G := PGL(2,125); involutions := [ [ G!(1, 13)(2, 121)(3, 15)(4, 97)(5, 27)(6, 116)(7, 81)(8, 71)(9, 61)(10, 26)(11, 115)(12, 45)(14, 21)(16, 91)(17, 66)(18, 94)(19, 105)(20, 75)(22, 49)(23, 82)(24, 50)(25, 64)(28, 31)(29, 43)(30, 103)(32, 68)(33, 65)(34, 102)(35, 95)(36, 56)(37, 123)(38, 44)(39, 112)(40, 108)(41, 79)(42, 85)(46, 88)(47, 107)(48, 124)(51, 126)(52, 73)(53, 62)(54, 96)(55, 84)(57, 100)(58, 87)(59, 70)(60, 119)(63, 101)(67, 122)(69, 90)(72, 83)(74, 110)(76, 125)(77, 109)(78, 117)(80, 89)(86, 106)(92, 118)(93, 120)(98, 104)(99, 113)(111, 114), G!(1, 115)(2, 13)(3, 68)(4, 17)(5, 31)(6, 80)(7, 38)(8, 70)(9, 76)(10, 55)(11, 46)(12, 32)(14, 18)(15, 111)(16, 21)(19, 22)(20, 69)(23, 57)(24, 126)(25, 99)(26, 65)(27, 63)(28, 121)(29, 96)(30, 52)(33, 122)(34, 112)(35, 97)(36, 85)(37, 102)(39, 64)(40, 79)(41, 66)(42, 78)(43, 113)(44, 117)(45, 47)(48, 82)(49, 56)(50, 95)(51, 108)(53, 75)(54, 123)(58, 60)(59, 94)(61, 114)(62, 118)(67, 98)(71, 119)(72, 109)(73, 93)(74, 100)(77, 110)(81, 105)(83, 86)(84, 89)(87, 91)(88, 101)(90, 120)(92, 103)(104, 116)(106, 124)(107, 125), G!(1, 47)(2, 90)(3, 84)(4, 16)(5, 23)(6, 85)(7, 69)(8, 121)(9, 42)(10, 24)(11, 117)(12, 58)(13, 72)(14, 103)(15, 40)(17, 50)(18, 86)(19, 44)(20, 124)(21, 75)(22, 96)(25, 109)(26, 87)(27, 66)(28, 111)(29, 126)(30, 59)(31, 74)(32, 119)(33, 98)(34, 76)(35, 49)(36, 54)(37, 89)(38, 110)(39, 61)(41, 99)(43, 55)(45, 82)(46, 113)(48, 68)(51, 64)(52, 116)(53, 100)(56, 101)(57, 95)(60, 70)(62, 63)(65, 67)(71, 79)(73, 92)(77, 108)(78, 83)(80, 91)(81, 88)(93, 112)(94, 105)(97, 104)(102, 107)(106, 114)(115, 125)(118, 120)(122, 123) ] , [ G!(1, 8)(2, 51)(3, 83)(4, 31)(5, 11)(6, 116)(7, 78)(9, 49)(10, 106)(12, 121)(13, 77)(14, 40)(15, 80)(16, 25)(17, 27)(18, 90)(19, 117)(20, 57)(21, 42)(22, 34)(23, 101)(24, 105)(26, 75)(28, 68)(29, 124)(30, 44)(32, 88)(33, 47)(35, 56)(36, 39)(37, 63)(38, 41)(43, 55)(45, 115)(46, 73)(48, 79)(50, 60)(52, 61)(53, 98)(54, 102)(58, 86)(59, 113)(62, 123)(64, 126)(65, 82)(66, 72)(67, 97)(69, 76)(70, 125)(71, 87)(74, 120)(81, 110)(84, 118)(85, 119)(89, 108)(91, 96)(92, 94)(93, 122)(95, 114)(99, 100)(103, 104)(107, 112)(109, 111), G!