// THESE GENERATORS WERE OBTAINED USING THE BLT ALGORITHM. // To get standard generators sigma_i's // Bear in mind that sigma_i = gen_i*sigma_1*...*sigma_(i-1) G:=PSL(3,16); gens:=[ [G| (1, 213, 20)(2, 35, 22)(3, 195, 208)(4, 222, 181)(5, 177, 256)(6, 106, 170)(7, 202, 45)(8, 73, 111)(9, 117, 192)(10, 189, 67)(11, 42, 253)(12, 267, 220)(13, 17, 34)(14, 147, 146)(15, 273, 265)(16, 207, 159)(18, 229, 32)(19, 212, 167)(21, 210, 121)(23, 46, 199)(24, 59, 132)(25, 180, 76)(26, 243, 72)(27, 226, 271)(28, 116, 43)(29, 201, 172)(30, 44, 272)(31, 196, 250)(33, 163, 221)(36, 255, 80)(37, 123, 188)(38, 53, 225)(39, 266, 120)(40, 128, 54)(41, 82, 240)(47, 236, 157)(48, 119, 104)(49, 143, 75)(50, 248, 129)(51, 214, 115)(52, 151, 112)(55, 68, 78)(56, 198, 219)(57, 203, 175)(58, 127, 169)(60, 165, 217)(61, 134, 98)(62, 238, 103)(63, 122, 152)(64, 227, 96)(65, 247, 158)(66, 263, 140)(69, 211, 182)(70, 125, 149)(71, 161, 138)(74, 92, 133)(77, 260, 79)(81, 215, 113)(83, 95, 145)(84, 135, 86)(85, 126, 194)(87, 89, 245)(88, 237, 200)(90, 166, 234)(91, 139, 107)(93, 109, 235)(94, 241, 178)(97, 136, 259)(99, 268, 168)(100, 190, 137)(101, 183, 258)(105, 191, 218)(108, 164, 162)(110, 144, 187)(114, 269, 155)(118, 261, 153)(124, 173, 249)(130, 262, 141)(131, 184, 231)(142, 154, 264)(148, 223, 230)(150, 204, 254)(156, 216, 185)(160, 251, 205)(171, 228, 206)(174, 224, 233)(176, 242, 186)(193, 257, 270)(197, 246, 252)(209, 232, 244), (1, 37)(3, 179)(4, 18)(5, 245)(6, 41)(7, 101)(8, 144)(9, 177)(10, 230)(11, 238)(12, 91)(13, 31)(14, 241)(15, 152)(16, 153)(17, 228)(19, 251)(20, 150)(21, 252)(22, 259)(23, 212)(24, 244)(25, 32)(26, 128)(27, 194)(28, 209)(33, 206)(34, 59)(35, 66)(36, 119)(38, 160)(39, 213)(40, 226)(42, 200)(43, 221)(44, 161)(45, 233)(46, 149)(47, 72)(48, 125)(49, 122)(50, 65)(52, 140)(53, 82)(54, 156)(55, 131)(56, 184)(57, 175)(58, 171)(60, 269)(61, 64)(63, 216)(67, 242)(68, 89)(69, 181)(70, 142)(71, 183)(73, 249)(74, 272)(75, 155)(76, 115)(77, 240)(78, 87)(79, 261)(80, 95)(81, 191)(83, 106)(84, 159)(85, 273)(86, 111)(88, 154)(90, 165)(92, 214)(93, 114)(94, 107)(96, 207)(97, 254)(98, 110)(99, 148)(100, 208)(102, 234)(103, 118)(104, 162)(105, 215)(108, 253)(109, 130)(113, 198)(116, 129)(117, 246)(120, 136)(121, 197)(123, 263)(124, 270)(126, 271)(127, 248)(132, 133)(134, 193)(135, 225)(137, 185)(138, 168)(139, 220)(141, 243)(143, 166)(145, 167)(146, 178)(147, 203)(157, 217)(158, 