function G1()
  print "\nG is the group BO.7^(2+1).13^(14+1) of order 2^4 * 3 * 7^3 * 13^15
where BO is the binary octahedral group of order 48 and 7^(2+1) and
13^(14+1) denote extraspecial groups of prime exponent\n";
  G := PCGroup( \[ 23, 2, 3, 2, 2, 2, 7, 7, 7, 13, 13, 13, 13, 13, 13, 13, 13,
  13, 13, 13, 13, 13, 13, 13, 552, 1841, 576, 830, 646, 324, 555, 302, 601, 256,
  1351301, 884332, 181107, 3938, 1753, 741894, 7757, 291140, 3939, 13622, 9137,
  41416432420091015499416, 52077598518912845080135, 1056330756457617032838,
  8187045779430317015825, 1677345964566213013858, 11999292, 85660,
  45739981268394714252009, 38783078651610282281072, 28891399836522939996615,
  12276870816489906133718, 3106196230678193705881, 173321454, 71010,
  5433579412265022003, 70462762908752765783242, 12265871171630033028489,
  26846379113070947089408, 2167987645125993496423, 2098612340939842289664,
  2478495144, 488116550535392268638, 17658812, 154989609887460968690123,
  79899701557492407699394, 23518347543407621579865, 12157080160751424725648,
  4415577410994812678719, 35149565850, 585739860642395298989, 14366524,
  38581628962832365, 200028963732623661046332, 19370388559174897404923,
  28844556509000806748050, 1742332223860102110681, 2423172380409337281374,
  495023050740, 576865014335335938089, 3526912380, 268886228597322120021229,
  83644334682102608401716, 24661679388396006254651, 15641431670913940665842,
  4353425209674552181093, 6930322708710, 434867472319277987777, 2832565910,
  266342606256743, 96685656168936047366174, 22348923614380693660717,
  14246431756302398398260, 2355672233860434944363, 2795578924318229051836,
  96529494869664, 665613485509407770942, 687747880540, 187944832813511669145615,
  95577742897959121193894, 43266893914744432865469, 16297335661755177833300,
  4969946094100963128715, 1338542328857682, 780986489821038420345, 547089839472,
  1801133437089, 108933694047079924859776, 18932839623278612559903,
  14660362206621406681286, 2744456308419667675933, 3168320170827840524058,
  18488615917345068, 829799464339454566930, 131726644019420,
  205629266504512563084305, 119865627151003432985368, 47532994205516822023119,
  19362571822231964559158, 5591153429070662230705, 254490360274042206,
  638989170553153900271, 104015455696330, 11989799323, 285646305626548510697442,
  24933833494907876035601, 41485034297011893605032, 2559956376472384663791,
  3541063703075857649528, 3492173277093799704, 421605386120955741770,
  24880838467399548, 359786363508722206781779, 122359536316494079018122,
  36879962662745173493825, 20044282919125995409688, 6212392462762320813271,
  47787634318125678474, 532646148922285667517, 19531791125166500, 78834773,
  133453217592395126322644, 30149962193569921958851, 51072443316117676952250,
  4200736411451877606881, 3913807250655165009622, 165804, 32532351055031711951,
  4647478722147387580, 268987451541128713636341, 132722215253857457182460,
  40565549083466601509459, 23114156471185622582522, 6833631707501123368957,
  2256390, 25416719791178932375, 3630959970168419070, 520143 ]: Check := false );
  print "A group with factorized order ", FactoredOrder(G);
  print "has been constructed";
  Gn :=  \[ 1, 2, 3, 5, 6, 8, 9, 23, 24 ];
  return G, Gn;
end function;


function G2()
print "\nConstructing a group G = S4.2^5 of order 768.\n";
G := PCGroup( \[ 9, 2, 3, 2, 2, 2, 2, 2, 2, 2, 54, 7525, 8030, 23115, 7032,
  1389, 1326, 5404, 5413, 2182, 481, 3893, 7790, 1319, 2192, 13614, 6819, 1735,
  20752, 1465, 1762, 33056, 7793, 6506, 1007 ]: Check := false );
  print "A group with factorized order", FactoredOrder( G );
  print "has been constructed";
  Gn :=  \[ 1, 2, 3, 5, 10 ];
  return G, Gn;
end function;


function G3()