(1, 120)(2, 19)(3, 21)(4, 94)(5, 110)(6, 44)(7, 83)(8, 77)(9, 72)(10, 67)(11, 61)(12, 100)(13, 34)(14, 50)(15, 123)(16, 125)(17, 24)(18, 58)(20, 42)(22, 105)(23, 96)(25, 62)(26, 32)(27, 76)(28, 103)(29, 107)(30, 95)(31, 75)(33, 93)(35, 89)(36, 56)(37, 115)(38, 90)(39, 122)(40, 65)(41, 116)(43, 99)(45, 101)(46, 74)(47, 92)(48, 121)(49, 114)(51, 111)(52, 97)(53, 57)(54, 106)(55, 109)(59, 73)(60, 63)(64, 66)(68, 117)(69, 113)(70, 98)(71, 85)(78, 80)(79, 104)(81, 84)(82, 119)(86, 126)(87, 91)(88, 108)(102, 124)(112, 118), G!(1, 38)(2, 57)(3, 42)(4, 17)(5, 85)(6, 24)(7, 36)(8, 120)(9, 53)(10, 58)(11, 26)(12, 126)(13, 61)(14, 69)(15, 109)(16, 115)(18, 62)(19, 83)(20, 31)(21, 111)(22, 124)(23, 95)(25, 110)(27, 44)(28, 101)(29, 68)(30, 90)(32, 72)(33, 70)(34, 108)(35, 64)(37, 89)(39, 125)(40, 51)(41, 107)(43, 96)(45, 60)(46, 87)(47, 65)(48, 102)(49, 73)(50, 86)(52, 114)(54, 67)(55, 82)(56, 88)(59, 71)(63, 77)(66, 112)(74, 121)(75, 80)(76, 123)(78, 104)(79, 81)(84, 92)(91, 100)(93, 119)(94, 98)(97, 106)(99, 103)(105, 113)(116, 118)(117, 122) ] , [ G!(1, 2)(3, 74)(4, 20)(5, 66)(6, 100)(7, 42)(8, 116)(9, 102)(10, 110)(11, 91)(12, 47)(13, 117)(14, 54)(15, 77)(16, 35)(17, 95)(18, 56)(19, 38)(21, 23)(22, 104)(24, 69)(25, 75)(26, 99)(27, 90)(28, 81)(29, 105)(30, 111)(31, 33)(32, 76)(34, 50)(36, 124)(37, 85)(39, 103)(40, 126)(41, 63)(43, 89)(44, 70)(45, 78)(46, 64)(48, 80)(49, 114)(51, 106)(52, 53)(55, 113)(57, 96)(58, 73)(59, 87)(60, 119)(61, 120)(62, 71)(65, 82)(67, 125)(68, 97)(72, 79)(83, 112)(84, 123)(86, 92)(88, 94)(93, 121)(98, 115)(101, 108)(107, 122)(109, 118), G!(1, 87)(2, 120)(3, 64)(4, 114)(5, 72)(6, 56)(7, 71)(8, 18)(9, 10)(11, 69)(12, 83)(13, 70)(14, 52)(15, 81)(16, 116)(17, 48)(19, 106)(20, 59)(21, 31)(22, 117)(23, 49)(24, 84)(25, 113)(26, 95)(27, 82)(28, 96)(29, 30)(32, 94)(33, 109)(34, 93)(35, 51)(36, 101)(37, 45)(38, 78)(39, 122)(40, 58)(41, 46)(42, 77)(43, 126)(44, 66)(47, 100)(50, 86)(53, 90)(54, 110)(55, 111)(57, 74)(60, 102)(61, 80)(62, 89)(63, 105)(65, 118)(67, 92)(68, 97)(73, 98)(75, 112)(76, 103)(79, 115)(85, 104)(88, 123)(91, 108)(99, 121)(107, 125)(119, 124), G!(1, 48)(2, 8)(3, 109)(4, 66)(5, 78)(6, 79)(7, 33)(9, 10)(11, 118)(12, 49)(13, 88)(14, 54)(15, 59)(16, 26)(17, 91)(18, 80)(19, 24)(20, 34)(21, 38)(22, 56)(23, 41)(25, 69)(27, 104)(28, 62)(29, 124)(30, 70)(31, 115)(32, 103)(35, 72)(36, 83)(37, 120)(39, 99)(40, 121)(42, 105)(43, 61)(44, 89)(45, 111)(46, 63)(47, 90)(50, 64)(51, 77)(52, 107)(53, 95)(55, 86)(57, 106)(58, 68)(60, 65)(67, 119)(71, 122)(73, 92)(74, 75)(76, 82)(81, 101)(84, 87)(85, 96)(93, 108)(94, 98)(97, 110)(100, 113)(102, 117)(112, 116)(114, 125)(123, 126) ] , [ G!