← Prev (#72290178) Next (#72290180) →
Aliases
Subgroups
37559287250869 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 13 generators on 258 points:
(3,4,11,18)(5,19,25,12)(6,13,26,46)(7,14,31,51)(8,15,35,55)(9,16,38,58)(10,17,40,60)(20,61,66,41)(21,62,71,42)(22,63,75,43)(23,64,78,44)(24,65,80,45)(27,47,81,111)(28,48,82,112)(29,49,83,113)(30,50,84,114)(32,52,91,121)(33,53,92,122)(34,54,93,123)(36,56,97,127)(37,57,98,128)(39,59,100,130)(67,131,141,101)(68,132,142,102)(69,133,143,103)(70,134,144,104)(72,135,151,105)(73,136,152,106)(74,137,153,107)(76,138,157,108)(77,139,158,109)(79,140,160,110)(85,115,161,186)(86,116,162,187)(87,117,163,188)(88,118,164,189)(89,119,165,190)(90,120,166,191)(94,124,171,196)(95,125,172,197)(96,126,173,198)(99,129,175,200)(145,201,211,176)(146,202,212,177)(147,203,213,178)(148,204,214,179)(149,205,215,180)(150,206,216,181)(154,207,221,182)(155,208,222,183)(156,209,223,184)(159,210,225,185)(167,192,226,237)(168,193,227,238)(169,194,228,239)(170,195,229,240)(174,199,231,242)(217,243,248,232)(218,244,249,233)(219,245,250,234)(220,246,251,235)(224,247,253,236)(230,241,254,256)(252,257,258,255);(3,5,11,25)(4,12,18,19)(6,20,26,66)(7,21,31,71)(8,22,35,75)(9,23,38,78)(10,24,40,80)(13,41,46,61)(14,42,51,62)(15,43,55,63)(16,44,58,64)(17,45,60,65)(27,67,81,141)(28,68,82,142)(29,69,83,143)(30,70,84,144)(32,72,91,151)(33,73,92,152)(34,74,93,153)(36,76,97,157)(37,77,98,158)(39,79,100,160)(47,101,111,131)(48,102,112,132)(49,103,113,133)(50,104,114,134)(52,105,121,135)(53,106,122,136)(54,107,123,137)(56,108,127,138)(57,109,128,139)(59,110,130,140)(85,145,161,211)(86,146,162,212)(87,147,163,213)(88,148,164,214)(89,149,165,215)(90,150,166,216)(94,154,171,221)(95,155,172,222)(96,156,173,223)(99,159,175,225)(115,176,186,201)(116,177,187,202)(117,178,188,203)(118,179,189,204)(119,180,190,205)(120,181,191,206)(124,182,196,207)(125,183,197,208)(126,184,198,209)(129,185,200,210)(167,217,226,248)(168,218,227,249)(169,219,228,250)(170,220,229,251)(174,224,231,253)(192,232,237,243)(193,233,238,244)(194,234,239,245)(195,235,240,246)(199,236,242,247)(230,252,254,258)(241,255,256,257);(6,26)(13,46)(20,66)(27,81)(28,82)(29,83)(30,84)(41,61)(47,111)(48,112)(49,113)(50,114)(67,141)(68,142)(69,143)(70,144)(85,161)(86,162)(87,163)(88,164)(89,165)(90,166)(101,131)(102,132)(103,133)(104,134)(115,186)(116,187)(117,188)(118,189)(119,190)(120,191)(145,211)(146,212)(147,213)(148,214)(149,215)(150,216)(167,226)(168,227)(169,228)(170,229)(176,201)(177,202)(178,203)(179,204)(180,205)(181,206)(192,237)(193,238)(194,239)(195,240)(217,248)(218,249)(219,250)(220,251)(230,254)(232,243)(233,244)(234,245)(235,246)(241,256)(252,258)(255,257);(3,6)(4,13)(5,20)(7,27)(8,28)(9,29)(10,30)(11,26)(12,41)(14,47)(15,48)(16,49)(17,50)(18,46)(19,61)(21,67)(22,68)(23,69)(24,70)(25,66)(31,81)(32,85)(33,86)(34,87)(35,82)(36,88)(37,89)(38,83)(39,90)(40,84)(42,101)(43,102)(44,103