  print "\nConstructing a group G of order 2^11*3^13. A description of this 
group occurs in S.P. Glasby and R.B. Howlett, Extraspecial towers and Weil 
representations, J. Algebra (1992), 236-260. Note that every normal subgroup 
of G occurs in its derived series. Furthermore, G may be realized as 3 
split extns: GL(2,3).3^(2+1).2^(6+1).3^(8+1) where 2^(6+1) is the central 
product of 3 copies of Q8.\n";
  G := PCGroup( \[ 24, 2, 3, 2, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3,
  3, 3, 3, 3, 3, 193, 2162, 674, 338, 4035, 315, 627, 267, 16181, 12749, 677,
  209670, 88734, 29622, 10830, 2118, 2142, 165895, 35271944, 5738720, 1912952,
  1423088, 93440, 1472, 14024, 32659209, 9642273, 3214137, 570321, 207489, 2337,
  16041, 7905, 42083722, 6500770, 3364474, 1653778, 228202, 7258, 19162, 6514,
  4474, 38071307, 11010851, 1804091, 964307, 497771, 15683, 31259, 10547, 5435,
  2579, 44883084, 5256612, 3167484, 1550100, 67500, 33828, 134940, 30132, 1548,
  39191053, 10233253, 3846589, 1995925, 145261, 72709, 48541, 48565, 2317, 997,
  11975786511, 2993946663, 997982271, 504299607, 5308527, 4079823, 2015463,
  135423, 61719, 15663, 6471, 1887, 585925705744, 292962852904, 170604527680,
  48381567064, 50761840, 12690568, 1880224, 783544, 13003984, 6423784, 431104,
  196120, 13360, 11752, 5248, 620821905425, 310410952745, 180711751745,
  51155877977, 17916017, 120932489, 5474465, 1824953, 41306321, 20404457,
  138497, 131609, 155825, 62537, 15905, 494037024786, 125041066026, 28215558210,
  14277980250, 170201202, 1148857482, 23113890, 9105594, 130802898, 64613610,
  438018, 416154, 131634, 115242, 49602, 173107445779, 86553722923, 28851241027,
  13967769691, 537477235, 4976779, 15298747, 5038291, 5007595, 13686019,
  6221083, 1555507, 622411, 155875, 118531, 1625079988244, 695782047788,
  145240252484, 109686141020, 5079158900, 47029388, 188117156, 79737020,
  15870164, 15773420, 43110404, 19595804, 1306676, 1143404, 490244, 748868,
  1659896561685, 750198620205, 137967059013, 118456639581, 1773674613,
  443418765, 541956261, 184504509, 49877205, 49573101, 13686021, 13001757,
  15396789, 6158925, 1540005, 2438181, 383221186582, 191610593326, 82809962566,
  24624746590, 16688664694, 2266362022, 907223230, 156432598, 155478766,
  42923782, 40777630, 12877366, 11267758, 4829254, 4829278, 1253826625559 ]: Check := false );
  print "A group with factorized order", FactoredOrder( G );
  print "is defined";
  Gn :=  \[ 1, 2, 3, 5, 6, 8, 9, 15, 16, 24, 25 ];
  return G, Gn;
end function;


function G4()
  print "\nConstructing S3 wr S3 of degree 9 and order 2^4*3^4\n";
  G := PCGroup( \[ 8, 2, 3, 2, 2, 2, 3, 3, 3, 65, 290, 154, 195, 683, 6917,
  3469, 789, 229, 2694, 12110, 1374, 710, 1551, 2343 ]: Check := false );
  print "The factorized order of G is", FactoredOrder( G );
  Gn :=  \[ 1, 2, 3, 5, 6, 9 ];
  return G, Gn;
end function;


function G5()
  print "\nConstructing a group G of order 2^4*3^3*5^9. Now G = GL(2,3).3^2.5^9
where p^n denotes an elementary abelian group of order p^n. Note that that 
GL(2,3).3^2 has a primitive permutation representation of degree 9\n";
  G := PCGroup( \[ 16, 2, 3, 2, 2, 2, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 705, 1442,
  450, 226, 1155, 211, 419, 179, 18437, 11541, 6181, 1973, 453, 32262, 5398,
  4518, 1846, 1414, 720087, 6000103, 1555208, 259240, 81000056, 1012500072,
  101250088, 10904, 345609, 108000025, 4500000041, 18000057, 1800073, 1529,
  60105, 2970000026, 990000042, 158458, 9900074, 24750090, 2746, 32400000011,
  5184027, 69163, 864059, 86475, 43291, 225000107, 702000028, 234000044,
  4680060, 468076, 9452, 390108, 7560000013, 1209629, 2016045, 3150000061,
  315000077, 787500093, 52500109, 1620000014, 32400030, 54000046, 43262,
