G := sub; involutions := [ [ G!(1, 2)(3, 7)(4, 9)(5, 11)(6, 13)(8, 17)(10, 21)(12, 25)(14, 29)(15, 31)(16, 33)(18, 37)(19, 39)(20, 41)(22, 45)(23, 47)(24, 49)(26, 53)(27, 55)(28, 57)(30, 61)(32, 65)(34, 69)(35, 71)(36, 73)(38, 77)(40, 81)(42, 85)(43, 87)(44, 89)(46, 93)(48, 97)(50, 101)(51, 103)(52, 105)(54, 109)(56, 113)(58, 117)(59, 119)(60, 121)(62, 125)(63, 127)(64, 111)(66, 132)(67, 99)(68, 135)(70, 139)(72, 122)(74, 146)(75, 148)(76, 150)(78, 110)(79, 96)(80, 156)(82, 159)(83, 161)(84, 163)(86, 124)(88, 169)(90, 104)(91, 173)(92, 118)(94, 177)(95, 179)(98, 184)(100, 187)(102, 191)(106, 198)(107, 200)(108, 202)(112, 208)(114, 211)(115, 213)(116, 215)(120, 221)(123, 225)(126, 229)(128, 232)(129, 234)(130, 236)(131, 238)(133, 242)(134, 243)(136, 247)(137, 249)(138, 251)(140, 254)(141, 231)(142, 257)(143, 259)(144, 261)(145, 263)(147, 253)(149, 269)(151, 237)(152, 273)(153, 248)(154, 276)(155, 278)(157, 282)(158, 284)(160, 288)(162, 292)(164, 295)(165, 297)(166, 299)(167, 301)(168, 290)(170, 280)(171, 307)(172, 309)(174, 298)(175, 314)(176, 316)(178, 289)(180, 321)(181, 323)(182, 325)(183, 327)(185, 331)(186, 332)(188, 336)(189, 338)(190, 340)(192, 343)(193, 320)(194, 346)(195, 348)(196, 350)(197, 352)(199, 342)(201, 358)(203, 326)(204, 362)(205, 337)(206, 365)(207, 367)(209, 371)(210, 373)(212, 377)(214, 381)(216, 384)(217, 386)(218, 388)(219, 390)(220, 379)(222, 369)(223, 396)(224, 398)(226, 387)(227, 403)(228, 405)(230, 378)(233, 411)(235, 414)(239, 353)(240, 421)(241, 423)(244, 428)(245, 430)(246, 432)(250, 437)(252, 440)(255, 407)(256, 445)(258, 449)(260, 453)(262, 457)(264, 328)(265, 461)(266, 463)(267, 465)(268, 455)(270, 447)(271, 382)(272, 472)(274, 462)(275, 477)(277, 454)(279, 483)(281, 486)(283, 490)(285, 492)(286, 494)(287, 376)(291, 501)(293, 360)(294, 504)(296, 506)(300, 510)(302, 391)(303, 514)(304, 516)(305, 518)(306, 520)(308, 522)(310, 526)(311, 512)(312, 528)(313, 529)(315, 525)(317, 517)(318, 344)(319, 523)(322, 538)(324, 541)(329, 548)(330, 550)(333, 555)(334, 557)(335, 559)(339, 564)(341, 567)(345, 572)(347, 576)(349, 580)(351, 584)(354, 588)(355, 590)(356, 592)(357, 582)(359, 574)(361, 599)(363, 589)(364, 604)(366, 581)(368, 610)(370, 613)(372, 617)(374, 619)(375, 621)(380, 628)(383, 631)(385, 633)(389, 637)(392, 641)(393, 643)(394, 645)(395, 647)(397, 649)(399, 653)(400, 639)(401, 655)(402, 656)(404, 652)(406, 644)(408, 650)(409, 612)(410, 664)(412, 666)(413, 565)(415, 668)(416, 551)(417, 671)(418, 594)(419, 674)(420, 667)(422, 676)(424, 543)(425, 679)(426, 611)(427, 680)(429, 683)(431, 685)(433, 573)(434, 630)(435, 562)(436, 593)(438, 540)(439, 691)(441, 687)(442, 695)(443, 696)(444, 