211)(163, 186)(169, 223)(172, 201)(173, 264)(176, 182)(180, 250)(187, 199)(189, 202)(190, 235)(192, 256)(195, 262)(196, 247)(205, 257)(210, 218)(219, 231)(222, 224)(227, 237)(232, 268)(236, 265)(239, 266), (1, 180)(3, 190)(4, 151)(5, 143)(6, 197)(7, 202)(8, 159)(10, 67)(11, 29)(12, 212)(13, 34)(14, 228)(15, 265)(16, 111)(18, 78)(19, 267)(20, 76)(21, 86)(22, 35)(23, 254)(24, 249)(25, 213)(26, 178)(27, 242)(28, 217)(30, 272)(31, 61)(32, 55)(33, 36)(37, 105)(38, 113)(39, 130)(40, 87)(41, 138)(42, 172)(43, 60)(46, 204)(47, 62)(48, 92)(49, 177)(50, 233)(51, 205)(52, 222)(53, 215)(54, 89)(56, 198)(57, 175)(58, 169)(59, 173)(63, 142)(64, 149)(65, 114)(68, 229)(69, 148)(70, 96)(71, 240)(72, 94)(73, 207)(74, 119)(75, 256)(79, 260)(80, 163)(81, 225)(82, 161)(83, 118)(84, 121)(85, 184)(88, 109)(90, 234)(91, 259)(93, 237)(95, 153)(97, 107)(98, 196)(99, 108)(100, 195)(101, 144)(102, 239)(103, 236)(104, 133)(106, 252)(110, 183)(112, 181)(115, 160)(116, 165)(117, 192)(120, 262)(122, 264)(123, 218)(124, 132)(125, 227)(126, 131)(128, 245)(129, 174)(134, 250)(135, 210)(136, 139)(137, 208)(140, 263)(141, 266)(145, 261)(146, 206)(147, 171)(150, 199)(152, 154)(155, 247)(156, 216)(157, 238)(158, 269)(162, 268)(164, 168)(167, 220)(170, 246)(176, 226)(182, 223)(186, 271)(187, 258)(188, 191)(193, 257)(194, 231)(200, 235)(201, 253)(209, 232)(211, 230)(214, 251)(221, 255)(224, 248)(241, 243) ], [G| (1, 213, 20)(2, 35, 22)(3, 195, 208)(4, 222, 181)(5, 177, 256)(6, 106, 170)(7, 202, 45)(8, 73, 111)(9, 117, 192)(10, 189, 67)(11, 42, 253)(12, 267, 220)(13, 17, 34)(14, 147, 146)(15, 273, 265)(16, 207, 159)(18, 229, 32)(19, 212, 167)(21, 210, 121)(23, 46, 199)(24, 59, 132)(25, 180, 76)(26, 243, 72)(27, 226, 271)(28, 116, 43)(29, 201, 172)(30, 44, 272)(31, 196, 250)(33, 163, 221)(36, 255, 80)(37, 123, 188)(38, 53, 225)(39, 266, 120)(40, 128, 54)(41, 82, 240)(47, 236, 157)(48, 119, 104)(49, 143, 75)(50, 248, 129)(51, 214, 115)(52, 151, 112)(55, 68, 78)(56, 198, 219)(57, 203, 175)(58, 127, 169)(60, 165, 217)(61, 134, 98)(62, 238, 103)(63, 122, 152)(64, 227, 96)(65, 247, 158)(66, 263, 140)(69, 211, 182)(70, 125, 149)(71, 161, 138)(74, 92, 133)(77, 260, 79)(81, 215, 113)(83, 95, 145)(84, 135, 86)(85, 126, 194)(87, 89, 245)(88, 237, 200)(90, 166, 234)(91, 139, 107)(93, 109, 235)(94, 241, 178)(97, 136, 259)(99, 268, 168)(100, 190, 137)(101, 183, 258)(105, 191, 218)(108, 164, 162)(110, 144, 187)(114, 269, 