(1, 115)(2, 37)(3, 7)(4, 107)(5, 45)(6, 113)(8, 32)(9, 24)(10, 98)(11, 65)(12, 44)(13, 33)(14, 61)(15, 69)(16, 57)(17, 101)(18, 20)(19, 66)(21, 50)(22, 83)(23, 64)(25, 28)(26, 126)(27, 38)(29, 102)(30, 59)(31, 82)(34, 117)(35, 75)(36, 68)(39, 106)(40, 103)(41, 100)(42, 53)(43, 78)(46, 89)(47, 67)(48, 72)(49, 124)(51, 104)(52, 55)(54, 80)(56, 71)(58, 123)(60, 62)(63, 105)(70, 108)(73, 77)(74, 93)(76, 99)(79, 91)(81, 90)(84, 109)(85, 119)(86, 114)(87, 121)(88, 96)(92, 120)(94, 95)(97, 122)(110, 118)(111, 112)(116, 125), G!(1, 76)(2, 116)(3, 29)(4, 9)(5, 121)(6, 63)(7, 85)(8, 119)(10, 98)(11, 89)(12, 45)(13, 37)(14, 96)(15, 24)(16, 125)(17, 115)(18, 68)(19, 26)(20, 95)(21, 40)(22, 123)(23, 41)(25, 112)(27, 35)(28, 78)(30, 53)(31, 42)(32, 117)(33, 90)(34, 100)(36, 58)(38, 60)(39, 109)(43, 66)(44, 47)(46, 108)(48, 111)(49, 52)(50, 114)(51, 84)(54, 65)(55, 73)(56, 75)(57, 113)(59, 83)(61, 69)(62, 122)(64, 105)(67, 93)(70, 77)(71, 110)(72, 81)(74, 99)(79, 107)(80, 97)(82, 126)(86, 124)(87, 92)(88, 103)(91, 101)(94, 106)(102, 104)(118, 120), G!(1, 125)(2, 87)(3, 117)(4, 102)(5, 69)(6, 62)(7, 94)(8, 71)(9, 48)(10, 80)(11, 73)(12, 40)(13, 25)(14, 55)(15, 17)(16, 31)(18, 28)(19, 85)(20, 45)(21, 109)(22, 39)(23, 105)(24, 99)(26, 52)(27, 32)(29, 86)(30, 108)(33, 121)(34, 112)(35, 68)(36, 60)(37, 119)(38, 47)(41, 91)(42, 49)(43, 118)(44, 63)(46, 64)(50, 58)(51, 101)(53, 76)(54, 65)(56, 113)(57, 123)(59, 81)(61, 83)(66, 89)(67, 70)(72, 75)(74, 107)(77, 88)(78, 96)(79, 98)(82, 106)(84, 92)(90, 116)(93, 100)(95, 104)(97, 122)(103, 120)(110, 115)(111, 126)(114, 124) ] , [ G!(1, 66)(2, 43)(3, 79)(4, 8)(5, 109)(6, 13)(7, 104)(9, 76)(10, 20)(11, 91)(12, 64)(14, 24)(15, 105)(16, 53)(17, 80)(18, 107)(19, 55)(21, 28)(22, 96)(23, 69)(25, 84)(26, 30)(27, 56)(29, 51)(31, 81)(32, 117)(33, 94)(34, 61)(35, 113)(36, 60)(37, 54)(38, 102)(39, 90)(40, 83)(41, 75)(42, 95)(44, 89)(45, 48)(46, 93)(47, 125)(49, 103)(50, 92)(52, 63)(57, 111)(58, 122)(59, 73)(62, 74)(65, 118)(67, 114)(68, 110)(70, 121)(71, 116)(72, 78)(77, 120)(82, 88)(85, 119)(86, 98)(87, 101)(97, 108)(99, 126)(100, 124)(106, 123)(112, 115), G!