Finite Group DatabasebetaFinite Group Databasebeta| order | 23040 |
| isoclinism | isoclinic class of #72209933 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #72209614 |
| commutator, hypocenter | G | C1 |
| Fitting, cosocle | #585 | A6 |
| socle | C2 | #72209666 |
| LCS | G | |
| UCS | C1 ◁ C4 | |
465 conjugacy classes of subgroups; only the 5 normal subgroups are shown.
This group has 465 conjugacy classes of subgroups — too many to draw. Only its 5 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Permutation generators:
(1,2,10,3)(4,15,57,21)(5,16,58,22)(6,32,59,33)(7,40,60,41)(8,11,61,17)(9,12,62,18)(13,71,19,72)(14,79,20,80)(23,116,128,28)(24,121,221,122)(25,90,53,55)(26,69,222,99)(27,89,154,49)(29,135,205,136)(30,65,223,95)(31,92,56,70)(34,157,224,158)(35,164,214,51)(36,151,225,156)(37,76,186,103)(38,150,226,155)(39,105,210,78)(42,193,108,194)(43,197,227,198)(44,184,206,191)(45,185,81,192)(46,182,138,189)(47,183,203,190)(48,209,180,54)(50,124,228,212)(52,66,112,96)(63,97,93,67)(64,149,94,153)(68,234,98,235)(73,245,100,246)(74,114,101,88)(75,242,102,131)(77,133,104,244)(82,271,106,272)(83,265,107,269)(84,263,109,178)(85,264,110,268)(86,115,111,91)(87,218,113,173)(117,297,309,298)(118,215,311,276)(119,280,233,134)(120,219,277,132)(123,230,217,279)(125,239,216,127)(126,172,146,211)(129,312,296,313)(130,139,166,261)(137,290,202,255)(140,322,220,320)(141,305,196,324)(142,167,195,325)(143,147,240,207)(144,294,367,260)(145,170,201,328)(148,329,152,330)(159,248,323,284)(160,247,336,283)(161,340,302,343)(162,317,301,341)(163,339,369,342)(165,175,356,347)(168,274,357,176)(169,352,334,353)(171,254,270,289)(174,188,187,181)(177,282,319,237)(179,253,200,232)(199,361,236,307)(204,362,208,327)(213,351,318,368)(229,358,278,370)(231,304,281,349)(238,257,273,292)(241,359,243,314)(249,374,285,354)(250,348,286,375)(251,373,287,376)(252,259,288,293)(256,379,291,346)(258,267,266,262)(275,355,295,345)(299,321,308,316)(300,365,364,360)(303,366,363,350)(306,377,372,383)(310,332,338,335)(315,384,331,344)(326,378,371,382)(333,381,337,380);(1,4,5)(2,11,12)(3,17,18)(6,34,35)(7,42,43)(8,48,49)(9,54,55)(10,57,58)(13,73,74)(14,81,82)(15,86,52)(16,91,53)(19,100,101)(20,45,106)(21,111,112)(22,115,25)(23,117,118)(24,114,123)(26,125,127)(28,129,130)(29,137,138)(30,92,143)(31,147,69)(32,148,149)(33,152,153)(36,169,170)(37,174,40)(38,175,168)(39,162,178)(41,186,187)(44,203,142)(46,205,202)(47,195,206)(50,213,185)(51,215,64)(56,207,99)(59,224,214)(60,108,227)(61,180,89)(62,209,90)(63,229,230)(65,211,146)(67,231,232)(68,176,109)(70,240,223)(71,241,122)(72,243,121)(75,256,257)(76,258,79)(77,259,255)(78,250,182)(80,103,266)(83,110,171)(84,98,274)(85,270,107)(87,275,193)(88,217,221)(93,278,279)(94,164,276)(95,172,126)(97,281,253)(102,291,292)(104,293,290)(105,286,189)(113,295,194)(116,296,166)(119,306,307)(120,302,264)(124,310,234)(128,309,311)(131,300,184)(132,249,183)(133,248,272)(134,315,320)(135,173,321)(136,218,316)(140,208,273)(141,145,236)(144,326,327)(150,160,198)(151,333,265)(155,336,197)(156,337,269)(157,297,312)(158,298,313)(159,308,181)(161,268,277)(163,167,177)(165,345,348)(188,323,299)(190,219,285)(191,242,364)(192,228,318)(196,201,199)(204,238,220)(210,301,263)(212,338,235)(216,239,222)(225,334,328)(226,347,357)(233,372,361)(237,303,305)(244,284,271