)(45,104)(51,111)(52,115)(53,116)(54,117)(55,112)(56,118)(57,119)(58,113)(59,120)(60,114)(62,131)(63,132)(64,133)(65,134)(71,141)(72,145)(73,146)(74,147)(75,142)(76,148)(77,149)(78,143)(79,150)(80,144)(91,161)(92,162)(93,163)(94,167)(95,168)(96,169)(97,164)(98,165)(99,170)(100,166)(105,176)(106,177)(107,178)(108,179)(109,180)(110,181)(121,186)(122,187)(123,188)(124,192)(125,193)(126,194)(127,189)(128,190)(129,195)(130,191)(135,201)(136,202)(137,203)(138,204)(139,205)(140,206)(151,211)(152,212)(153,213)(154,217)(155,218)(156,219)(157,214)(158,215)(159,220)(160,216)(171,226)(172,227)(173,228)(174,230)(175,229)(182,232)(183,233)(184,234)(185,235)(196,237)(197,238)(198,239)(199,241)(200,240)(207,243)(208,244)(209,245)(210,246)(221,248)(222,249)(223,250)(224,252)(225,251)(231,254)(236,255)(242,256)(247,257)(253,258);(7,31)(14,51)(21,71)(27,81)(32,91)(33,92)(34,93)(42,62)(47,111)(52,121)(53,122)(54,123)(67,141)(72,151)(73,152)(74,153)(85,161)(86,162)(87,163)(94,171)(95,172)(96,173)(101,131)(105,135)(106,136)(107,137)(115,186)(116,187)(117,188)(124,196)(125,197)(126,198)(145,211)(146,212)(147,213)(154,221)(155,222)(156,223)(167,226)(168,227)(169,228)(174,231)(176,201)(177,202)(178,203)(182,207)(183,208)(184,209)(192,237)(193,238)(194,239)(199,242)(217,248)(218,249)(219,250)(224,253)(230,254)(232,243)(233,244)(234,245)(236,247)(241,256)(252,258)(255,257);(3,7)(4,14)(5,21)(6,27)(8,32)(9,33)(10,34)(11,31)(12,42)(13,47)(15,52)(16,53)(17,54)(18,51)(19,62)(20,67)(22,72)(23,73)(24,74)(25,71)(26,81)(28,85)(29,86)(30,87)(35,91)(36,94)(37,95)(38,92)(39,96)(40,93)(41,101)(43,105)(44,106)(45,107)(46,111)(48,115)(49,116)(50,117)(55,121)(56,124)(57,125)(58,122)(59,126)(60,123)(61,131)(63,135)(64,136)(65,137)(66,141)(68,145)(69,146)(70,147)(75,151)(76,154)(77,155)(78,152)(79,156)(80,153)(82,161)(83,162)(84,163)(88,167)(89,168)(90,169)(97,171)(98,172)(99,174)(100,173)(102,176)(103,177)(104,178)(108,182)(109,183)(110,184)(112,186)(113,187)(114,188)(118,192)(119,193)(120,194)(127,196)(128,197)(129,199)(130,198)(132,201)(133,202)(134,203)(138,207)(139,208)(140,209)(142,211)(143,212)(144,213)(148,217)(149,218)(150,219)(157,221)(158,222)(159,224)(160,223)(164,226)(165,227)(166,228)(170,230)(175,231)(179,232)(180,233)(181,234)(185,236)(189,237)(190,238)(191,239)(195,241)(200,242)(204,243)(205,244)(206,245)(210,247)(214,248)(215,249)(216,250)(220,252)(225,253)(229,254)(235,255)(240,256)(246,257)(251,258);(8,35)(15,55)(22,75)(28,82)(32,91)(36,97)(37,98)(43,63)(48,112)(52,121)(56,127)(57,128)(68,142)(72,151)(76,157)(77,158)(85,161)(88,164)(89,165)(94,171)(95,172)(99,175)(102,132)(105,135)(108,138)(109,139)(115,186)(118,189)(119,190)(124,196)(125,197)(129,200)(145,211)(148,214)(149,215)(154,221)(155,222)(159,225)(167,226)(168,227)(170,229)(174,231)(176,201)(179,204)(180,205)(182,207)(183,208)(185,210)(192,237)(193,238)(195,240)(199,242)(217,248)(218,249)(220,251)(224,253)(230,254