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