143)(139,149)(140,145)(150,372)(151,353)(152,359)(153,360)(154,366)(155,367)(156,373)(157,354)(158,355)(159,361)(160,362)(161,368)(162,374)(163,350)(164,356)(165,357)(166,363)(167,369)(168,370)(169,351)(170,352)(171,358)(172,364)(173,365)(174,371)(175,459)(176,460)(177,466)(178,472)(179,453)(180,454)(181,455)(182,461)(183,467)(184,473)(185,474)(186,450)(187,456)(188,462)(189,468)(190,469)(191,470)(192,451)(193,457)(194,463)(195,464)(196,465)(197,471)(198,452)(199,458)(200,566)(201,572)(202,553)(203,559)(204,560)(205,561)(206,567)(207,573)(208,554)(209,555)(210,556)(211,562)(212,568)(213,574)(214,550)(215,551)(216,557)(217,563)(218,569)(219,570)(220,571)(221,552)(222,558)(223,564)(224,565)(250,270)(252,257)(253,263)(254,269)(255,265)(256,271)(259,264)(261,266)(262,272)(268,273)(275,482)(276,488)(277,494)(278,495)(279,476)(280,477)(281,483)(282,489)(283,490)(284,496)(285,497)(286,478)(287,484)(288,485)(289,491)(290,492)(291,498)(292,479)(293,480)(294,486)(295,487)(296,493)(297,499)(298,475)(299,481)(300,594)(301,595)(302,576)(303,582)(304,588)(305,589)(306,590)(307,596)(308,577)(309,583)(310,584)(311,585)(312,591)(313,597)(314,578)(315,579)(316,580)(317,586)(318,592)(319,598)(320,599)(321,575)(322,581)(323,587)(324,593)(375,380)(376,386)(377,392)(378,398)(382,387)(383,393)(384,399)(385,395)(389,394)(391,396)(400,617)(401,623)(402,604)(403,605)(404,611)(405,612)(406,618)(407,624)(408,600)(409,606)(410,607)(411,613)(412,619)(413,620)(414,601)(415,602)(416,608)(417,614)(418,615)(419,621)(420,622)(421,603)(422,609)(423,610)(424,616)(500,515)(501,521)(503,508)(504,514)(505,510)(506,516)(507,522)(512,517)(513,523)(519,524);(1,75,3,100,4,50,2,25)(5,125,10,250,20,500,15,375)(6,200,13,350,24,550,17,400)(7,150,11,325,23,600,19,425)(8,225,14,300,22,525,16,450)(9,175,12,275,21,575,18,475)(26,76,78,103,104,54,52,27)(28,101,79,53,102,29,51,77)(30,126,85,253,120,504,65,377)(31,201,88,353,124,554,67,402)(32,151,86,328,123,604,69,427)(33,226,89,303,122,529,66,452)(34,176,87,278,121,579,68,477)(35,251,95,503,115,379,55,127)(36,326,98,603,119,429,57,152)(37,276,96,578,118,479,59,177)(38,351,99,553,117,404,56,202)(39,301,97,528,116,454,58,227)(40,376,80,128,110,254,70,502)(41,451,83,228,114,304,72,527)(42,401,81,203,113,354,74,552)(43,476,84,178,112,279,71,577)(44,426,82,153,111,329,73,602)(45,501,90,378,105,129,60,252)(46,576,93,478,109,179,62,277)(47,526,91,453,108,229,64,302)(48,601,94,428,107,154,61,327)(49,551,92,403,106,204,63,352)(130,135,260,270,520,515,390,380)(131,210,263,370,524,565,392,405)(132,160,261,345,523,615,394,430)(133,235,264,320,522,540,391,455)(134,185,262,295,521,590,393,480)(136,335,273,620,519,440,382,155)(137,285,271,595,518,490,384,180)(138,360,274,570,517,415,381,205)(139,310,272,545,516,465,383,230)(140,385,255,145,510,265,395,505)(141,460,258,245,514,315,397,530)(142,410,256,220,513,365,399,555)(143,485,259,195,512,290,396,580)(144,435,257,170,511,340,398,605)(146,585,268,495,509,190,387,280)(147,535,266,470,508,240,389,305)(148