  67500078, 6750094, 830, 69120015, 11520047, 720000063, 23119, 288095,
  2400111 ]: Check := false );
  print "A group with factorized order", FactoredOrder( G );
  print "is constructed";
  Gn :=  \[ 1, 2, 3, 5, 6, 8, 17 ];
  return G, Gn;
end function;


function G6()
  print "\nConstructing  the group S4 wr S4 wr S4 which is a primitive 
permutation group of degree 64 = 4^3 and order 2^63*3^21. This takes a 
minute or two!\n";
  G := PCGroup( \[ 84, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2,
  2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3,
  3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
  2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 504, 1681, 1598, 6051, 3111, 20164,
  10168, 6892, 1936, 544660, 48389, 24281, 16301, 1265, 1306793, 112902, 7146,
  2526, 9666, 3048702, 16135, 5551, 5635, 6967891, 870920, 435548, 435632,
  72836, 1004312, 2903049, 1451613, 1451697, 27141, 2218029, 9580042, 177502,
  59314, 798598, 4857058, 387083, 193715, 290567, 10560407, 135862284, 67931232,
  90575028, 11322120, 177588, 292626445, 146313313, 195084469, 24385801,
  4572637, 286453, 627056654, 313528418, 418037942, 3266186, 272930, 1337720847,
  668860515, 891814071, 6967563, 10451379, 436227, 2842656784, 22208356,
  7402936, 236888332, 412120, 6019743761, 47029349, 15676601, 501645581,
  23515145, 654041, 49642002, 33094842, 66189582, 613806, 104509459, 69673147,
  139346191, 52255327, 968623, 224737099796, 112368549992, 599298932924,
  18728091920, 1170506084, 73157300, 1807364, 452696, 4976437876754084,
  470877732885, 235438866537, 1255673954493, 39239811345, 2452488549, 153281205,
  3785733, 237657, 10426822217959161, 984562532374, 492281266282, 2625500086462,
  82046877970, 5127930214, 40062646, 495622, 1979482, 21801537364821838,
  2054739197975, 1027369599083, 5479304528063, 171228266771, 668860775, 1033223,
  1033307, 45498860587452323, 4280706662424, 2140353331308, 11415217766592,
  1393459476, 11147674044, 464487180, 8602800, 2151684, 94789292890523640,
  8903869857817, 4451934929005, 23743652954305, 2898395413, 23187161533,
  966132493, 17892529, 1119493, 197161729212287053, 18492652781594,
  9246326390894, 49313740751042, 6019744022, 48157950398, 250823438, 2323634,
  9291014, 409489745287055522, 38355131695131, 19177565847663, 102280351187139,
  12485394711, 6242697663, 4818099, 4818183, 849312064299075831, 79449915654172,
  9698476144, 3232825540, 6620826304792, 103450411540, 2873623396, 39912796,
  9979312, 1759289276048083276, 164379135836189, 20065812593, 6688604357,
  13698261319961, 214035333653, 5945426789, 82576733, 5162417,
  3639908846996031905, 339716880728094, 41469345906, 13823115462,
  28309740060954, 442339688982, 1535902566, 10667358, 42665394,
  7522478283791796726, 701350979567647, 85614133363, 28538044615,
  58445914964251, 57076089367, 22021471, 22021555, 15530277747183061579,
  22072393760, 58859716808, 470877733148, 941755466348, 17439916988, 181667336,
  45418076, 32031197853565061792, 45482508321, 121286688969, 970293510429,
  1940587020909, 35936797629, 374343177, 23397981, 66003680425528003317,
  93640458274, 249707888842, 1997663109406, 3995326218862, 9248441278, 48170506,
  192677470, 135889930287851768650, 192631799843, 513684799691, 4109478396191,
  513684800111, 99091979, 99092063, 279544999449295063967, 131371805360259108,
  65685902680129656, 1773519372363497676, 10947650446688544, 202734267531636,
  12670891721412, 469292286996, 78215382120, 8768009999746740,
  404767184082960421, 202383592041480313, 5464356985119965389,
  33730598673580321, 624640716177781, 39040044761797, 1445927584789,
  26776437865, 18009966276773641, 1246256856255430694, 623128428127715450,