684)(446, 560)(448, 658)(450, 704)(451, 615)(452, 682)(456, 636)(458, 677)(459, 711)(460, 712)(464, 716)(466, 563)(467, 545)(468, 719)(469, 720)(470, 721)(471, 723)(473, 727)(474, 717)(475, 729)(476, 730)(478, 726)(479, 669)(480, 724)(481, 640)(482, 735)(484, 553)(485, 536)(487, 625)(488, 578)(489, 739)(491, 661)(493, 629)(495, 733)(496, 734)(497, 746)(498, 614)(499, 748)(500, 665)(502, 620)(503, 561)(505, 751)(507, 749)(508, 635)(509, 583)(511, 750)(513, 608)(515, 757)(519, 742)(521, 760)(524, 763)(527, 765)(530, 736)(531, 575)(532, 700)(533, 766)(534, 618)(535, 705)(537, 770)(539, 772)(542, 774)(544, 777)(546, 780)(547, 773)(549, 782)(552, 785)(554, 786)(556, 789)(558, 791)(566, 797)(568, 793)(569, 801)(570, 802)(571, 790)(577, 810)(579, 788)(585, 783)(586, 817)(587, 818)(591, 822)(595, 825)(596, 826)(597, 827)(598, 829)(600, 833)(601, 823)(602, 835)(603, 836)(605, 832)(606, 775)(607, 830)(609, 841)(616, 845)(622, 839)(623, 840)(624, 852)(626, 854)(627, 771)(632, 857)(634, 855)(638, 856)(642, 863)(646, 848)(648, 866)(651, 869)(654, 871)(657, 842)(659, 806)(660, 872)(662, 811)(663, 875)(670, 860)(672, 849)(673, 851)(675, 858)(678, 838)(681, 814)(686, 865)(688, 804)(689, 859)(690, 878)(692, 879)(693, 803)(694, 831)(697, 799)(698, 794)(699, 837)(701, 815)(702, 820)(703, 881)(706, 880)(707, 846)(708, 787)(709, 807)(710, 843)(713, 834)(714, 808)(715, 824)(718, 821)(722, 884)(725, 800)(728, 819)(731, 805)(732, 784)(737, 816)(738, 864)(740, 813)(741, 868)(743, 778)(744, 874)(745, 779)(747, 885)(752, 781)(753, 795)(754, 776)(755, 877)(756, 882)(758, 844)(759, 792)(761, 873)(762, 847)(764, 876)(767, 867)(768, 850)(769, 886)(796, 889)(798, 890)(809, 892)(812, 891)(828, 895)(853, 896)(861, 888)(862, 893)(870, 887)(883, 894), G!(1, 3)(2, 5)(4, 10)(6, 14)(7, 15)(8, 18)(9, 19)(11, 23)(12, 26)(13, 27)(16, 34)(17, 35)(20, 42)(21, 43)(22, 46)(24, 50)(25, 51)(28, 58)(29, 59)(30, 62)(31, 63)(32, 66)(33, 67)(36, 74)(37, 75)(38, 78)(39, 79)(40, 82)(41, 83)(44, 90)(45, 91)(47, 95)(48, 98)(49, 99)(52, 106)(53, 107)(54, 110)(55, 111)(56, 114)(57, 115)(60, 122)(61, 123)(64, 129)(65, 130)(68, 136)(69, 137)(70, 140)(71, 141)(72, 143)(73, 144)(76, 151)(77, 152)(80, 157)(81, 138)(84, 145)(85, 164)(86, 166)(87, 167)(88, 149)(89, 170)(92, 175)(93, 133)(94, 178)(96, 181)(97, 182)(100, 188)(101, 189)(102, 192)(103, 193)(104, 195)(105, 196)(108, 203)(109, 204)(112, 209)(113, 190)(116, 197)(117, 216)(118, 218)(119, 219)(120, 201)(121, 222)(124, 227)(125, 185)(126, 230)(127, 179)(128, 233)(131, 239)(132, 240)(134, 244)(135, 245)(139, 252)(142, 258)(146, 264)(147, 266)(148, 267)(150, 270)(153, 275)(154, 277)(155, 279)(156, 280)(158, 285)(159, 286)(160, 