)(245,358,304)(246,370,349)(247,332,262)(251,254,260)(252,351,341)(267,283,335)(280,331,322)(282,363,324)(287,289,294)(288,368,317)(319,369,325)(339,377,379)(340,365,378)(342,383,346)(343,360,382)(344,352,376)(350,354,380)(353,373,384)(355,375,356)(362,367,371)(366,374,381);(1,6,7)(2,13,14)(3,19,20)(4,23,24)(5,28,29)(8,50,51)(9,37,45)(10,59,60)(11,63,64)(12,67,68)(15,87,88)(16,76,42)(17,93,94)(18,97,98)(21,113,114)(22,103,108)(25,124,84)(26,119,44)(27,32,82)(30,144,145)(31,132,140)(33,106,154)(34,135,159)(35,165,160)(36,171,172)(38,176,52)(39,179,180)(40,181,148)(41,188,152)(43,96,72)(46,90,173)(47,207,156)(48,210,200)(49,104,137)(53,212,109)(54,133,217)(55,218,138)(56,219,220)(57,128,221)(58,116,205)(61,228,164)(62,186,81)(65,134,83)(66,71,227)(69,237,238)(70,120,236)(73,234,247)(74,252,248)(75,195,125)(77,202,89)(78,261,111)(79,262,241)(80,267,243)(85,143,131)(86,105,139)(91,155,276)(92,277,199)(95,280,107)(99,282,273)(100,235,283)(101,288,284)(102,142,216)(110,240,242)(112,226,274)(115,150,215)(117,122,299)(118,304,286)(121,308,309)(123,209,244)(126,294,204)(127,177,196)(129,272,314)(130,317,318)(136,323,224)(141,239,319)(146,260,208)(147,151,203)(149,332,278)(153,335,229)(157,338,185)(158,310,192)(161,167,344)(162,230,313)(163,265,346)(166,341,213)(168,351,266)(169,170,354)(174,255,355)(175,182,298)(178,358,293)(183,360,331)(184,353,287)(187,290,345)(189,297,347)(190,365,315)(191,352,251)(193,245,321)(194,246,316)(197,329,231)(198,330,281)(201,223,367)(206,222,233)(211,225,270)(214,356,336)(232,348,295)(249,254,377)(250,311,349)(253,375,275)(256,257,340)(258,357,368)(259,263,370)(264,380,306)(268,381,372)(269,379,369)(271,359,296)(279,312,301)(285,289,383)(291,292,343)(300,327,342)(302,325,384)(303,361,350)(305,376,333)(307,366,363)(320,382,326)(322,378,371)(324,373,337)(328,374,334)(339,364,362);(1,8)(2,15)(3,21)(4,25)(5,30)(6,36)(7,44)(9,52)(10,61)(11,55)(12,69)(13,75)(14,83)(16,89)(17,90)(18,99)(19,102)(20,107)(22,49)(23,104)(24,45)(26,125)(27,126)(28,131)(29,139)(31,54)(32,150)(33,155)(34,160)(35,149)(37,173)(38,63)(39,144)(40,182)(41,189)(42,64)(43,199)(46,202)(47,145)(48,143)(50,134)(51,142)(53,57)(56,209)(58,223)(59,225)(60,206)(62,112)(65,211)(66,127)(67,151)(68,179)(70,91)(71,133)(72,244)(73,248)(74,122)(76,124)(77,128)(78,237)(79,263)(80,178)(81,221)(82,140)(84,274)(85,238)(86,147)(87,233)(88,171)(92,115)(93,226)(94,108)(95,172)(96,239)(97,156)(98,200)(100,284)(101,121)(103,212)(105,282)(106,220)(109,176)(110,273)(111,207)(113,119)(114,270)(116,242)(117,300)(118,130)(120,294)(123,204)(129,293)(132,319)(135,305)(136,324)(137,138)(141,276)(146,154)(148,169)(152,334)(153,214)(157,317)(158,341)(159,308)(161,213)(162,338)(163,306)(164,195)(165,342)(166,311)(167,194)(168,265)(170,198)(174,303)(175,231)(177,219)(180,240)(181,359)(183,361)(184,290)(185,254)(186,218)(187,363)(188,314)(190,307)(191,255)(192,289)(193,325)(196,215)(197,328)(201,203)(205,261)(208,217)(210,367)(216,222)(224,336)(227,236)(228,280)(229,333)(230,232)(234,362)(235,327)(241,256)(243,291)(245,348)(246,375)(247,332)(249,275)(250,321)(251,315)(252,376)(253,279)(257,272)(258,371)(259,296)(260,277)(262,330)(264,322)(266,326)(267,329)(268,320)(269,357)(271,292)(278,337)(281,347)(283,335)(285,295)(286,316)(287,331)(288,373)(297,343)(298,340)(299,323)(301,310)(302,318