)(232,243)(233,244)(235,246)(236,247)(241,256)(252,258)(255,257);(3,8)(4,15)(5,22)(6,28)(7,32)(9,36)(10,37)(11,35)(12,43)(13,48)(14,52)(16,56)(17,57)(18,55)(19,63)(20,68)(21,72)(23,76)(24,77)(25,75)(26,82)(27,85)(29,88)(30,89)(31,91)(33,94)(34,95)(38,97)(39,99)(40,98)(41,102)(42,105)(44,108)(45,109)(46,112)(47,115)(49,118)(50,119)(51,121)(53,124)(54,125)(58,127)(59,129)(60,128)(61,132)(62,135)(64,138)(65,139)(66,142)(67,145)(69,148)(70,149)(71,151)(73,154)(74,155)(78,157)(79,159)(80,158)(81,161)(83,164)(84,165)(86,167)(87,168)(90,170)(92,171)(93,172)(96,174)(100,175)(101,176)(103,179)(104,180)(106,182)(107,183)(110,185)(111,186)(113,189)(114,190)(116,192)(117,193)(120,195)(122,196)(123,197)(126,199)(130,200)(131,201)(133,204)(134,205)(136,207)(137,208)(140,210)(141,211)(143,214)(144,215)(146,217)(147,218)(150,220)(152,221)(153,222)(156,224)(160,225)(162,226)(163,227)(166,229)(169,230)(173,231)(177,232)(178,233)(181,235)(184,236)(187,237)(188,238)(191,240)(194,241)(198,242)(202,243)(203,244)(206,246)(209,247)(212,248)(213,249)(216,251)(219,252)(223,253)(228,254)(234,255)(239,256)(245,257)(250,258);(9,38)(16,58)(23,78)(29,83)(33,92)(36,97)(39,100)(44,64)(49,113)(53,122)(56,127)(59,130)(69,143)(73,152)(76,157)(79,160)(86,162)(88,164)(90,166)(94,171)(96,173)(99,175)(103,133)(106,136)(108,138)(110,140)(116,187)(118,189)(120,191)(124,196)(126,198)(129,200)(146,212)(148,214)(150,216)(154,221)(156,223)(159,225)(167,226)(169,228)(170,229)(174,231)(177,202)(179,204)(181,206)(182,207)(184,209)(185,210)(192,237)(194,239)(195,240)(199,242)(217,248)(219,250)(220,251)(224,253)(230,254)(232,243)(234,245)(235,246)(236,247)(241,256)(252,258)(255,257);(3,9)(4,16)(5,23)(6,29)(7,33)(8,36)(10,39)(11,38)(12,44)(13,49)(14,53)(15,56)(17,59)(18,58)(19,64)(20,69)(21,73)(22,76)(24,79)(25,78)(26,83)(27,86)(28,88)(30,90)(31,92)(32,94)(34,96)(35,97)(37,99)(40,100)(41,103)(42,106)(43,108)(45,110)(46,113)(47,116)(48,118)(50,120)(51,122)(52,124)(54,126)(55,127)(57,129)(60,130)(61,133)(62,136)(63,138)(65,140)(66,143)(67,146)(68,148)(70,150)(71,152)(72,154)(74,156)(75,157)(77,159)(80,160)(81,162)(82,164)(84,166)(85,167)(87,169)(89,170)(91,171)(93,173)(95,174)(98,175)(101,177)(102,179)(104,181)(105,182)(107,184)(109,185)(111,187)(112,189)(114,191)(115,192)(117,194)(119,195)(121,196)(123,198)(125,199)(128,200)(131,202)(132,204)(134,206)(135,207)(137,209)(139,210)(141,212)(142,214)(144,216)(145,217)(147,219)(149,220)(151,221)(153,223)(155,224)(158,225)(161,226)(163,228)(165,229)(168,230)(172,231)(176,232)(178,234)(180,235)(183,236)(186,237)(188,239)(190,240)(193,241)(197,242)(201,243)(203,245)(205,246)(208,247)(211,248)(213,250)(215,251)(218,252)(222,253)(227,254)(233,255)(238,256)(244,257)(249,258);(10,40)(17,60)(24,80)(30,84)(34,93)(37,98)(39,100)(45,65)(50,114)(54,123)(57,128)(59,130)(70,144)(74,153)(77,158)(79,160)(87,163)(89,165)(90,166)(95,172)(96,173)(99,175)(104,134)(107,137