  16824467559448314062, 103854738021286178, 1923235889283446, 4451934929606,
  54962160662, 741989155946, 36967825193437022, 3834636480785940519,
  1917318240392970363, 51767592490610196687, 319553040065495331, 73057393705335,
  169114338327, 253671507051, 75831435798775731, 11791507178416767016,
  5895753589208383612, 159185346908626354384, 149767657095460, 9098385168531916,
  379099382022940, 10530538390720, 1755089732884, 155454442625730568,
  36237314743427137577, 18118657371713568893, 489203749036266356945,
  460261580341541, 27960891005731277, 1165037125239581, 32362142368961,
  599298934037, 318492027623671901, 111300323854811922474, 55650161927405961342,
  1502554372039960953042, 1413660568191270, 85879879517602254, 132530678268702,
  1227135911106, 16566334784790, 652150340479477938, 341666110438027296811,
  170833055219013648511, 4612492490913368506579, 4339609186074919,
  3254706889556431, 3767021864131, 5650532795671, 1334633252175694087,
  1048293747934856478764, 986274815017088, 328758271672532,
  87357812327904706856, 404434316332892708, 11234286564803444, 234047636768108,
  39007939462592, 2729931647944921436, 3214767493666893201453, 3024576099385473,
  1008192033128661, 267897291138907767081, 1240265236754203173,
  34451812132062069, 717746086085997, 13291594188225, 5581193584864022961,
  9853961230587650900014, 9270983261159554, 3090327753720022,
  821163435882304241962, 3801682573529186854, 3911196063302518, 27161083774318,
  366674630936002, 11405047750427619334, 30190859940523866587183,
  28404714672488579, 9468238224163031, 2515904995043655549227,
  143798868029473319, 83216937518447, 124825406277059, 23295416666487020123,
  2147887374925872, 28996479561498840, 1174357422240694572,
  17835553350280544892, 330288025005196236, 5160750390707736, 860125065119340,
  47561475670745277744, 6575165433446449, 88764733351526617,
  3594971700736819501, 54598632704940442237, 1011085790832231373,
  15798215481755161, 292559545960045, 97064236027032626821, 20120006226346034,
  271620084055671002, 11000613404254667054, 167071816077117751934,
  114589722960987086, 596821473756698, 8057089895695982, 198011041440505918010,
  61543548457058355, 830837904170287323, 33648935118896628015,
  6309175334793118335, 1825571566781979, 2738357350172271,
  403787221677463638639, 25601849229564238865891380, 12800924614782119432945800,
  1092345567128074191611363548, 2133487435797019905491248,
  16667870592164218012036, 1041741912010263626452, 51444045037543883812,
  6430505629692986488, 383288006860, 52169805977225241462571061,
  26084902988612620731285641, 2225911721694943635736363229,
  4347483831435436788547889, 33964717433089349910917, 2122794839568084370133,
  104829374793485648933, 13103671849185707129, 38389663620662981, 585779782445,
  106271826990644010386718774, 53135913495322005193359498,
  4534264618267477776499998942, 8855985582553667532226866,
  69187387363700527595910, 4324211710231282975446, 213541319023767061542,
  1668291554873181306, 530335605882, 216408084053675075696590903,
  108204042026837537848295563, 9233411586290136563054543071,
  18034007004472922974716211, 140890679722444710740359, 8805667482652794421975,
  434847776921125651495, 3397248257196295291, 79623006028039963, 809967105499,
  440545028252124261239488568, 220272514126062130619744396,
  18796587872090635146218176736, 36712085687677021769957684,
  286813169434976732578184, 280090985776344466136, 3457913404646229032,
  110653228948679296124, 732827381552, 896547776793796742171590713,
  448273888396898371085795469, 38252705143201994332654534881,
  74712314732816395180966197, 583689958850128087351689, 570009725439578211033,
  7037157104192324649, 225189027334154355837, 164933369629509489, 1118526001713,