155)(118, 261, 153)(124, 173, 249)(130, 262, 141)(131, 184, 231)(142, 154, 264)(148, 223, 230)(150, 204, 254)(156, 216, 185)(160, 251, 205)(171, 228, 206)(174, 224, 233)(176, 242, 186)(193, 257, 270)(197, 246, 252)(209, 232, 244), (1, 37)(3, 179)(4, 18)(5, 245)(6, 41)(7, 101)(8, 144)(9, 177)(10, 230)(11, 238)(12, 91)(13, 31)(14, 241)(15, 152)(16, 153)(17, 228)(19, 251)(20, 150)(21, 252)(22, 259)(23, 212)(24, 244)(25, 32)(26, 128)(27, 194)(28, 209)(33, 206)(34, 59)(35, 66)(36, 119)(38, 160)(39, 213)(40, 226)(42, 200)(43, 221)(44, 161)(45, 233)(46, 149)(47, 72)(48, 125)(49, 122)(50, 65)(52, 140)(53, 82)(54, 156)(55, 131)(56, 184)(57, 175)(58, 171)(60, 269)(61, 64)(63, 216)(67, 242)(68, 89)(69, 181)(70, 142)(71, 183)(73, 249)(74, 272)(75, 155)(76, 115)(77, 240)(78, 87)(79, 261)(80, 95)(81, 191)(83, 106)(84, 159)(85, 273)(86, 111)(88, 154)(90, 165)(92, 214)(93, 114)(94, 107)(96, 207)(97, 254)(98, 110)(99, 148)(100, 208)(102, 234)(103, 118)(104, 162)(105, 215)(108, 253)(109, 130)(113, 198)(116, 129)(117, 246)(120, 136)(121, 197)(123, 263)(124, 270)(126, 271)(127, 248)(132, 133)(134, 193)(135, 225)(137, 185)(138, 168)(139, 220)(141, 243)(143, 166)(145, 167)(146, 178)(147, 203)(157, 217)(158, 211)(163, 186)(169, 223)(172, 201)(173, 264)(176, 182)(180, 250)(187, 199)(189, 202)(190, 235)(192, 256)(195, 262)(196, 247)(205, 257)(210, 218)(219, 231)(222, 224)(227, 237)(232, 268)(236, 265)(239, 266), (1, 203)(2, 252)(3, 13)(6, 241)(7, 53)(8, 171)(9, 114)(10, 71)(11, 30)(12, 185)(14, 74)(15, 238)(16, 32)(17, 208)(18, 159)(19, 218)(20, 175)(21, 234)(22, 197)(23, 157)(24, 64)(25, 49)(27, 141)(28, 259)(29, 61)(31, 196)(33, 221)(34, 195)(35, 246)(36, 81)(38, 202)(39, 58)(40, 247)(41, 182)(42, 272)(43, 97)(44, 253)(45, 225)(46, 236)(47, 199)(48, 162)(50, 187)(51, 153)(52, 190)(54, 158)(55, 268)(56, 165)(57, 213)(59, 96)(60, 198)(62, 273)(63, 200)(65, 128)(66, 154)(67, 161)(68, 99)(69, 240)(70, 125)(72, 243)(73, 206)(75, 180)(76, 143)(77, 205)(78, 168)(79, 160)(80, 215)(82, 211)(83, 95)(84, 231)(85, 194)(86, 131)(88, 152)(89, 245)(90, 121)(91, 107)(92, 146)(93, 109)(94, 106)(98, 201)(100, 151)(101, 244)(102, 239)(103, 265)(104, 108)(105, 167)(110, 129)(111, 228)(112, 137)(113, 255)(115, 118)(116, 136)(117, 155)(119, 164)(120, 127)(122, 237)(123, 188)(124, 270)(130, 271)(132, 227)(133, 147)(134, 172)(135, 184)(138, 189)(140, 264)(142, 263)(144, 248)(148, 223)(150, 254)(156, 220)(166, 