G := sub<Sym(119)|(1, 26)(2, 21)(3, 28)(4, 29)(5, 72)(6, 47)(7, 52)(8, 13)(9, 12)(10, 65)(11, 43)(14, 96)(15, 90)(16, 64)(17, 38)(18, 102)(19, 66)(20, 87)(22, 56)(23,49)(24, 98)(25, 81)(27, 53)(30, 112)(31, 40)(32, 73)(33, 51)(34, 44)(35,109)(36, 62)(37, 71)(39, 50)(41, 95)(42, 105)(45, 100)(46, 58)(48, 111)(54, 57)(55, 99)(59, 85)(60, 103)(61, 79)(67, 69)(68, 93)(70, 74)(75, 107)(76, 86)(77, 97)(78, 91)(80, 82)(84, 101)(88, 117)(89, 115)(92, 119)(94, 113)(106, 110),(1, 46)(2, 23)(3, 56)(4, 111)(5, 30)(6, 39)(7, 85)(8, 27)(9, 13)(10, 38)(11,69)(12, 44)(14, 102)(15, 68)(16, 73)(17, 78)(18, 41)(19, 49)(20, 107)(21, 47)(22, 25)(24, 83)(26, 113)(28, 37)(29, 80)(31, 104)(32, 72)(33, 109)(34, 53)(35, 106)(36, 43)(40, 118)(42, 76)(45, 71)(48, 55)(50, 62)(51, 90)(52, 89)(54, 70)(57, 75)(58, 110)(59, 88)(60, 86)(61,103)(63, 98)(64, 82)(65, 100)(66, 67)(79, 96)(81, 91)(84, 105)(92, 97)(93, 94)(95, 101)(99, 112)(108, 116),(1, 27)(2, 62)(3, 89)(4, 56)(5, 61)(6, 87)(7, 25)(8, 92)(9, 10)(11, 64)(12, 24)(13, 67)(14, 20)(15, 114)(16, 93)(17, 106)(18, 80)(19, 71)(21, 88)(22, 73)(26, 47)(29, 50)(30, 85)(31, 96)(32, 34)(33, 78)(35, 53)(36, 110)(37, 70)(38, 43)(39, 77)(40, 75)(42, 79)(44, 54)(45, 104)(46, 86)(48, 101)(49, 99)(51, 105)(52, 58)(57, 94)(59, 108)(60, 116)(63, 102)(65, 91)(66, 111)(68, 117)(69, 84)(72, 98)(74, 119)(76, 81)(82, 90)(97, 113)(100, 112)(103, 118)(107, 109)>;

involutions :=

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

];

geometries := [* *];


for i in [1..#involutions] do
	G1 := sub<G|involutions[i][2],involutions[i][3]>;
	G2 := sub<G|involutions[i][1],involutions[i][3]>;
	G3 := sub<G|involutions[i][1],involutions[i][2]>;
	Append(~geometries,CosetGeometry(G,{G1,G2,G3}));
end for;