)(304,383)(309,364)(312,384)(313,344)(339,356)(345,380)(346,350)(349,377)(351,365)(352,378)(353,382)(354,358)(355,381)(360,368)(366,379)(369,372)(370,374);(1,9)(2,16)(3,22)(4,26)(5,31)(6,37)(7,45)(8,52)(10,62)(11,65)(12,70)(13,76)(14,42)(15,89)(17,95)(18,92)(19,103)(20,108)(21,49)(23,119)(24,44)(25,125)(27,86)(28,132)(29,140)(30,54)(32,105)(33,78)(34,161)(35,166)(36,173)(38,50)(39,71)(40,183)(41,190)(43,200)(46,171)(47,208)(48,96)(51,176)(53,216)(55,211)(56,58)(57,222)(59,186)(60,81)(61,112)(63,134)(64,83)(66,180)(67,120)(68,236)(69,91)(72,210)(73,249)(74,253)(75,124)(77,87)(79,264)(80,268)(82,139)(84,195)(85,141)(88,202)(90,172)(93,280)(94,107)(97,277)(98,199)(99,115)(100,285)(101,232)(102,212)(104,113)(106,261)(109,142)(110,196)(111,154)(114,137)(116,219)(117,301)(118,153)(121,230)(122,279)(123,201)(126,147)(127,240)(128,233)(129,266)(130,214)(131,319)(133,144)(135,167)(136,325)(138,270)(143,239)(145,217)(146,207)(148,331)(149,311)(150,282)(151,294)(152,315)(155,237)(156,260)(157,339)(158,342)(159,344)(160,213)(162,309)(163,256)(164,274)(165,341)(168,272)(169,287)(170,184)(174,231)(175,303)(177,242)(178,320)(179,227)(181,360)(182,361)(185,362)(187,281)(188,365)(189,307)(191,328)(192,327)(193,324)(194,305)(197,255)(198,290)(203,204)(205,220)(206,221)(209,223)(215,273)(218,225)(224,302)(226,228)(229,286)(234,254)(235,289)(238,276)(241,306)(243,372)(244,367)(245,373)(246,376)(247,377)(248,275)(250,278)(251,334)(252,375)(257,265)(258,296)(259,371)(262,380)(263,322)(267,381)(269,292)(271,357)(283,383)(284,295)(288,348)(291,369)(293,326)(297,366)(298,350)(299,312)(300,310)(304,335)(308,313)(314,351)(316,333)(317,356)(318,336)(321,337)(323,384)(329,355)(330,345)(332,349)(338,364)(340,346)(343,379)(347,363)(352,374)(353,354)(358,382)(359,368)(370,378);(1,4)(2,11)(3,17)(5,27)(6,38)(7,46)(8,53)(9,26)(10,57)(12,66)(13,77)(14,84)(15,90)(16,65)(18,96)(19,104)(20,109)(21,55)(22,95)(23,75)(24,114)(25,61)(28,133)(29,141)(30,146)(31,86)(32,151)(33,156)(34,162)(35,167)(36,93)(37,50)(39,177)(40,184)(41,191)(42,195)(43,201)(44,137)(45,171)(47,199)(48,92)(49,211)(51,64)(52,216)(54,207)(56,111)(58,154)(59,226)(60,138)(62,222)(63,225)(67,155)(68,204)(69,239)(70,180)(71,242)(72,131)(73,250)(74,254)(76,87)(78,260)(79,265)(80,269)(81,270)(82,273)(83,176)(85,140)(88,221)(89,172)(91,143)(94,164)(97,150)(98,208)(99,127)(100,286)(101,289)(102,128)(103,113)(105,294)(106,238)(107,274)(108,142)(110,220)(112,125)(115,240)(116,244)(117,302)(118,305)(119,124)(120,237)(121,185)(122,192)(123,200)(126,223)(129,315)(130,136)(132,144)(134,218)(135,166)(139,215)(145,227)(147,209)(148,258)(149,193)(152,266)(153,194)(157,247)(158,283)(159,246)(160,310)(161,309)(163,175)(165,349)(168,178)(169,326)(170,183)(173,280)(174,243)(179,217)(181,350)(182,255)(186,228)(187,241)(188,366)(189,290)(190,328)(196,205)(197,361)(198,307)(202,206)(203,236)(210,319)(212,233)(213,300)(214,325)(219,367)(224,301)(229,285)(230,362)(231,372)(232,235)(234,253)(245,323)(248,316)(249,278)(251,259)(252,312)(256,303)(257,264)(261,276)(262,378)(263,357)(267,382)(268,292)(271,322)(272,320)(275,333)(277,282)(279,327)(281,306)(284,321)(287,293)(288,313)(291,363)(295,337)(296,331)(297,365)(298,360)(299,375)(304,356)(308,348)(311,324)(314,346)(317,335)(318,364)(329,352)(330,353)(332,341)(334,371)(336,338)(339,377)(