210)(169, 266)(170, 178)(173, 257)(174, 224)(176, 186)(177, 256)(181, 222)(183, 232)(191, 212)(192, 269)(193, 249)(207, 229)(209, 258)(214, 261)(216, 267)(217, 219)(226, 262)(251, 260) ], [G| (1, 213, 20)(2, 35, 22)(3, 195, 208)(4, 222, 181)(5, 177, 256)(6, 106, 170)(7, 202, 45)(8, 73, 111)(9, 117, 192)(10, 189, 67)(11, 42, 253)(12, 267, 220)(13, 17, 34)(14, 147, 146)(15, 273, 265)(16, 207, 159)(18, 229, 32)(19, 212, 167)(21, 210, 121)(23, 46, 199)(24, 59, 132)(25, 180, 76)(26, 243, 72)(27, 226, 271)(28, 116, 43)(29, 201, 172)(30, 44, 272)(31, 196, 250)(33, 163, 221)(36, 255, 80)(37, 123, 188)(38, 53, 225)(39, 266, 120)(40, 128, 54)(41, 82, 240)(47, 236, 157)(48, 119, 104)(49, 143, 75)(50, 248, 129)(51, 214, 115)(52, 151, 112)(55, 68, 78)(56, 198, 219)(57, 203, 175)(58, 127, 169)(60, 165, 217)(61, 134, 98)(62, 238, 103)(63, 122, 152)(64, 227, 96)(65, 247, 158)(66, 263, 140)(69, 211, 182)(70, 125, 149)(71, 161, 138)(74, 92, 133)(77, 260, 79)(81, 215, 113)(83, 95, 145)(84, 135, 86)(85, 126, 194)(87, 89, 245)(88, 237, 200)(90, 166, 234)(91, 139, 107)(93, 109, 235)(94, 241, 178)(97, 136, 259)(99, 268, 168)(100, 190, 137)(101, 183, 258)(105, 191, 218)(108, 164, 162)(110, 144, 187)(114, 269, 155)(118, 261, 153)(124, 173, 249)(130, 262, 141)(131, 184, 231)(142, 154, 264)(148, 223, 230)(150, 204, 254)(156, 216, 185)(160, 251, 205)(171, 228, 206)(174, 224, 233)(176, 242, 186)(193, 257, 270)(197, 246, 252)(209, 232, 244), (1, 132)(2, 248)(3, 202)(4, 71)(5, 13)(6, 190)(7, 70)(8, 164)(9, 92)(10, 247)(11, 146)(12, 257)(14, 189)(15, 47)(16, 153)(17, 165)(18, 148)(19, 113)(20, 140)(21, 224)(22, 48)(23, 210)(24, 35)(25, 122)(26, 52)(27, 77)(28, 251)(29, 110)(30, 206)(31, 144)(32, 227)(33, 44)(34, 256)(36, 252)(37, 203)(38, 200)(39, 54)(40, 181)(41, 162)(42, 154)(43, 84)(45, 118)(46, 114)(50, 193)(51, 270)(53, 117)(55, 234)(56, 180)(57, 182)(58, 188)(59, 115)(60, 217)(61, 63)(62, 175)(64, 100)(65, 87)(66, 187)(67, 219)(68, 254)(69, 79)(72, 99)(73, 215)(74, 91)(75, 163)(76, 253)(78, 246)(80, 90)(81, 82)(83, 259)(85, 137)(86, 191)(89, 126)(93, 160)(94, 152)(95, 128)(96, 178)(97, 260)(98, 265)(102, 262)(103, 226)(104, 218)(105, 250)(106, 264)(108, 167)(109, 172)(112, 213)(116, 267)(119, 263)(120, 174)(121, 244)(123, 185)(124, 147)(127, 138)(129, 135)(130, 179)(131, 184)(133, 237)(134, 229)(136, 155)(139, 225)(142, 241)(143, 228)(145, 176)(149, 159)(150, 255)(151, 201)(156, 242)(157, 