(1, 55)(2, 56)(3, 72)(4, 107)(5, 109)(6, 100)(7, 25)(8, 38)(9, 110)(10, 44)(11, 42)(12, 123)(13, 47)(14, 103)(15, 46)(16, 125)(17, 99)(18, 30)(19, 49)(20, 117)(21, 126)(22, 88)(23, 78)(24, 101)(26, 31)(27, 39)(28, 64)(29, 119)(32, 50)(33, 82)(34, 105)(35, 95)(36, 57)(37, 66)(40, 84)(41, 58)(43, 80)(45, 60)(48, 73)(51, 83)(52, 74)(53, 76)(54, 111)(59, 118)(61, 112)(62, 89)(63, 70)(65, 124)(67, 86)(68, 96)(69, 75)(71, 122)(77, 79)(81, 85)(87, 115)(90, 91)(92, 93)(94, 121)(97, 116)(98, 102)(104, 106)(108, 114)(113, 120), G!(1, 74)(2, 17)(3, 22)(4, 51)(5, 16)(6, 79)(7, 25)(8, 101)(9, 35)(10, 87)(11, 38)(12, 48)(13, 82)(14, 110)(15, 28)(18, 59)(19, 20)(21, 62)(23, 30)(24, 126)(26, 106)(27, 95)(29, 76)(31, 81)(32, 68)(33, 39)(34, 104)(36, 120)(37, 118)(40, 103)(41, 47)(42, 69)(43, 88)(44, 86)(45, 71)(46, 102)(49, 125)(50, 57)(52, 65)(53, 111)(54, 100)(55, 73)(56, 80)(58, 77)(60, 61)(63, 78)(64, 75)(66, 96)(67, 124)(70, 119)(72, 105)(83, 97)(84, 92)(85, 117)(89, 121)(90, 93)(91, 108)(94, 99)(98, 115)(107, 112)(109, 123)(113, 116)(114, 122) ] , [ G!(1, 118)(2, 119)(3, 83)(4, 64)(5, 107)(6, 97)(7, 66)(8, 57)(9, 67)(10, 20)(11, 58)(12, 84)(13, 115)(14, 48)(15, 19)(16, 31)(17, 73)(18, 30)(21, 71)(22, 50)(23, 114)(24, 75)(25, 33)(26, 126)(27, 88)(28, 42)(29, 69)(32, 93)(34, 55)(35, 122)(36, 108)(37, 117)(38, 121)(39, 52)(40, 76)(41, 46)(43, 61)(44, 80)(45, 96)(47, 103)(49, 99)(51, 91)(53, 111)(54, 113)(56, 116)(59, 77)(60, 123)(62, 109)(63, 112)(65, 86)(68, 81)(70, 98)(72, 106)(74, 79)(78, 92)(82, 125)(85, 124)(87, 95)(89, 104)(90, 102)(94, 120)(100, 110)(101, 105), G!(1, 51)(2, 125)(3, 115)(4, 44)(5, 9)(6, 26)(7, 79)(8, 82)(10, 91)(11, 77)(12, 48)(13, 74)(14, 67)(15, 96)(16, 114)(17, 87)(18, 56)(19, 89)(20, 42)(21, 72)(22, 123)(23, 66)(24, 98)(25, 73)(27, 99)(28, 49)(29, 95)(30, 36)(31, 113)(32, 93)(33, 81)(34, 85)(35, 112)(37, 126)(38, 45)(39, 92)(40, 83)(41, 59)(43, 60)(46, 63)(47, 65)(50, 88)(52, 121)(53, 116)(54, 111)(55, 105)(57, 78)(58, 94)(61, 68)(62, 102)(64, 86)(69, 106)(70, 76)(71, 120)(75, 119)(80, 100)(84, 109)(90, 118)(97, 101)(103, 117)(104, 107)(108, 110)(122, 124), G!(1, 39)(2, 92)(3, 69)(4, 12)(5, 33)(6, 57)(7, 85)(8, 115)(9, 18)(10, 66)(11, 31)(13, 58)(14, 25)(15, 125)(16, 30)(17, 48)(19, 120)(20, 117)(21, 111)(22, 116)(23, 36)(24, 59)(26, 73)(27, 29)(28, 106)(32, 53)(34, 61)(35, 78)(37, 43)(38, 62)(40, 87)(41, 63)(42, 118)(44, 110)(45, 46)(47, 103)(49, 126)(50, 72)(51, 75)(52, 79)(54, 89)(55, 100)(56, 107)(60, 81)(64, 113)(65, 96)(67, 68)(70, 76)(71, 121)(74, 112)(77, 90)(80, 108)(82, 102)(83, 97)(84, 86)(88, 99)(91, 123)(93, 122)(94, 119)(95, 104)(98, 114)(101, 109)(105, 124) ] , [ G!