340,351)(342,383)(343,368)(344,376)(345,354)(347,369)(355,374)(358,381)(359,379)(370,380)(373,384);(1,5)(2,12)(3,18)(4,27)(6,39)(7,47)(8,30)(9,56)(10,58)(11,66)(13,78)(14,85)(15,69)(16,92)(17,96)(19,105)(20,110)(21,99)(22,70)(23,120)(24,123)(25,126)(26,111)(28,134)(29,142)(31,62)(32,76)(33,103)(34,163)(35,168)(36,144)(37,72)(38,177)(40,185)(41,192)(42,196)(43,202)(44,145)(45,204)(46,199)(48,65)(49,91)(50,131)(51,139)(52,209)(53,146)(54,112)(55,127)(57,154)(59,210)(60,203)(61,223)(63,219)(64,215)(67,233)(68,171)(71,186)(73,251)(74,255)(75,237)(77,260)(79,193)(80,194)(81,208)(82,274)(83,238)(84,140)(86,222)(87,151)(88,179)(89,115)(90,239)(93,132)(94,276)(95,180)(97,119)(98,270)(100,287)(101,290)(102,282)(104,294)(106,176)(107,273)(108,141)(109,220)(113,156)(114,200)(116,280)(117,303)(118,257)(121,184)(122,191)(124,150)(125,207)(128,277)(129,316)(130,272)(133,218)(135,322)(136,320)(137,227)(138,236)(143,211)(147,216)(148,275)(149,265)(152,295)(153,269)(155,212)(157,340)(158,343)(159,345)(160,306)(161,291)(162,175)(164,261)(165,350)(166,271)(167,178)(169,249)(170,279)(172,240)(173,244)(174,300)(181,349)(182,254)(183,327)(187,364)(188,304)(189,289)(190,362)(195,205)(197,232)(198,253)(201,206)(213,243)(214,357)(217,221)(224,369)(225,367)(226,319)(228,242)(229,371)(230,328)(231,338)(234,307)(235,361)(241,318)(245,374)(246,354)(247,351)(248,315)(250,259)(252,378)(256,302)(258,333)(262,312)(263,325)(264,305)(266,337)(267,313)(268,324)(278,326)(281,310)(283,368)(284,331)(285,334)(286,293)(288,382)(292,311)(296,321)(297,341)(298,317)(299,381)(301,347)(308,380)(309,363)(314,383)(323,355)(329,344)(330,384)(332,365)(335,360)(336,372)(339,379)(342,346)(348,370)(352,376)(353,373)(356,366)(358,375)(359,377);(1,2,10,3)(4,11,57,17)(5,12,58,18)(6,13,59,19)(7,14,60,20)(8,15,61,21)(9,16,62,22)(23,63,128,93)(24,64,221,94)(25,55,53,90)(26,65,222,95)(27,66,154,96)(28,67,116,97)(29,68,205,98)(30,69,223,99)(31,70,56,92)(32,71,33,72)(34,73,224,100)(35,74,214,101)(36,75,225,102)(37,76,186,103)(38,77,226,104)(39,78,210,105)(40,79,41,80)(42,81,108,45)(43,82,227,106)(44,83,206,107)(46,84,138,109)(47,85,203,110)(48,86,180,111)(49,52,89,112)(50,87,228,113)(51,88,164,114)(54,91,209,115)(117,229,309,278)(118,230,311,279)(119,134,233,280)(120,219,277,132)(121,149,122,153)(123,215,217,276)(124,218,212,173)(125,211,216,172)(126,127,146,239)(129,231,296,281)(130,232,166,253)(131,151,242,156)(133,155,244,150)(135,234,136,235)(137,176,202,274)(139,179,261,200)(140,236,220,199)(141,204,196,208)(142,171,195,270)(143,147,240,207)(144,237,367,282)(145,238,201,273)(148,241,152,243)(157,245,158,246)(159,247,323,283)(160,248,336,284)(161,249,302,285)(162,250,301,286)(163,251,369,287)(165,252,356,288)(167,254,325,289)(168,255,357,290)(169,256,334,291)(170,257,328,292)(174,258,187,266)(175,259,347,293)(177,260,319,294)(178,182,263,189)(181,262,188,267)(183,264,190,268)(184,265,191,269)(185,193,192,194)(197,271,198,272)(213,275,318,295)(297,358,298,370)(299,335,308,332)(300,333,364,337)(303,371,363,326)(304,313,349,312)(305,362,324,327)(306,315,372,331)(307,320,361,322)(310,316,338,321)(314,329,359,330)(317,348,341,375)(339,373,342,376)(340,374,343,354)(344,377,384,383)(345,351,355,368)(346,352,379,353)(350,378,366,382)(360,380,365,381)37 conjugacy classes — view the full character table.