,610,269,445,507,165,386,330)(149,560,267,420,506,215,388,355)(156,211,338,373,624,569,442,407)(157,161,336,348,623,619,444,432)(158,236,339,323,622,544,441,457)(159,186,337,298,621,594,443,482)(162,286,346,598,618,494,434,182)(163,361,349,573,617,419,431,207)(164,311,347,548,616,469,433,232)(166,461,333,248,614,319,447,532)(167,411,331,223,613,369,449,557)(168,486,334,198,612,294,446,582)(169,436,332,173,611,344,448,607)(171,586,343,498,609,194,437,282)(172,536,341,473,608,244,439,307)(174,561,342,423,606,219,438,357)(181,212,288,371,599,568,492,409)(183,237,289,321,597,543,491,459)(184,187,287,296,596,593,493,484)(188,362,299,571,592,418,481,209)(189,312,297,546,591,468,483,234)(191,462,283,246,589,318,497,534)(192,412,281,221,588,368,499,559)(193,487,284,196,587,293,496,584)(197,537,291,471,583,243,489,309)(199,562,292,421,581,218,488,359)(206,213,363,374,574,567,417,406)(208,238,364,324,572,542,416,456)(214,313,372,549,566,467,408,231)(216,463,358,249,564,317,422,531)(217,413,356,224,563,367,424,556)(222,538,366,474,558,242,414,306)(233,239,314,322,547,541,466,458)(241,464,308,247,539,316,472,533)33 conjugacy classes — view the full character table.
| maximal subgroup of | SO+(4,𝔽5), C2×#72219547, #72277416, … |
| maximal normal subgroup of | C2×#72219547, #72277849 |
| maximal quotient of | C2×#72219547 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((1,102,50,53,104,4,28,75,77,26)(2,79,100,101,78,3,51,25,29,52)(5,135,375,390,145,20,515,250,260,505)(6,237,425,443,249,24,543,325,337,531)(7,214,475,491,223,23,566,275,289,557)(8,186,400,419,197,22,594,350,361,583)(9,163,450,467,171,21,617,300,313,609)(10,270,125,130,265,15,380,500,520,385)(11,372,175,183,369,19,408,575,597,411)(12,349,225,231,343,18,431,525,549,437)(13,321,150,159,317,17,459,600,621,463)(14,298,200,207,291,16,482,550,573,489)(27,103)(30,164,427,392,224,120,616,328,263,556)(31,136,477,440,198,124,519,278,335,582)(32,238,402,493,172,123,542,353,287,608)(33,210,452,416,146,122,565,303,364,509)(34,187,377,469,245,121,593,253,311,530)(35,299,177,132,344,115,481,578,523,436)(36,271,227,180,318,119,384,528,595,462)(37,373,152,233,292,118,407,603,547,488)(38,345,202,156,266,117,430,553,624,389)(39,322,127,209,365,116,458,503,571,410)(40,409,552,522,464,110,371,203,133,316)(41,381,602,570,438,114,274,153,205,342)(42,483,527,623,412,113,297,228,157,368)(43,455,577,546,386,112,320,178,234,269)(44,432,502,599,485,111,348,128,181,290)(45,544,302,262,584,105,236,453,393,196)(46,516,352,310,558,109,139,403,465,222)(47,618,277,363,532,108,162,478,417,248)(48,590,327,286,506,107,185,428,494,149)(49,567,252,339,605,106,213,378,441,170)(54,76)(55,188,479,394,173,95,592,276,261,607)(56,160,404,442,147,99,615,351,338,508)(57,137,454,490,246,98,518,301,285,534)(58,239,379,418,220,97,541,251,362,555)(59,211,429,466,199,96,569,326,314,581)(60,323,229,134,293,90,457,526,521,487)(61,295,154,182,267,94,480,601,598,388)(62,272,204,230,366,93,383,551,545,414)(63,374,129,158,340,92,406,501,