(1, 18)(2, 12)(3, 71)(4, 116)(5, 88)(6, 50)(7, 74)(8, 69)(9, 113)(10, 106)(11, 23)(13, 120)(14, 46)(15, 24)(16, 28)(17, 102)(19, 47)(20, 118)(21, 38)(22, 63)(25, 119)(26, 45)(27, 37)(29, 59)(30, 52)(31, 96)(32, 91)(33, 115)(34, 77)(35, 49)(36, 94)(39, 93)(40, 89)(41, 87)(42, 104)(43, 54)(44, 70)(48, 99)(51, 90)(53, 108)(55, 58)(56, 81)(57, 112)(60, 97)(61, 123)(62, 100)(64, 85)(65, 103)(66, 117)(67, 83)(68, 105)(72, 126)(73, 86)(75, 114)(76, 125)(78, 124)(79, 92)(80, 101)(82, 98)(84, 109)(95, 121)(107, 110)(111, 122), G!(1, 28)(2, 34)(3, 74)(4, 82)(5, 17)(6, 117)(7, 85)(8, 90)(9, 23)(10, 107)(11, 119)(12, 58)(13, 126)(14, 101)(15, 86)(16, 105)(18, 104)(19, 121)(20, 67)(21, 26)(22, 69)(24, 50)(25, 27)(29, 91)(30, 38)(31, 77)(32, 122)(33, 118)(35, 109)(36, 102)(37, 46)(39, 65)(40, 44)(41, 95)(42, 115)(43, 52)(45, 49)(47, 100)(48, 120)(51, 59)(53, 113)(54, 106)(55, 87)(56, 97)(57, 93)(60, 124)(61, 88)(62, 64)(63, 68)(66, 80)(70, 94)(71, 111)(72, 84)(73, 110)(75, 114)(76, 89)(78, 96)(79, 108)(81, 125)(83, 98)(92, 103)(99, 116)(112, 123), G!(1, 121)(2, 30)(3, 123)(4, 52)(5, 92)(6, 103)(7, 24)(8, 61)(9, 41)(10, 17)(11, 44)(12, 74)(13, 57)(14, 64)(15, 86)(16, 31)(18, 27)(19, 45)(20, 65)(21, 118)(22, 90)(23, 84)(25, 43)(26, 48)(28, 95)(29, 96)(32, 119)(33, 71)(34, 102)(35, 75)(36, 37)(38, 109)(39, 55)(40, 101)(42, 77)(46, 126)(47, 82)(49, 89)(50, 112)(51, 70)(53, 91)(54, 73)(56, 58)(59, 104)(60, 110)(62, 125)(63, 116)(66, 68)(67, 111)(69, 85)(72, 120)(76, 98)(78, 124)(79, 105)(80, 113)(81, 99)(83, 115)(87, 88)(93, 108)(94, 122)(97, 106)(100, 117)(107, 114) ] , [ G!(1, 4)(2, 117)(3, 29)(5, 20)(6, 91)(7, 72)(8, 105)(9, 11)(10, 89)(12, 54)(13, 98)(14, 86)(15, 94)(16, 122)(17, 111)(18, 90)(19, 57)(21, 123)(22, 26)(23, 42)(24, 110)(25, 48)(27, 118)(28, 40)(30, 39)(31, 106)(32, 97)(33, 58)(34, 68)(35, 63)(36, 70)(37, 45)(38, 121)(41, 69)(43, 44)(46, 71)(47, 85)(49, 116)(50, 92)(51, 104)(52, 115)(53, 126)(55, 114)(56, 79)(59, 67)(60, 61)(62, 81)(64, 76)(65, 74)(66, 109)(73, 124)(75, 101)(77, 112)(78, 82)(80, 120)(83, 107)(84, 99)(87, 119)(88, 108)(93, 95)(96, 125)(100, 103)(102, 113), G!