)(109,139)(110,140)(117,188)(119,190)(120,191)(125,197)(126,198)(129,200)(147,213)(149,215)(150,216)(155,222)(156,223)(159,225)(168,227)(169,228)(170,229)(174,231)(178,203)(180,205)(181,206)(183,208)(184,209)(185,210)(193,238)(194,239)(195,240)(199,242)(218,249)(219,250)(220,251)(224,253)(230,254)(233,244)(234,245)(235,246)(236,247)(241,256)(252,258)(255,257);(3,10)(4,17)(5,24)(6,30)(7,34)(8,37)(9,39)(11,40)(12,45)(13,50)(14,54)(15,57)(16,59)(18,60)(19,65)(20,70)(21,74)(22,77)(23,79)(25,80)(26,84)(27,87)(28,89)(29,90)(31,93)(32,95)(33,96)(35,98)(36,99)(38,100)(41,104)(42,107)(43,109)(44,110)(46,114)(47,117)(48,119)(49,120)(51,123)(52,125)(53,126)(55,128)(56,129)(58,130)(61,134)(62,137)(63,139)(64,140)(66,144)(67,147)(68,149)(69,150)(71,153)(72,155)(73,156)(75,158)(76,159)(78,160)(81,163)(82,165)(83,166)(85,168)(86,169)(88,170)(91,172)(92,173)(94,174)(97,175)(101,178)(102,180)(103,181)(105,183)(106,184)(108,185)(111,188)(112,190)(113,191)(115,193)(116,194)(118,195)(121,197)(122,198)(124,199)(127,200)(131,203)(132,205)(133,206)(135,208)(136,209)(138,210)(141,213)(142,215)(143,216)(145,218)(146,219)(148,220)(151,222)(152,223)(154,224)(157,225)(161,227)(162,228)(164,229)(167,230)(171,231)(176,233)(177,234)(179,235)(182,236)(186,238)(187,239)(189,240)(192,241)(196,242)(201,244)(202,245)(204,246)(207,247)(211,249)(212,250)(214,251)(217,252)(221,253)(226,254)(232,255)(237,256)(243,257)(248,258);(1,2)
Conjugacy classes & character table
8194 conjugacy classes. The character table is too large to display.
Relationships
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((3,4,11,18)(5,19,25,12)(6,13,26,46)(7,14,31,51)(8,15,35,55)(9,16,38,58)(10,17,40,60)(20,61,66,41)(21,62,71,42)(22,63,75,43)(23,64,78,44)(24,65,80,45)(27,47,81,111)(28,48,82,112)(29,49,83,113)(30,50,84,114)(32,52,91,121)(33,53,92,122)(34,54,93,123)(36,56,97,127)(37,57,98,128)(39,59,100,130)(67,131,141,101)(68,132,142,102)(69,133,143,103)(70,134,144,104)(72,135,151,105)(73,136,152,106)(74,137,153,107)(76,138,157,108)(77,139,158,109)(79,140,160,110)(85,115,161,186)(86,116,162,187)(87,117,163,188)(88,118,164,189)(89,119,165,190)(90,120,166,191)(94,124,171,196)(95,125,172,197)(96,126,173,198)(99,129,175,200)(145,201,211,176)(146,202,212,177)(147,203,213,178)(148,204,214,179)(149,205,215,180)(150,206,216,181)(154,207,221,182)(155,208,222,183)(156,209,223,184)(159,210,225,185)(167,192,226,237)(168,193,227,238)(169,194,228,239)(170,195,229,240)(174,199,231,242)(217,243,248,232)(218,244,249,233)(219,245,250,234)(220,246,251,235)(224,247,253,236)(230,241,254,256)(252,257,258,255), (3,5,11,25)(4,12,18,19)(6,20,26,66)(7,21,31,71)(8,22,35,75)(9,23,38,78)(10,24,40,80)(13,41,46,61)(14,42,51,62)(15,43,55,63)(16,44,58,64)(17,45,60,65)(27,67,81,141)(28,68,82,142)(29,69,83,143)(30,70,84,144)(32,72,91,151)(33,73,92,152)(34,74,93,153)(36,76,97,157)(37,77,98,158)(39,79,100,160)(47,101,111,131)(48,102,112,