289)(161, 290)(162, 293)(163, 294)(165, 298)(168, 303)(169, 304)(171, 308)(172, 310)(173, 311)(174, 313)(176, 317)(177, 318)(180, 322)(183, 328)(184, 329)(186, 333)(187, 334)(191, 341)(194, 347)(198, 353)(199, 355)(200, 356)(202, 359)(205, 364)(206, 366)(207, 368)(208, 369)(210, 374)(211, 375)(212, 378)(213, 379)(214, 382)(215, 383)(217, 387)(220, 392)(221, 393)(223, 397)(224, 399)(225, 400)(226, 402)(228, 406)(229, 407)(231, 409)(232, 325)(234, 390)(235, 415)(236, 321)(237, 417)(238, 418)(241, 424)(242, 425)(243, 413)(246, 419)(247, 433)(248, 435)(249, 338)(250, 422)(251, 438)(253, 442)(254, 412)(255, 444)(256, 446)(257, 447)(259, 451)(260, 454)(261, 455)(262, 458)(263, 459)(265, 462)(268, 467)(269, 468)(271, 471)(272, 473)(273, 474)(274, 476)(276, 479)(278, 481)(281, 487)(282, 488)(283, 475)(284, 491)(287, 496)(288, 497)(291, 502)(292, 489)(295, 410)(296, 495)(297, 507)(299, 484)(300, 511)(301, 323)(302, 513)(305, 519)(306, 521)(307, 431)(309, 524)(312, 450)(314, 530)(315, 532)(316, 533)(319, 535)(320, 536)(324, 542)(326, 544)(327, 545)(330, 551)(331, 552)(332, 540)(335, 546)(336, 560)(337, 562)(339, 549)(340, 565)(342, 569)(343, 539)(344, 571)(345, 573)(346, 574)(348, 578)(349, 581)(350, 582)(351, 585)(352, 586)(354, 589)(357, 594)(358, 595)(360, 598)(361, 600)(362, 601)(363, 603)(365, 606)(367, 608)(370, 614)(371, 615)(372, 602)(373, 618)(376, 623)(377, 624)(380, 629)(381, 616)(384, 537)(385, 622)(386, 634)(388, 611)(389, 638)(391, 640)(394, 646)(395, 648)(396, 558)(398, 651)(401, 577)(403, 657)(404, 659)(405, 660)(408, 662)(411, 665)(414, 643)(416, 670)(420, 675)(421, 627)(423, 550)(426, 605)(427, 681)(428, 621)(429, 684)(430, 593)(432, 652)(434, 687)(436, 688)(437, 567)(439, 692)(440, 564)(441, 694)(443, 697)(445, 698)(448, 701)(449, 702)(452, 706)(453, 707)(456, 709)(457, 703)(460, 705)(461, 713)(463, 700)(464, 596)(465, 612)(466, 557)(469, 591)(470, 722)(472, 725)(477, 731)(478, 553)(480, 733)(482, 736)(483, 610)(485, 592)(486, 650)(490, 740)(492, 742)(493, 678)(494, 555)(498, 718)(499, 676)(500, 548)(501, 749)(503, 750)(504, 751)(505, 752)(506, 753)(508, 754)(509, 728)(510, 727)(512, 755)(514, 664)(515, 708)(516, 541)(517, 672)(518, 759)(520, 756)(522, 761)(523, 613)(525, 559)(526, 716)(527, 715)(528, 766)(529, 732)(531, 730)(534, 768)(538, 771)(543, 776)(547, 781)(554, 787)(556, 790)(561, 793)(563, 794)(566, 798)(568, 800)(570, 803)(572, 804)(575, 807)(576, 808)(579, 812)(580, 813)(583, 815)(584, 809)(587, 811)(588, 819)(590, 806)(597, 828)(599, 831)(604, 837)(607, 839)(609, 842)(617, 846)(619, 848)(620, 784)(625, 824)(626, 782)(628, 855)(630, 856)(631, 857)(632, 858)(633, 859)(635, 860)(636, 834)(637, 