622,435)(64,346,179,206,319,91,434,576,574,461)(65,433,604,524,413,85,347,151,131,367)(66,405,529,572,387,89,370,226,208,268)(67,382,579,620,486,88,273,176,155,294)(68,484,504,548,460,87,296,126,232,315)(69,456,554,596,439,86,324,201,184,341)(70,568,354,264,533,80,212,401,391,247)(71,540,279,312,507,84,235,476,468,148)(72,517,329,360,606,83,138,426,415,174)(73,619,254,288,580,82,161,376,492,195)(74,591,304,336,559,81,189,451,444,221)(140,510)(141,612,190,563,244,514,168,585,217,536)(142,589,240,611,218,513,191,535,169,562)(143,561,165,539,192,512,219,610,241,588)(144,538,215,587,166,511,242,560,193,614)(167,613)(194,586)(216,564)(243,537)(255,395)(256,497,305,448,359,399,283,470,332,421)(257,474,355,496,333,398,306,420,284,447)(258,446,280,424,307,397,334,495,356,473)(259,423,330,472,281,396,357,445,308,499)(282,498)(309,471)(331,449)(358,422), 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(1,6,11,16,21)(2,12,22,7,17)(3,18,8,23,13)(4,24,19,14,9)(25,525,400,275,150)(26,531,411,291,171)(27,537,422,282,167)(28,543,408,298,163)(29,549,419,289,159)(30,530,405,280,155)(31,536,416,296,151)(32,542,402,287,172)(33,548,413,278,168)(34,529,424,294,164)(35,535,410,285,160)(36,541,421,276,156)(37,547,407,292,152)(38,528,418,283,173)(39,534,404,299,169)(40,540,415,290,165)(41,546,401,281,161)(42,527,412,297,157)(43,533,423,288,153)(44,539,409,279,174)(45,545,420,295,170)(46,526,406,286,166)(47,532,417,277,162)(48,538,403,293,158)(49,544,414,284,154)(50,425,175,550,300)(51,431,186,566,321)(52,437,197,557,317)(53,443,183,573,313)(54,449,194,564,309)(55,430,180,555,305)(56,436,191,571,301)(57,442,177,562,322)(58,448,188,553,318)(59,429,199,569,314)(60,435,185,560,310)(61,441,196,551,306)(62,447,182,567,302)(63,428,193,558,323)(64,434,179,574,319)(65,440,190,565,315)(66,446,176,556,311)(67,427,187,572,307)(68,433,198,563,303)(69,439,184,554,324)(70,445,195,570,320)(71,426,181,561,316)(72,432,192,552,312)(73,438,178,568,308)(74,444,189,559,304)(75,325,575,200,450)(76,331,586,216,471)(77,337,597,207,467)(78,343,583,223,463)(79,349,594,214,459)(80,330,580,205,455)(81,336,591,221,451)(82,342,577,212,472)(83,348,588,203,468)(84,329,599,219,464)(85,335,585,210,460)(86,341,596,201,456)(87,347,582,217,452)(88,328,593,208,473)(89,334,579,224,469)(90,340,590,215,465)(91,346,576,206,461)(92,327,587,222,457)(93,333,598,213,453)(94,339,584,204,474)(95,345,595,220,470)(96,326,581,211,466)(97,332,592,202,462)(98,338,578,218,458)(99,344,589,209,454)(100,225,350,475,600)(101,231,361,491,621)(102,237,372,482,617)(103,243,358,498,613)(104,249,369,489,609)(105,230,355,480,605)(106,236,366,496,601)(107,242,352,487,622)(108,248,363,478,618)(109,229,374,494,614)(110,235,360,485,610)(111,241,371,476,606)(112,247,357,492,602)(113,228,368,483,623)(114,234,354,499,619)(115,240,365,490,615)(116,246,351,481,611)(117,227,362,497,607)(118,233,373,488,603)(119,239,359,479,624)(120,245,370,495,620)(121,226,356,486,616)(122,232,367,477,612)(123,238,353,493,608)(124,244,364,484,604)