(1, 23)(2, 53)(3, 104)(4, 47)(5, 79)(6, 54)(7, 113)(8, 80)(9, 30)(10, 76)(11, 17)(12, 94)(13, 74)(14, 62)(15, 66)(16, 93)(18, 107)(19, 26)(20, 73)(21, 64)(22, 40)(24, 41)(25, 111)(27, 44)(28, 46)(29, 119)(31, 69)(32, 108)(33, 102)(34, 97)(35, 92)(36, 86)(37, 125)(38, 59)(39, 75)(42, 49)(43, 83)(45, 67)(48, 121)(50, 87)(51, 57)(52, 101)(55, 120)(56, 100)(58, 118)(60, 114)(61, 81)(63, 115)(65, 90)(68, 124)(70, 126)(71, 99)(72, 117)(77, 122)(78, 82)(84, 98)(85, 88)(89, 91)(95, 123)(96, 110)(103, 105)(106, 109)(112, 116), G!(1, 80)(2, 40)(3, 105)(4, 124)(5, 18)(6, 89)(7, 106)(8, 36)(9, 114)(10, 30)(11, 25)(12, 14)(13, 61)(15, 94)(16, 27)(17, 108)(19, 51)(20, 56)(21, 50)(22, 47)(23, 32)(24, 119)(26, 42)(28, 109)(29, 37)(31, 101)(33, 52)(34, 82)(35, 110)(38, 98)(39, 75)(41, 118)(43, 62)(44, 76)(45, 74)(46, 96)(48, 73)(49, 125)(53, 69)(54, 103)(55, 93)(57, 123)(58, 66)(59, 87)(60, 111)(63, 72)(64, 120)(65, 85)(67, 112)(68, 79)(70, 84)(71, 102)(77, 90)(78, 113)(81, 83)(86, 107)(88, 115)(91, 97)(92, 116)(95, 117)(99, 100)(104, 126)(121, 122) ] , [ G!(1, 68)(2, 75)(3, 84)(4, 96)(5, 22)(6, 66)(7, 26)(8, 34)(9, 76)(10, 13)(11, 71)(12, 125)(14, 46)(15, 108)(16, 113)(17, 115)(18, 39)(19, 80)(20, 42)(21, 98)(23, 50)(24, 120)(25, 101)(27, 54)(28, 97)(29, 81)(30, 109)(31, 63)(32, 86)(33, 37)(35, 57)(36, 124)(38, 59)(40, 44)(41, 79)(43, 69)(45, 117)(47, 94)(48, 122)(49, 106)(51, 70)(52, 102)(53, 83)(55, 72)(56, 105)(58, 123)(60, 88)(61, 90)(62, 95)(64, 67)(65, 78)(73, 107)(74, 119)(77, 112)(82, 89)(85, 87)(91, 126)(92, 100)(93, 104)(99, 110)(103, 111)(114, 121)(116, 118), G!(1, 30)(2, 15)(3, 65)(4, 114)(5, 49)(6, 39)(7, 12)(8, 96)(9, 120)(10, 72)(11, 46)(13, 86)(14, 103)(16, 37)(17, 23)(18, 121)(19, 47)(20, 40)(21, 111)(22, 89)(24, 51)(25, 95)(26, 70)(27, 107)(28, 56)(29, 64)(31, 123)(32, 83)(33, 116)(34, 92)(35, 55)(36, 69)(38, 59)(41, 109)(42, 85)(43, 118)(44, 78)(45, 74)(48, 94)(50, 106)(52, 58)(53, 112)(54, 90)(57, 80)(60, 73)(61, 98)(62, 115)(63, 68)(66, 81)(67, 105)(71, 87)(75, 122)(76, 124)(77, 125)(79, 126)(82, 93)(84, 101)(88, 110)(91, 113)(97, 99)(100, 117)(102, 104)(108, 119), G!(1, 35)(2, 78)(3, 83)(4, 28)(5, 113)(6, 95)(7, 46)(8, 14)(9, 41)(10, 88)(11, 22)(12, 120)(13, 48)(15, 98)(16, 21)(17, 72)(18, 65)(19, 96)(20, 76)(23, 67)(24, 36)(25, 50)(26, 52)(27, 110)(29, 106)(30, 119)(31, 34)(32, 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geometries := [* *]; for i in [1..#involutions] do G1 := sub; G2 := sub; G3 := sub; Append(~geometries,CosetGeometry(G,{G1,G2,G3})); end for;