  1824010994166689923728408634, 912005497083344961864204430,
  77824469084445436745745432802, 152000916180557493644034358,
  4638699834611739918730, 14316974798184383530, 28633949596368766078,
  1011387496198, 3709852869491572726227271739, 1854926434745786363113635983,
  158287055764973769652363591907, 309154405790964393852272951,
  9434643731413708308875, 29119270775968236587, 58238541551936472191,
  341241454405879751, 1542794483975, 7543367501299531209995452476,
  3771683750649765604997726352, 321850346722113331626472636644,
  9591887793603936780600, 2455523275162607815754208, 102313469798441992323888,
  3789387770312666383572, 473673471289083299112, 1394229089628,
  15334058527231833935072723005, 7667029263615916967536361617,
  654253163828558247896436179173, 19498263711588330504505,
  4991555510166612609073633, 207981479590275525378865, 7703017762602797237461,
  962877220325349655849, 705232339105482781, 2125627954525,
  31162764103729210900309082174, 15581382051864605450154541202,
  1329611268425779665079854170342, 39625503671937574895930,
  10144128940016019173278178, 422672039167334132220722, 15654519969160523416790,
  122300937259066590506, 1919922023858, 63314822305989507860945436735,
  31657411152994753930472718483, 2701432418388885668733671964903,
  80508959841396977566011, 20610293719397626256818659, 858762238308234427368243,
  31806008826230904718551, 248484443954928944427, 1455963538798413939,
  2925595463091, 128608232809041187842545418304, 64304116404520593921272709268,
  5487284599852424014615271178472, 163533824677837610680636,
  41864659117526428334162404, 27255637446306268447540, 252367013391724709080,
  8075744428535190652204, 2641162571272, 261173642012206719926399926337,
  130586821006103359963199963285, 11143408725854153383526396854505,
  332099459345762532458813, 85017461592515208309375461, 55349909890960422077237,
  512499165657040946393, 16399973301025310246189, 3002924798771726537,
  4022693760521, 530261636812662128335418032194, 265130818406331064167709016214,
  22624496504006917475644502704362, 674262538671699687113022,
  674262538671699687113190, 1040528609061264950490, 2081057218122529899822,
  3629905481310, 1076351979201821633636072423491,
  538175989600910816818036211863, 45924351112611056368472423399659,
  1368652317303748618617151, 1368652317303748618617319, 2112117773616896017627,
  4224235547233792034095, 6187845039893252383, 5526124760671,
  2184361369556638021202617565252, 65099041746754587328664,
  21699680582251529109740, 182030114129719835100218130752,
  355527566659609052930114108, 9875765740544695914726284,
  274326826126241553188228, 34290853265780194149848, 4984347823796,
  4432037561419265550266180567109, 132085012239791916318873,
  44028337413263972106477, 369336463451605462522181714241,
  721360280178916918988636733, 20037785560525469971907469,
  556605154459040832554373, 69575644307380104070617, 12739680964486105461,
  7584877121205, 8990704767450510116254252007494, 267943881972149315960986,
  89314627324049771987182, 749225397287542509687854334274,
  1463330854077231464234091070, 40648079279923096228725646,
  1129113313331197117465990, 8821197760399977481690, 6838428897034,
  18234668824124978263952285761607, 543435478929429598568603,
  181145159643143199523055, 1519555735343748188662690480451,
  2967882295593258180981817919, 82441174877590505027273615,
  2290032635488625139647879, 17890879964754883904987, 26207343698371414475,
  10402117193483, 36975856226697872590792135016520, 1101966387829121130430620,
  367322129276373710143728, 3081321352224822715899344585028,
  6018205766064106866990907968, 2612068474854213049910160,
  18139364408709812848008, 580459661078714011092444, 9374747594592,