| maximal quotient of | #72227900 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((1,2,10,3)(4,15,57,21)(5,16,58,22)(6,32,59,33)(7,40,60,41)(8,11,61,17)(9,12,62,18)(13,71,19,72)(14,79,20,80)(23,116,128,28)(24,121,221,122)(25,90,53,55)(26,69,222,99)(27,89,154,49)(29,135,205,136)(30,65,223,95)(31,92,56,70)(34,157,224,158)(35,164,214,51)(36,151,225,156)(37,76,186,103)(38,150,226,155)(39,105,210,78)(42,193,108,194)(43,197,227,198)(44,184,206,191)(45,185,81,192)(46,182,138,189)(47,183,203,190)(48,209,180,54)(50,124,228,212)(52,66,112,96)(63,97,93,67)(64,149,94,153)(68,234,98,235)(73,245,100,246)(74,114,101,88)(75,242,102,131)(77,133,104,244)(82,271,106,272)(83,265,107,269)(84,263,109,178)(85,264,110,268)(86,115,111,91)(87,218,113,173)(117,297,309,298)(118,215,311,276)(119,280,233,134)(120,219,277,132)(123,230,217,279)(125,239,216,127)(126,172,146,211)(129,312,296,313)(130,139,166,261)(137,290,202,255)(140,322,220,320)(141,305,196,324)(142,167,195,325)(143,147,240,207)(144,294,367,260)(145,170,201,328)(148,329,152,330)(159,248,323,284)(160,247,336,283)(161,340,302,343)(162,317,301,341)(163,339,369,342)(165,175,356,347)(168,274,357,176)(169,352,334,353)(171,254,270,289)(174,188,187,181)(177,282,319,237)(179,253,200,232)(199,361,236,307)(204,362,208,327)(213,351,318,368)(229,358,278,370)(231,304,281,349)(238,257,273,292)(241,359,243,314)(249,374,285,354)(250,348,286,375)(251,373,287,376)(252,259,288,293)(256,379,291,346)(258,267,266,262)(275,355,295,345)(299,321,308,316)(300,365,364,360)(303,366,363,350)(306,377,372,383)(310,332,338,335)(315,384,331,344)(326,378,371,382)(333,381,337,380), (1,4,5)(2,11,12)(3,17,18)(6,34,35)(7,42,43)(8,48,49)(9,54,55)(10,57,58)(13,73,74)(14,81,82)(15,86,52)(16,91,53)(19,100,101)(20,45,106)(21,111,112)(22,115,25)(23,117,118)(24,114,123)(26,125,127)(28,129,130)(29,137,138)(30,92,143)(31,147,69)(32,148,149)(33,152,153)(36,169,170)(37,174,40)(38,175,168)(39,162,178)(41,186,187)(44,203,142)(46,205,202)(47,195,206)(50,213,185)(51,215,64)(56,207,99)(59,224,214)(60,108,227)(61,180,89)(62,209,90)(63,229,230)(65,211,146)(67,231,232)(68,176,109)(70,240,223)(71,241,122)(72,243,121)(75,256,257)(76,258,79)(77,259,255)(78,250,182)(80,103,266)(83,110,171)(84,98,274)(85,270,107)(87,275,193)(88,217,221)(93,278,279)(94,164,276)(95,172,126)(97,281,253)(102,291,292)(104,293,290)(105,286,189)(113,295,194)(116,296,166)(119,306,307)(120,302,264)(124,310,234)(128,309,311)(131,300,184)(132,249,183)(133,248,272)(134,315,320)(135,173,321)(136,218,316)(140,208,273)(141,145,236)(144,326,327)(150,160,198)(151,333,265)(155,336,197)(156,337,269)(157,297,312)(158,298,313)(159,308,181)(161,268,277)(163,167,177)(165,345,348)(188,323,299)(190,219,285)(191,242,364)(192,228,318)(196,201,199)(204,238,220)(210,301,263)(212,338,235)(216,239,222)(225,334,328)(226,347,357)(233,372,361)(237,303,305)(244,284,271)(245,358,304)(246,370,349)(247,332,262)(251,254,260)(252,351,341)(267,283,335)(280,331,322)(282,363,324)(287,289,294)(288,368,317)(319,369,325)(339,377,379)(340,365,378)(342,383,346)(343,360,382)(344,352,376)(350,354,380)(353,373,384)(355,375,356)(362,367,371)(366,374,381), (1,6,7)(2,13,14)(3,19,20)(4,23,24)(5,28,29)(8,50,51