158)(161, 233)(168, 235)(169, 232)(170, 249)(171, 183)(173, 245)(177, 231)(186, 211)(194, 223)(196, 205)(198, 273)(199, 271)(207, 208)(209, 238)(214, 243)(216, 222)(220, 268)(221, 258)(230, 236)(266, 269), (1, 139)(2, 87)(3, 208)(4, 136)(5, 84)(6, 156)(7, 104)(8, 38)(9, 238)(10, 144)(11, 41)(12, 200)(13, 85)(14, 33)(15, 218)(16, 68)(17, 194)(18, 113)(19, 114)(20, 107)(21, 141)(22, 89)(23, 26)(24, 59)(25, 112)(27, 198)(28, 43)(29, 83)(30, 173)(31, 209)(32, 81)(34, 126)(35, 245)(36, 99)(37, 123)(39, 143)(42, 240)(44, 124)(45, 48)(46, 72)(47, 236)(49, 266)(50, 214)(51, 248)(52, 76)(53, 111)(54, 128)(55, 207)(56, 226)(57, 175)(58, 190)(60, 234)(61, 134)(62, 117)(63, 94)(64, 174)(65, 93)(66, 140)(67, 187)(69, 193)(70, 205)(71, 153)(73, 225)(74, 133)(75, 120)(77, 260)(78, 159)(80, 268)(82, 253)(86, 177)(88, 220)(90, 217)(91, 213)(95, 172)(96, 224)(97, 222)(100, 127)(101, 258)(103, 192)(105, 265)(106, 185)(108, 228)(109, 158)(110, 189)(115, 129)(118, 138)(119, 202)(121, 130)(122, 178)(125, 251)(131, 184)(135, 256)(137, 169)(142, 204)(145, 201)(146, 163)(147, 221)(148, 223)(149, 160)(150, 154)(151, 180)(152, 241)(155, 212)(161, 261)(162, 206)(164, 171)(165, 166)(167, 269)(168, 255)(170, 216)(176, 242)(179, 239)(181, 259)(182, 257)(191, 273)(196, 244)(197, 246)(199, 243)(210, 262)(211, 270)(215, 229)(219, 271)(227, 233)(232, 250)(235, 247)(237, 267)(249, 272)(254, 264) ], [G| (1, 213, 20)(2, 35, 22)(3, 195, 208)(4, 222, 181)(5, 177, 256)(6, 106, 170)(7, 202, 45)(8, 73, 111)(9, 117, 192)(10, 189, 67)(11, 42, 253)(12, 267, 220)(13, 17, 34)(14, 147, 146)(15, 273, 265)(16, 207, 159)(18, 229, 32)(19, 212, 167)(21, 210, 121)(23, 46, 199)(24, 59, 132)(25, 180, 76)(26, 243, 72)(27, 226, 271)(28, 116, 43)(29, 201, 172)(30, 44, 272)(31, 196, 250)(33, 163, 221)(36, 255, 80)(37, 123, 188)(38, 53, 225)(39, 266, 120)(40, 128, 54)(41, 82, 240)(47, 236, 157)(48, 119, 104)(49, 143, 75)(50, 248, 129)(51, 214, 115)(52, 151, 112)(55, 68, 78)(56, 198, 219)(57, 203, 175)(58, 127, 169)(60, 165, 217)(61, 134, 98)(62, 238, 103)(63, 122, 152)(64, 227, 96)(65, 247, 158)(66, 263, 140)(69, 211, 182)(70, 125, 149)(71, 161, 138)(74, 92, 133)(77, 260, 79)(81, 215, 113)(83, 95, 145)(84, 135, 86)(85, 126, 194)(87, 89, 245)(88, 237, 200)(90, 166, 234)(91, 139, 107)(93, 109, 235)(94, 241, 178)(97, 136, 259)(99, 268, 168)(100, 190, 137)(101, 183, 258)(105, 191, 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