  74964749610291577307359397019721, 2234123635598766127448221,
  744707878532922042482929, 6247062467524298108946616418629,
  12201293881883394744036360769, 5295700469567445635433361,
  36775697705329483580809, 1176822326570543474542045, 53870650935541238305,
  14254753189729, 151955573534374818866269048012874, 4528628991078579988070558,
  1509542997026193329357042, 12662964461197901572189087334726,
  96610751809676373078835778, 74545333186478682932618, 149090666372957365863902,
  12842119991222, 307963295696332966235638603972683, 9178021421919255442489503,
  3059340473973085147496691, 25663607974694413852969883664711,
  195797790334277449439773251, 151078541924596797408651,
  302157083849193594815967, 110653228948679297655, 19520022384567,
  145293513463771107950668, 6199189907787567272558836,
  793496308196808610887500104, 50783763724595751096799986328,
  940440068973995390681482216, 19592501436958237305865780,
  2449062679619779663234696, 17579435364364, 294360884420107699224653,
  12559397735257928500248821, 1607602910113014848031818057,
  102886586247232950274036335257, 1905307152726536116185859049,
  39693899015136169087206965, 4961737376892021135902345, 227130312052552239821,
  26711609577485, 596269483825346365096014, 25440831309881444910760182,
  3256426407664824948577272138, 208411290090548796708945396378,
  3859468335010162902017508330, 80405590312711727125366326,
  628168674318060368168586, 24048058765410, 1207634397620954663485519,
  51525734298494065642045687, 6595293990207240402181816651,
  422098815373263385739636245147, 7816644729134507143326598123,
  162846765190302232152639031, 1272240353049236188694155, 465908332415491771171,
  36528696856675, 2445459655182433193558096, 104339611954450482925142264,
  13355470330169661814418178380, 854750101130858356122763395740,
  247323524632771515081819116, 1288143357462351641052728,
  41220587438795252513638028, 32875827171512, 4951301030245914120290385,
  211255510623825669132386553, 27040705359849685648945447245,
  1730605143030379881532508603037, 500753802960179363869361133,
  2608092723750934186821177, 83458967160029893978228365, 955112081451758127993,
  49922552369337, 10023365500253923706929234, 427663594677500744828977402,
  54740940118720095338109075790, 13685235029680023834527269534,
  5279797465154330183075386, 10559594930308660366149262, 44916767985934,
  20288257880032038346555475, 865632336214700302786363643,
  110800939035481638756654514511, 27700234758870409689163629215,
  10686818965613583985018427, 21373637931227167970035343,
  1956814996145065429967, 68186900795663 ]: Check := false );
  print "A group with factorized order", FactoredOrder( G );
  print "has been constructed";
  Gn :=  \[ 1, 2, 3, 5, 9, 13, 21, 37, 53, 85 ];
  return G, Gn;
end function;


function G7()
  print "\nConstructing the group G = Aut(F).F*.F+ where F=GF(2^11) and 
F+,F*,Aut(F) denote the additive, multiplicative and automorphism groups of F. 
Note that |G| = 11*23*89*2^11.\n";
  G := PCGroup( \[ 14, 11, 23, 89, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 617, 659,
  21254, 229281, 169487, 6304764, 573178, 423672, 30262853, 1375603, 1016769,
  141226630, 3209716, 2372418, 645607431, 7336469, 5422627, 2905233416,
  16507030, 12200868, 31523809, 36682263, 1657217, 138704730, 80700952, 3645834,
  605256971, 176074777, 7954503, 2622780172, 381495322, 17234712, 2281692657,
  2006087, 1482781 ]: Check := false );
  print "A split extension with factorized order ", FactoredOrder( G );
  print "is defined";
  Gn :=  \[ 1, 2, 3, 4, 15 ];
  return G, Gn;
end function;


function G8()
  print "\nConstructing the group G = Aut(F).F*.F+ where F=GF(3^10) and 
F+,F*,Aut(F) denote the additive, multiplicative and automorphism groups of F. 