)(9,37,45)(10,59,60)(11,63,64)(12,67,68)(15,87,88)(16,76,42)(17,93,94)(18,97,98)(21,113,114)(22,103,108)(25,124,84)(26,119,44)(27,32,82)(30,144,145)(31,132,140)(33,106,154)(34,135,159)(35,165,160)(36,171,172)(38,176,52)(39,179,180)(40,181,148)(41,188,152)(43,96,72)(46,90,173)(47,207,156)(48,210,200)(49,104,137)(53,212,109)(54,133,217)(55,218,138)(56,219,220)(57,128,221)(58,116,205)(61,228,164)(62,186,81)(65,134,83)(66,71,227)(69,237,238)(70,120,236)(73,234,247)(74,252,248)(75,195,125)(77,202,89)(78,261,111)(79,262,241)(80,267,243)(85,143,131)(86,105,139)(91,155,276)(92,277,199)(95,280,107)(99,282,273)(100,235,283)(101,288,284)(102,142,216)(110,240,242)(112,226,274)(115,150,215)(117,122,299)(118,304,286)(121,308,309)(123,209,244)(126,294,204)(127,177,196)(129,272,314)(130,317,318)(136,323,224)(141,239,319)(146,260,208)(147,151,203)(149,332,278)(153,335,229)(157,338,185)(158,310,192)(161,167,344)(162,230,313)(163,265,346)(166,341,213)(168,351,266)(169,170,354)(174,255,355)(175,182,298)(178,358,293)(183,360,331)(184,353,287)(187,290,345)(189,297,347)(190,365,315)(191,352,251)(193,245,321)(194,246,316)(197,329,231)(198,330,281)(201,223,367)(206,222,233)(211,225,270)(214,356,336)(232,348,295)(249,254,377)(250,311,349)(253,375,275)(256,257,340)(258,357,368)(259,263,370)(264,380,306)(268,381,372)(269,379,369)(271,359,296)(279,312,301)(285,289,383)(291,292,343)(300,327,342)(302,325,384)(303,361,350)(305,376,333)(307,366,363)(320,382,326)(322,378,371)(324,373,337)(328,374,334)(339,364,362), (1,8)(2,15)(3,21)(4,25)(5,30)(6,36)(7,44)(9,52)(10,61)(11,55)(12,69)(13,75)(14,83)(16,89)(17,90)(18,99)(19,102)(20,107)(22,49)(23,104)(24,45)(26,125)(27,126)(28,131)(29,139)(31,54)(32,150)(33,155)(34,160)(35,149)(37,173)(38,63)(39,144)(40,182)(41,189)(42,64)(43,199)(46,202)(47,145)(48,143)(50,134)(51,142)(53,57)(56,209)(58,223)(59,225)(60,206)(62,112)(65,211)(66,127)(67,151)(68,179)(70,91)(71,133)(72,244)(73,248)(74,122)(76,124)(77,128)(78,237)(79,263)(80,178)(81,221)(82,140)(84,274)(85,238)(86,147)(87,233)(88,171)(92,115)(93,226)(94,108)(95,172)(96,239)(97,156)(98,200)(100,284)(101,121)(103,212)(105,282)(106,220)(109,176)(110,273)(111,207)(113,119)(114,270)(116,242)(117,300)(118,130)(120,294)(123,204)(129,293)(132,319)(135,305)(136,324)(137,138)(141,276)(146,154)(148,169)(152,334)(153,214)(157,317)(158,341)(159,308)(161,213)(162,338)(163,306)(164,195)(165,342)(166,311)(167,194)(168,265)(170,198)(174,303)(175,231)(177,219)(180,240)(181,359)(183,361)(184,290)(185,254)(186,218)(187,363)(188,314)(190,307)(191,255)(192,289)(193,325)(196,215)(197,328)(201,203)(205,261)(208,217)(210,367)(216,222)(224,336)(227,236)(228,280)(229,333)(230,232)(234,362)(235,327)(241,256)(243,291)(245,348)(246,375)(247,332)(249,275)(250,321)(251,315)(252,376)(253,279)(257,272)(258,371)(259,296)(260,277)(262,330)(264,322)(266,326)(267,329)(268,320)(269,357)(271,292)(278,337)(281,347)(283,335)(285,295)(286,316)(287,331)(288,373)(297,343)(298,340)(299,323)(301,310)(302,318)(304,383)(309,364)(312,384)(313,344)(339,356)(345,380)(346,350)(349,377)(351,365)(352,378)(353,382)(354,358)(355,381)(360,368)(366,379)(369,372)(370,374), (1,9)(2,16)(3,22)(4,26)(5,31)(6,37)(7,45)(8,52