132)(49,103,113,133)(50,104,114,134)(52,105,121,135)(53,106,122,136)(54,107,123,137)(56,108,127,138)(57,109,128,139)(59,110,130,140)(85,145,161,211)(86,146,162,212)(87,147,163,213)(88,148,164,214)(89,149,165,215)(90,150,166,216)(94,154,171,221)(95,155,172,222)(96,156,173,223)(99,159,175,225)(115,176,186,201)(116,177,187,202)(117,178,188,203)(118,179,189,204)(119,180,190,205)(120,181,191,206)(124,182,196,207)(125,183,197,208)(126,184,198,209)(129,185,200,210)(167,217,226,248)(168,218,227,249)(169,219,228,250)(170,220,229,251)(174,224,231,253)(192,232,237,243)(193,233,238,244)(194,234,239,245)(195,235,240,246)(199,236,242,247)(230,252,254,258)(241,255,256,257), (6,26)(13,46)(20,66)(27,81)(28,82)(29,83)(30,84)(41,61)(47,111)(48,112)(49,113)(50,114)(67,141)(68,142)(69,143)(70,144)(85,161)(86,162)(87,163)(88,164)(89,165)(90,166)(101,131)(102,132)(103,133)(104,134)(115,186)(116,187)(117,188)(118,189)(119,190)(120,191)(145,211)(146,212)(147,213)(148,214)(149,215)(150,216)(167,226)(168,227)(169,228)(170,229)(176,201)(177,202)(178,203)(179,204)(180,205)(181,206)(192,237)(193,238)(194,239)(195,240)(217,248)(218,249)(219,250)(220,251)(230,254)(232,243)(233,244)(234,245)(235,246)(241,256)(252,258)(255,257), (3,6)(4,13)(5,20)(7,27)(8,28)(9,29)(10,30)(11,26)(12,41)(14,47)(15,48)(16,49)(17,50)(18,46)(19,61)(21,67)(22,68)(23,69)(24,70)(25,66)(31,81)(32,85)(33,86)(34,87)(35,82)(36,88)(37,89)(38,83)(39,90)(40,84)(42,101)(43,102)(44,103)(45,104)(51,111)(52,115)(53,116)(54,117)(55,112)(56,118)(57,119)(58,113)(59,120)(60,114)(62,131)(63,132)(64,133)(65,134)(71,141)(72,145)(73,146)(74,147)(75,142)(76,148)(77,149)(78,143)(79,150)(80,144)(91,161)(92,162)(93,163)(94,167)(95,168)(96,169)(97,164)(98,165)(99,170)(100,166)(105,176)(106,177)(107,178)(108,179)(109,180)(110,181)(121,186)(122,187)(123,188)(124,192)(125,193)(126,194)(127,189)(128,190)(129,195)(130,191)(135,201)(136,202)(137,203)(138,204)(139,205)(140,206)(151,211)(152,212)(153,213)(154,217)(155,218)(156,219)(157,214)(158,215)(159,220)(160,216)(171,226)(172,227)(173,228)(174,230)(175,229)(182,232)(183,233)(184,234)(185,235)(196,237)(197,238)(198,239)(199,241)(200,240)(207,243)(208,244)(209,245)(210,246)(221,248)(222,249)(223,250)(224,252)(225,251)(231,254)(236,255)(242,256)(247,257)(253,258), (7,31)(14,51)(21,71)(27,81)(32,91)(33,92)(34,93)(42,62)(47,111)(52,121)(53,122)(54,123)(67,141)(72,151)(73,152)(74,153)(85,161)(86,162)(87,163)(94,171)(95,172)(96,173)(101,131)(105,135)(106,136)(107,137)(115,186)(116,187)(117,188)(124,196)(125,197)(126,198)(145,211)(146,212)(147,213)(154,221)(155,222)(156,223)(167,226)(168,227)(169,228)(174,231)(176,201)(177,202)(178,203)(182,207)(183,208)(184,209)(192,237)(193,238)(194,239)(199,242)(217,248)(218,249)(219,250)(224,253)(230,254)(232,243)(233,244)(234,245)(236,247)(241,256)(252,258)(255,257), (3,7)(4,14)(5,21)(6,27)(8,32)(9,33)(10,34)(11,31)(12,42)(13,47)(15,52)(16,53)(17,54)