Note that |G| = 2^4*5*11^2*61*3^10\n";
  G := PCGroup( \[ 18, 2, 5, 2, 2, 2, 11, 11, 61, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
  36, 1622, 2450, 146, 4323, 6501, 201, 10804, 16222, 256, 25925, 38903, 1283,
  332646, 498984, 1500, 4181767, 6272665, 28697372, 43046054, 193707044,
  7845132140, 2182410170, 450174644, 2869732809, 1046017605627, 95657805,
  143486703, 645689961, 26150440239, 5425800057, 371980575, 85231064170,
  2872660990348, 315670654, 473505976, 2130776686, 63924759658, 5120746012,
  250207984, 2510442253451, 2059511572829, 1033103855, 1549655777, 6973450787,
  55795577213, 5030873615, 530716241, 4232770850892, 1806533997870, 3357587424,
  5036381130, 22663714872, 52909635738, 3645080130, 351297552, 391346524813,
  523779379231, 10847590033, 16271385043, 73221232477, 32633910643, 8078539513,
  899646439, 7834529973614, 499492936832, 34867253570, 52300880348,
  174340253426, 104894712554, 7344813092, 226281470, 2860379596815,
  3856240650273, 111575211315, 167362816965, 148788205719, 5590664745,
  4907919579, 724100397, 1840657246576, 110399683714, 355645985956,
  395171240974, 138379047136, 17820243646, 11153719096, 389447566,
  6178534718417, 1082845843235, 836833216085, 334773462743, 83915770049,
  56605479587, 245666645, 804849515 ]: Check := false );
  print "A split extension with factorized order", FactoredOrder( G );
  print "is defined";
  Gn :=  \[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 19 ];
  return G, Gn;
end function;


function G9()
  print "\nConstructing the Borel subgroup G of GL(5, 3) which has order 
2^5*3^10. There is a monomorphism from G into GL(5,3) given by\n
     (G.1,...,G.5,G.6,...,G.15) -> (I+E_11,..,I+E_55,I+E_12,...,I+E15).\n";
  G := PCGroup( \[ 15, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5765, 2900,
  10101, 5076, 17406, 17317, 8692, 19897, 29213, 14648, 22388, 777609, 194439,
  37914, 1283065, 320815, 761890, 41710, 2099561, 524951, 831161, 89246,
  27293772, 3411777, 158082, 44089948, 5511313, 9644758, 283435214,
  17714774 ]: Check := false );
  print "A group with factorized order", FactoredOrder( G );
  print "has been defined";
  Gn :=  \[ 1, 6, 10, 13, 15, 16 ];
  /* Could also take Gn := \[ 1, 2, 3, 4, 5, 6, 10, 13, 15, 16 ]; */
  return G, Gn;
end function;


function G10()
  print "\nConstructing the Borel subgroup G of GL(4,8) which has order 
2^18*7^4. There is a monomorphism from G into GL(4,8) given by\n 
    (G.1...,G.4,G.5,G.6,G.7...,G.22) -> (I+(W-1)*E_11,..,I+(W-1)*E_44,\n
	I+E_12,I+W*E_12,I+W^2*E_12...,I+W^2*E14)\n
 where W satisfies W^3+W^2+1=0\n";
  G := PCGroup( \[ 22, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
  2, 2, 2, 1584664, 75486, 316937, 181131, 739514, 264138, 2897693, 138035,
  91615, 90933, 90603, 543342, 310516, 206016, 204454, 127652, 1207391, 431253,
  457697, 285239, 199021, 4553526, 216908, 126004, 125058, 124596, 827959,
  473165, 274725, 272635, 170225, 1793848, 640718, 595046, 370844, 258754,
  2271768589, 15454265, 160393, 159183, 158589, 405672974, 33116218, 343434,
  340816, 212798, 865435663, 44154939, 732395, 456449, 318487, 3152658470,
  21446738, 13787240, 13021310, 12638356, 556351527, 45416531, 29196393,
  27574399, 17031317, 1174519848, 59924564, 61636714, 37666944, 25682070,
  207704555539, 201850965, 36348297236, 423886934, 76158337045, 555090007 ]: Check := false );
  print "A group with factorized order", FactoredOrder( G );
  print "has been defined";
  Gn :=  \[ 1, 5, 14, 20, 23 ];
  /* Could also take Gn := \[ 1, 2, 3, 4, 5, 14, 20, 23 ]; */
  return G, Gn;
end function;


function G11()
  print "\nConstructing the group G = Aut(F).F*.F+ where F=GF(2^13) and 
F+,F*,Aut(F) denote the additive, multiplicative and automorphism groups of F. 