833)(639, 861)(641, 770)(642, 814)(644, 778)(645, 865)(647, 862)(649, 867)(653, 822)(654, 821)(655, 872)(656, 838)(658, 836)(661, 874)(663, 774)(666, 854)(667, 817)(668, 769)(669, 835)(671, 820)(673, 827)(674, 801)(677, 847)(679, 877)(680, 830)(682, 791)(683, 852)(685, 788)(686, 850)(689, 863)(690, 873)(691, 840)(693, 876)(695, 780)(696, 802)(699, 805)(704, 853)(710, 826)(711, 773)(712, 871)(714, 777)(717, 823)(719, 875)(720, 816)(721, 779)(723, 866)(724, 786)(726, 841)(729, 775)(734, 797)(735, 832)(737, 844)(738, 843)(739, 882)(741, 783)(743, 885)(744, 792)(745, 881)(746, 789)(747, 810)(748, 772)(757, 795)(758, 869)(760, 829)(762, 884)(763, 864)(764, 883)(765, 818)(767, 796)(785, 888)(799, 887)(825, 886)(845, 893)(849, 896)(851, 892)(868, 895)(870, 894)(878, 891)(879, 890)(880, 889), G!(1, 4)(2, 6)(3, 8)(5, 12)(7, 16)(9, 20)(10, 22)(11, 24)(13, 28)(14, 30)(15, 32)(17, 36)(18, 38)(19, 40)(21, 44)(23, 48)(25, 52)(26, 54)(27, 56)(29, 60)(31, 64)(33, 68)(34, 70)(35, 72)(37, 76)(39, 80)(41, 84)(42, 86)(43, 88)(45, 92)(46, 94)(47, 96)(49, 100)(50, 102)(51, 104)(53, 108)(55, 112)(57, 116)(58, 118)(59, 120)(61, 124)(62, 126)(63, 128)(65, 131)(66, 133)(67, 134)(69, 138)(71, 142)(73, 145)(74, 147)(75, 149)(77, 153)(78, 154)(79, 155)(81, 158)(82, 160)(83, 162)(85, 165)(87, 168)(89, 171)(90, 172)(91, 174)(93, 176)(95, 180)(97, 183)(98, 185)(99, 186)(101, 190)(103, 194)(105, 197)(106, 199)(107, 201)(109, 205)(110, 206)(111, 207)(113, 210)(114, 212)(115, 214)(117, 217)(119, 220)(121, 223)(122, 224)(123, 226)(125, 228)(127, 231)(129, 235)(130, 237)(132, 241)(135, 246)(136, 248)(137, 250)(139, 253)(140, 255)(141, 256)(143, 260)(144, 262)(146, 265)(148, 268)(150, 271)(151, 272)(152, 274)(156, 281)(157, 283)(159, 287)(161, 291)(163, 215)(164, 296)(166, 300)(167, 302)(169, 305)(170, 306)(173, 312)(175, 315)(177, 319)(178, 277)(179, 320)(181, 324)(182, 326)(184, 330)(187, 335)(188, 337)(189, 339)(191, 342)(192, 344)(193, 345)(195, 349)(196, 351)(198, 354)(200, 357)(202, 360)(203, 361)(204, 363)(208, 370)(209, 372)(211, 376)(213, 380)(216, 385)(218, 389)(219, 391)(221, 394)(222, 395)(225, 401)(227, 404)(229, 408)(230, 366)(232, 410)(233, 412)(234, 413)(236, 416)(238, 419)(239, 420)(240, 422)(242, 426)(243, 427)(244, 429)(245, 431)(247, 434)(249, 436)(251, 439)(252, 441)(254, 443)(257, 448)(258, 450)(259, 452)(261, 456)(263, 432)(264, 460)(266, 464)(267, 466)(269, 469)(270, 470)(273, 475)(275, 478)(276, 480)(278, 482)(279, 484)(280, 485)(282, 489)(284, 383)(285, 493)(286, 495)(288, 498)(289, 499)(290, 500)(292, 381)(293, 503)(294, 373)(295, 505)(297, 396)(298, 508)(299, 509)(301, 512)(303, 515)(304, 517)(307, 386)(308, 523)(309, 