(18,51)(19,62)(20,67)(22,72)(23,73)(24,74)(25,71)(26,81)(28,85)(29,86)(30,87)(35,91)(36,94)(37,95)(38,92)(39,96)(40,93)(41,101)(43,105)(44,106)(45,107)(46,111)(48,115)(49,116)(50,117)(55,121)(56,124)(57,125)(58,122)(59,126)(60,123)(61,131)(63,135)(64,136)(65,137)(66,141)(68,145)(69,146)(70,147)(75,151)(76,154)(77,155)(78,152)(79,156)(80,153)(82,161)(83,162)(84,163)(88,167)(89,168)(90,169)(97,171)(98,172)(99,174)(100,173)(102,176)(103,177)(104,178)(108,182)(109,183)(110,184)(112,186)(113,187)(114,188)(118,192)(119,193)(120,194)(127,196)(128,197)(129,199)(130,198)(132,201)(133,202)(134,203)(138,207)(139,208)(140,209)(142,211)(143,212)(144,213)(148,217)(149,218)(150,219)(157,221)(158,222)(159,224)(160,223)(164,226)(165,227)(166,228)(170,230)(175,231)(179,232)(180,233)(181,234)(185,236)(189,237)(190,238)(191,239)(195,241)(200,242)(204,243)(205,244)(206,245)(210,247)(214,248)(215,249)(216,250)(220,252)(225,253)(229,254)(235,255)(240,256)(246,257)(251,258), (8,35)(15,55)(22,75)(28,82)(32,91)(36,97)(37,98)(43,63)(48,112)(52,121)(56,127)(57,128)(68,142)(72,151)(76,157)(77,158)(85,161)(88,164)(89,165)(94,171)(95,172)(99,175)(102,132)(105,135)(108,138)(109,139)(115,186)(118,189)(119,190)(124,196)(125,197)(129,200)(145,211)(148,214)(149,215)(154,221)(155,222)(159,225)(167,226)(168,227)(170,229)(174,231)(176,201)(179,204)(180,205)(182,207)(183,208)(185,210)(192,237)(193,238)(195,240)(199,242)(217,248)(218,249)(220,251)(224,253)(230,254)(232,243)(233,244)(235,246)(236,247)(241,256)(252,258)(255,257), (3,8)(4,15)(5,22)(6,28)(7,32)(9,36)(10,37)(11,35)(12,43)(13,48)(14,52)(16,56)(17,57)(18,55)(19,63)(20,68)(21,72)(23,76)(24,77)(25,75)(26,82)(27,85)(29,88)(30,89)(31,91)(33,94)(34,95)(38,97)(39,99)(40,98)(41,102)(42,105)(44,108)(45,109)(46,112)(47,115)(49,118)(50,119)(51,121)(53,124)(54,125)(58,127)(59,129)(60,128)(61,132)(62,135)(64,138)(65,139)(66,142)(67,145)(69,148)(70,149)(71,151)(73,154)(74,155)(78,157)(79,159)(80,158)(81,161)(83,164)(84,165)(86,167)(87,168)(90,170)(92,171)(93,172)(96,174)(100,175)(101,176)(103,179)(104,180)(106,182)(107,183)(110,185)(111,186)(113,189)(114,190)(116,192)(117,193)(120,195)(122,196)(123,197)(126,199)(130,200)(131,201)(133,204)(134,205)(136,207)(137,208)(140,210)(141,211)(143,214)(144,215)(146,217)(147,218)(150,220)(152,221)(153,222)(156,224)(160,225)(162,226)(163,227)(166,229)(169,230)(173,231)(177,232)(178,233)(181,235)(184,236)(187,237)(188,238)(191,240)(194,241)(198,242)(202,243)(203,244)(206,246)(209,247)(212,248)(213,249)(216,251)(219,252)(223,253)(228,254)(234,255)(239,256)(245,257)(250,258), (9,38)(16,58)(23,78)(29,83)(33,92)(36,97)(39,100)(44,64)(49,113)(53,122)(56,127)(59,130)(69,143)(73,152)(76,157)(79,160)(86,162)(88,164)(90,166)(94,171)(96,173)(99,175)(103,133)(106,136)(108,138)(110,140)(116,187)(118,189)(120,191)(124,196)(126,198)(129,200)(146,212)(148,214)(150,216)(154,221)(156,223)(159,225)(167,226)(169,228)(170