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

involutions :=

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

];

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;