(126,131,136,141,146)(127,137,147,132,142)(128,143,133,148,138)(129,149,144,139,134)(251,256,261,266,271)(252,262,272,257,267)(253,268,258,273,263)(254,274,269,264,259)(376,381,386,391,396)(377,387,397,382,392)(378,393,383,398,388)(379,399,394,389,384)(501,506,511,516,521)(502,512,522,507,517)(503,518,508,523,513)(504,524,519,514,509), (1,6)(2,12)(3,18)(4,24)(5,20)(8,13)(9,19)(10,15)(11,21)(17,22)(25,237)(26,243)(27,249)(28,225)(29,231)(30,232)(31,238)(32,244)(33,245)(34,226)(35,227)(36,233)(37,239)(38,240)(39,246)(40,247)(41,228)(42,234)(43,235)(44,241)(45,242)(46,248)(47,229)(48,230)(49,236)(50,349)(51,325)(52,331)(53,337)(54,343)(55,344)(56,345)(57,326)(58,332)(59,338)(60,339)(61,340)(62,346)(63,327)(64,333)(65,334)(66,335)(67,341)(68,347)(69,328)(70,329)(71,330)(72,336)(73,342)(74,348)(75,431)(76,437)(77,443)(78,449)(79,425)(80,426)(81,432)(82,438)(83,444)(84,445)(85,446)(86,427)(87,433)(88,439)(89,440)(90,441)(91,447)(92,428)(93,434)(94,435)(95,436)(96,442)(97,448)(98,429)(99,430)(100,543)(101,549)(102,525)(103,531)(104,537)(105,538)(106,544)(107,545)(108,526)(109,532)(110,533)(111,539)(112,540)(113,546)(114,527)(115,528)(116,534)(117,535)(118,541)(119,547)(120,548)(121,529)(122,530)(123,536)(124,542)(125,135)(126,141)(127,147)(129,134)(131,136)(132,142)(133,148)(138,143)(139,149)(140,145)(150,372)(151,353)(152,359)(153,360)(154,366)(155,367)(156,373)(157,354)(158,355)(159,361)(160,362)(161,368)(162,374)(163,350)(164,356)(165,357)(166,363)(167,369)(168,370)(169,351)(170,352)(171,358)(172,364)(173,365)(174,371)(175,459)(176,460)(177,466)(178,472)(179,453)(180,454)(181,455)(182,461)(183,467)(184,473)(185,474)(186,450)(187,456)(188,462)(189,468)(190,469)(191,470)(192,451)(193,457)(194,463)(195,464)(196,465)(197,471)(198,452)(199,458)(200,566)(201,572)(202,553)(203,559)(204,560)(205,561)(206,567)(207,573)(208,554)(209,555)(210,556)(211,562)(212,568)(213,574)(214,550)(215,551)(216,557)(217,563)(218,569)(219,570)(220,571)(221,552)(222,558)(223,564)(224,565)(250,270)(252,257)(253,263)(254,269)(255,265)(256,271)(259,264)(261,266)(262,272)(268,273)(275,482)(276,488)(277,494)(278,495)(279,476)(280,477)(281,483)(282,489)(283,490)(284,496)(285,497)(286,478)(287,484)(288,485)(289,491)(290,492)(291,498)(292,479)(293,480)(294,486)(295,487)(296,493)(297,499)(298,475)(299,481)(300,594)(301,595)(302,576)(303,582)(304,588)(305,589)(306,590)(307,596)(308,577)(309,583)(310,584)(311,585)(312,591)(313,597)(314,578)(315,579)(316,580)(317,586)(318,592)(319,598)(320,599)(321,575)(322,581)(323,587)(324,593)(375,380)(376,386)(377,392)(378,398)(382,387)(383,393)(384,399)(385,395)(389,394)(391,396)(400,617)(401,623)(402,604)(403,605)(404,611)(405,612)(406,618)(407,624)(408,600)(409,606)(410,607)(411,613)(412,619)(413,620)(414,601)(415,602)(416,608)(417,614)(418,615)(419,621)(420,622)(421,603)(422,609)(423,610)(424,616)(500,515)(501,521)(503,508)(504,514)(505,510)(506,516)(507,522)(512,517)(513,523)(519,524), 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