,229)(174,231)(177,202)(179,204)(181,206)(182,207)(184,209)(185,210)(192,237)(194,239)(195,240)(199,242)(217,248)(219,250)(220,251)(224,253)(230,254)(232,243)(234,245)(235,246)(236,247)(241,256)(252,258)(255,257), (3,9)(4,16)(5,23)(6,29)(7,33)(8,36)(10,39)(11,38)(12,44)(13,49)(14,53)(15,56)(17,59)(18,58)(19,64)(20,69)(21,73)(22,76)(24,79)(25,78)(26,83)(27,86)(28,88)(30,90)(31,92)(32,94)(34,96)(35,97)(37,99)(40,100)(41,103)(42,106)(43,108)(45,110)(46,113)(47,116)(48,118)(50,120)(51,122)(52,124)(54,126)(55,127)(57,129)(60,130)(61,133)(62,136)(63,138)(65,140)(66,143)(67,146)(68,148)(70,150)(71,152)(72,154)(74,156)(75,157)(77,159)(80,160)(81,162)(82,164)(84,166)(85,167)(87,169)(89,170)(91,171)(93,173)(95,174)(98,175)(101,177)(102,179)(104,181)(105,182)(107,184)(109,185)(111,187)(112,189)(114,191)(115,192)(117,194)(119,195)(121,196)(123,198)(125,199)(128,200)(131,202)(132,204)(134,206)(135,207)(137,209)(139,210)(141,212)(142,214)(144,216)(145,217)(147,219)(149,220)(151,221)(153,223)(155,224)(158,225)(161,226)(163,228)(165,229)(168,230)(172,231)(176,232)(178,234)(180,235)(183,236)(186,237)(188,239)(190,240)(193,241)(197,242)(201,243)(203,245)(205,246)(208,247)(211,248)(213,250)(215,251)(218,252)(222,253)(227,254)(233,255)(238,256)(244,257)(249,258), (10,40)(17,60)(24,80)(30,84)(34,93)(37,98)(39,100)(45,65)(50,114)(54,123)(57,128)(59,130)(70,144)(74,153)(77,158)(79,160)(87,163)(89,165)(90,166)(95,172)(96,173)(99,175)(104,134)(107,137)(109,139)(110,140)(117,188)(119,190)(120,191)(125,197)(126,198)(129,200)(147,213)(149,215)(150,216)(155,222)(156,223)(159,225)(168,227)(169,228)(170,229)(174,231)(178,203)(180,205)(181,206)(183,208)(184,209)(185,210)(193,238)(194,239)(195,240)(199,242)(218,249)(219,250)(220,251)(224,253)(230,254)(233,244)(234,245)(235,246)(236,247)(241,256)(252,258)(255,257), (3,10)(4,17)(5,24)(6,30)(7,34)(8,37)(9,39)(11,40)(12,45)(13,50)(14,54)(15,57)(16,59)(18,60)(19,65)(20,70)(21,74)(22,77)(23,79)(25,80)(26,84)(27,87)(28,89)(29,90)(31,93)(32,95)(33,96)(35,98)(36,99)(38,100)(41,104)(42,107)(43,109)(44,110)(46,114)(47,117)(48,119)(49,120)(51,123)(52,125)(53,126)(55,128)(56,129)(58,130)(61,134)(62,137)(63,139)(64,140)(66,144)(67,147)(68,149)(69,150)(71,153)(72,155)(73,156)(75,158)(76,159)(78,160)(81,163)(82,165)(83,166)(85,168)(86,169)(88,170)(91,172)(92,173)(94,174)(97,175)(101,178)(102,180)(103,181)(105,183)(106,184)(108,185)(111,188)(112,190)(113,191)(115,193)(116,194)(118,195)(121,197)(122,198)(124,199)(127,200)(131,203)(132,205)(133,206)(135,208)(136,209)(138,210)(141,213)(142,215)(143,216)(145,218)(146,219)(148,220)(151,222)(152,223)(154,224)(157,225)(161,227)(162,228)(164,229)(167,230)(171,231)(176,233)(177,234)(179,235)(182,236)(186,238)(187,239)(189,240)(192,241)(196,242)(201,244)(202,245)(204,246)(207,247)(211,249)(212,250)(214,251)(217,252)(221,253)(226,254)(232,255)(237,256)(243,257)(248,258), (1,2));
Finite Group Databasebeta