)(10,62)(11,65)(12,70)(13,76)(14,42)(15,89)(17,95)(18,92)(19,103)(20,108)(21,49)(23,119)(24,44)(25,125)(27,86)(28,132)(29,140)(30,54)(32,105)(33,78)(34,161)(35,166)(36,173)(38,50)(39,71)(40,183)(41,190)(43,200)(46,171)(47,208)(48,96)(51,176)(53,216)(55,211)(56,58)(57,222)(59,186)(60,81)(61,112)(63,134)(64,83)(66,180)(67,120)(68,236)(69,91)(72,210)(73,249)(74,253)(75,124)(77,87)(79,264)(80,268)(82,139)(84,195)(85,141)(88,202)(90,172)(93,280)(94,107)(97,277)(98,199)(99,115)(100,285)(101,232)(102,212)(104,113)(106,261)(109,142)(110,196)(111,154)(114,137)(116,219)(117,301)(118,153)(121,230)(122,279)(123,201)(126,147)(127,240)(128,233)(129,266)(130,214)(131,319)(133,144)(135,167)(136,325)(138,270)(143,239)(145,217)(146,207)(148,331)(149,311)(150,282)(151,294)(152,315)(155,237)(156,260)(157,339)(158,342)(159,344)(160,213)(162,309)(163,256)(164,274)(165,341)(168,272)(169,287)(170,184)(174,231)(175,303)(177,242)(178,320)(179,227)(181,360)(182,361)(185,362)(187,281)(188,365)(189,307)(191,328)(192,327)(193,324)(194,305)(197,255)(198,290)(203,204)(205,220)(206,221)(209,223)(215,273)(218,225)(224,302)(226,228)(229,286)(234,254)(235,289)(238,276)(241,306)(243,372)(244,367)(245,373)(246,376)(247,377)(248,275)(250,278)(251,334)(252,375)(257,265)(258,296)(259,371)(262,380)(263,322)(267,381)(269,292)(271,357)(283,383)(284,295)(288,348)(291,369)(293,326)(297,366)(298,350)(299,312)(300,310)(304,335)(308,313)(314,351)(316,333)(317,356)(318,336)(321,337)(323,384)(329,355)(330,345)(332,349)(338,364)(340,346)(343,379)(347,363)(352,374)(353,354)(358,382)(359,368)(370,378), (1,4)(2,11)(3,17)(5,27)(6,38)(7,46)(8,53)(9,26)(10,57)(12,66)(13,77)(14,84)(15,90)(16,65)(18,96)(19,104)(20,109)(21,55)(22,95)(23,75)(24,114)(25,61)(28,133)(29,141)(30,146)(31,86)(32,151)(33,156)(34,162)(35,167)(36,93)(37,50)(39,177)(40,184)(41,191)(42,195)(43,201)(44,137)(45,171)(47,199)(48,92)(49,211)(51,64)(52,216)(54,207)(56,111)(58,154)(59,226)(60,138)(62,222)(63,225)(67,155)(68,204)(69,239)(70,180)(71,242)(72,131)(73,250)(74,254)(76,87)(78,260)(79,265)(80,269)(81,270)(82,273)(83,176)(85,140)(88,221)(89,172)(91,143)(94,164)(97,150)(98,208)(99,127)(100,286)(101,289)(102,128)(103,113)(105,294)(106,238)(107,274)(108,142)(110,220)(112,125)(115,240)(116,244)(117,302)(118,305)(119,124)(120,237)(121,185)(122,192)(123,200)(126,223)(129,315)(130,136)(132,144)(134,218)(135,166)(139,215)(145,227)(147,209)(148,258)(149,193)(152,266)(153,194)(157,247)(158,283)(159,246)(160,310)(161,309)(163,175)(165,349)(168,178)(169,326)(170,183)(173,280)(174,243)(179,217)(181,350)(182,255)(186,228)(187,241)(188,366)(189,290)(190,328)(196,205)(197,361)(198,307)(202,206)(203,236)(210,319)(212,233)(213,300)(214,325)(219,367)(224,301)(229,285)(230,362)(231,372)(232,235)(234,253)(245,323)(248,316)(249,278)(251,259)(252,312)(256,303)(257,264)(261,276)(262,378)(263,357)(267,382)(268,292)(271,322)(272,320)(275,333)(277,282)(279,327)(281,306)(284,321)(287,293)(288,313)(291,363)(295,337)(296,331)(297,365)(298,360)(299,375)(304,356)(308,348)(311,324)(314,346)(317,335)(318,364)(329,352)(330,353)(332,341)(334,371)(336,338)(339,377)(340,351)(342,383)(343,368)(344,376)(345,354)(347,369)(355,374)(358,381)(359