525)(310, 473)(311, 527)(313, 479)(314, 531)(316, 534)(317, 444)(318, 476)(321, 537)(322, 539)(323, 540)(325, 543)(327, 546)(328, 547)(329, 549)(331, 553)(332, 554)(333, 556)(334, 558)(336, 561)(338, 563)(340, 566)(341, 568)(343, 570)(346, 575)(347, 577)(348, 579)(350, 583)(352, 559)(353, 587)(355, 591)(356, 593)(358, 596)(359, 597)(362, 602)(364, 605)(365, 607)(367, 609)(368, 611)(369, 612)(371, 616)(374, 620)(375, 622)(377, 625)(378, 626)(379, 627)(382, 630)(384, 632)(387, 635)(388, 636)(390, 639)(392, 642)(393, 644)(397, 650)(398, 652)(399, 600)(400, 654)(402, 606)(403, 658)(405, 661)(406, 571)(407, 603)(409, 663)(411, 574)(414, 667)(415, 669)(417, 672)(418, 673)(421, 582)(423, 677)(424, 678)(425, 662)(428, 682)(430, 637)(433, 686)(435, 628)(437, 689)(438, 690)(440, 693)(442, 631)(445, 699)(446, 700)(447, 538)(449, 703)(451, 705)(453, 708)(454, 595)(455, 548)(457, 685)(458, 710)(459, 680)(461, 691)(462, 714)(463, 715)(465, 717)(467, 718)(468, 581)(471, 724)(472, 726)(474, 728)(477, 732)(481, 734)(483, 737)(486, 695)(487, 614)(488, 738)(490, 629)(491, 741)(492, 743)(494, 744)(496, 745)(497, 747)(501, 562)(502, 617)(504, 569)(506, 647)(507, 645)(510, 557)(511, 676)(513, 716)(514, 756)(516, 758)(518, 634)(519, 675)(520, 633)(521, 725)(522, 762)(524, 722)(526, 764)(528, 655)(529, 767)(530, 731)(532, 666)(533, 694)(535, 552)(536, 769)(541, 773)(542, 775)(544, 778)(545, 779)(550, 783)(551, 784)(555, 788)(560, 792)(564, 795)(565, 796)(567, 799)(572, 805)(573, 806)(576, 809)(578, 811)(580, 814)(584, 791)(585, 816)(586, 786)(588, 797)(589, 820)(590, 821)(592, 823)(594, 824)(598, 830)(599, 832)(601, 834)(604, 838)(608, 840)(610, 843)(613, 801)(615, 844)(618, 847)(619, 849)(621, 850)(623, 851)(624, 853)(638, 782)(640, 822)(641, 862)(643, 864)(646, 781)(648, 831)(649, 868)(651, 828)(653, 870)(656, 873)(657, 837)(659, 772)(660, 800)(664, 842)(665, 861)(668, 872)(670, 876)(671, 845)(674, 841)(679, 790)(681, 807)(683, 815)(684, 785)(687, 808)(688, 848)(692, 836)(696, 869)(697, 835)(698, 880)(701, 787)(702, 793)(704, 833)(706, 882)(707, 883)(709, 789)(711, 817)(712, 878)(713, 859)(719, 874)(720, 856)(721, 865)(723, 829)(727, 810)(729, 803)(730, 798)(733, 854)(735, 780)(736, 770)(739, 777)(740, 852)(742, 794)(746, 846)(748, 839)(749, 877)(750, 826)(751, 875)(752, 863)(753, 819)(754, 881)(755, 771)(757, 858)(759, 827)(760, 867)(761, 866)(763, 802)(765, 871)(766, 774)(768, 825)(776, 887)(804, 891)(812, 893)(813, 894)(818, 889)(855, 888)(857, 886)(860, 892)(879, 895)(884, 890)(885, 896) ] ]; geometries := [* *]; for i in [1..#involutions] do G1 := sub; G2 := sub; G3 := sub; Append(~geometries,CosetGeometry(G,{G1,G2,G3})); end for;