,379)(370,380)(373,384), (1,5)(2,12)(3,18)(4,27)(6,39)(7,47)(8,30)(9,56)(10,58)(11,66)(13,78)(14,85)(15,69)(16,92)(17,96)(19,105)(20,110)(21,99)(22,70)(23,120)(24,123)(25,126)(26,111)(28,134)(29,142)(31,62)(32,76)(33,103)(34,163)(35,168)(36,144)(37,72)(38,177)(40,185)(41,192)(42,196)(43,202)(44,145)(45,204)(46,199)(48,65)(49,91)(50,131)(51,139)(52,209)(53,146)(54,112)(55,127)(57,154)(59,210)(60,203)(61,223)(63,219)(64,215)(67,233)(68,171)(71,186)(73,251)(74,255)(75,237)(77,260)(79,193)(80,194)(81,208)(82,274)(83,238)(84,140)(86,222)(87,151)(88,179)(89,115)(90,239)(93,132)(94,276)(95,180)(97,119)(98,270)(100,287)(101,290)(102,282)(104,294)(106,176)(107,273)(108,141)(109,220)(113,156)(114,200)(116,280)(117,303)(118,257)(121,184)(122,191)(124,150)(125,207)(128,277)(129,316)(130,272)(133,218)(135,322)(136,320)(137,227)(138,236)(143,211)(147,216)(148,275)(149,265)(152,295)(153,269)(155,212)(157,340)(158,343)(159,345)(160,306)(161,291)(162,175)(164,261)(165,350)(166,271)(167,178)(169,249)(170,279)(172,240)(173,244)(174,300)(181,349)(182,254)(183,327)(187,364)(188,304)(189,289)(190,362)(195,205)(197,232)(198,253)(201,206)(213,243)(214,357)(217,221)(224,369)(225,367)(226,319)(228,242)(229,371)(230,328)(231,338)(234,307)(235,361)(241,318)(245,374)(246,354)(247,351)(248,315)(250,259)(252,378)(256,302)(258,333)(262,312)(263,325)(264,305)(266,337)(267,313)(268,324)(278,326)(281,310)(283,368)(284,331)(285,334)(286,293)(288,382)(292,311)(296,321)(297,341)(298,317)(299,381)(301,347)(308,380)(309,363)(314,383)(323,355)(329,344)(330,384)(332,365)(335,360)(336,372)(339,379)(342,346)(348,370)(352,376)(353,373)(356,366)(358,375)(359,377), (1,2,10,3)(4,11,57,17)(5,12,58,18)(6,13,59,19)(7,14,60,20)(8,15,61,21)(9,16,62,22)(23,63,128,93)(24,64,221,94)(25,55,53,90)(26,65,222,95)(27,66,154,96)(28,67,116,97)(29,68,205,98)(30,69,223,99)(31,70,56,92)(32,71,33,72)(34,73,224,100)(35,74,214,101)(36,75,225,102)(37,76,186,103)(38,77,226,104)(39,78,210,105)(40,79,41,80)(42,81,108,45)(43,82,227,106)(44,83,206,107)(46,84,138,109)(47,85,203,110)(48,86,180,111)(49,52,89,112)(50,87,228,113)(51,88,164,114)(54,91,209,115)(117,229,309,278)(118,230,311,279)(119,134,233,280)(120,219,277,132)(121,149,122,153)(123,215,217,276)(124,218,212,173)(125,211,216,172)(126,127,146,239)(129,231,296,281)(130,232,166,253)(131,151,242,156)(133,155,244,150)(135,234,136,235)(137,176,202,274)(139,179,261,200)(140,236,220,199)(141,204,196,208)(142,171,195,270)(143,147,240,207)(144,237,367,282)(145,238,201,273)(148,241,152,243)(157,245,158,246)(159,247,323,283)(160,248,336,284)(161,249,302,285)(162,250,301,286)(163,251,369,287)(165,252,356,288)(167,254,325,289)(168,255,357,290)(169,256,334,291)(170,257,328,292)(174,258,187,266)(175,259,347,293)(177,260,319,294)(178,182,263,189)(181,262,188,267)(183,264,190,268)(184,265,191,269)(185,193,192,194)(197,271,198,272)(213,275,318,295)(297,358,298,370)(299,335,308,332)(300,333,364,337)(303,371,363,326)(304,313,349,312)(305,362,324,327)(306,315,372,331)(307,320,361,322)(310,316,338,321)(314,329,359,330)(317,348,341,375)(339,373,342,376)(340,374,343,354)(344,377,384,383)(345,351,355,368)(346,352,379,353)(350,378,366,382)(360,380,365,381));