Note that |G| = 13*8191*2^13.\n";
  G := PCGroup( \[ 15, 13, 8191, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 781,
  737207, 25555923, 1965858, 127779604, 4914619, 613342085, 11795060,
  2862263046, 27521781, 13084631047, 62906902, 58880839688, 141540503,
  862512309, 314534424, 3795054130, 691975705, 16560236171, 1509765146,
  71761023372, 3271157787, 126543332383, 7045570588, 149358379964, 49760354 ]: Check := false );
  print "A group with factorized order", FactoredOrder( G );
  print "has been constructed";
  Gn :=  \[ 1, 2, 3, 16 ];
  return G, Gn;
end function;


function B26()
  print "\nThe following is a pc-presentation of the two generator Burnside group
B(2,6) of exponent 6 and order 2^28*3^25.\n";
  G := PCGroup( \[ 53, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
  3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
  2, 2, 2, 2, 2, 2, 2, 2, 7340029818406864600832, 20861889765461029952781,
  4388385445115933197194, 22625802303084004790126, 13948852280167437246163,
  36102641442251594553, 24486305337583516863571, 14584687009027498819184,
  3615046079512556341753, 111808714404982091886, 4207554747299148529504,
  2153320301151749470377, 12900530524500564008780, 2454406165128226921033,
  1307273154161475177261, 71140141826079638047277, 34815178976484606990538,
  12461529577092929408235, 3706322484621406344032, 1579562895997421003143,
  304196498536564204020, 41304104691901461212774, 13361607812173421734321,
  17154549257633550613795, 6686580303080088259188, 966019043679722614352,
  666581748752117940901, 169206610670529488730, 14629148867555057001031,
  3071827876379043963948, 19590397630103929720505, 7732893562221616279366,
  1210438359764092264035, 312278464362378037448, 30250760248991295157,
  71060951813440955922, 44007232388836001995988, 5193568646879689826845,
  22039197330923816852607, 6444872160980146015703, 2595762743080621318069,
  477469892706749482062, 235647150358599560261, 76299774116530654117,
  3494792038478236200, 118873394637749830758969, 44747201534538642352082,
  1225418165263347093925, 655133572688627140998, 1854843678520877711111,
  1102266091060910918464, 194486203312668139377, 69251631305200495040,
  23033777321426032843, 11595404250068158836, 51537731404539565989946,
  371213975627088518889, 26936796741392907049049, 7690150148617965121603,
  2820260405161439870775, 1201026794738067562694, 275795610534964143193,
  97795336708467289173, 4355408948705229035, 7855765014868106350,
  227416113863302563, 10907701307610363226667, 31933764383420060308000,
  1450846993135676797377, 3797514598164086153582, 1050148089535963910119,
  391418666445841058724, 132537727627867130333, 37711988299479734914,
  12505071484359411483, 5767796235960697484, 1604192448064204261,
  467410768101928782, 81906786513605280386964, 45712071539062192558073,
  155675571762707087833, 6745200979433200959807, 1856153471457230568080,
  906439603772084770483, 204380853983877858279, 68127039415755870296,
  22709013138585290407, 6340180553653272672, 2523223682065032761,
  704464505961475282, 3055578810595335, 88038395138504645672557,
  59493984963911462854578, 167565538168739489639, 7325053029302886448120,
  668499060149054709597, 65652236301880718558, 76345886230048230217,
  25448628743349410346, 8482876247783137091, 873415143072826942,
  942541805309237949, 97046127008092424, 21311522803692,
  175630947274528678423814, 6076235039723844946627, 205454915489898207570,
  11380123795676373971813, 3446730392028271892596, 1118373527024508873339,
  380449393806154690862, 126816464602051563895, 42272154867350521608,
  793435119766216646, 4696906096372280674, 88159457751802392, 338022248232051,
  2986232788435932202191, 1153388689506542531012, 3038552446998009289,
  94135016181485095518, 1203685317333444688067, 14052641507495237656,
  133742481876214140717, 44580827292071380514, 14860275764023793815,
  697333058489591052, 1651141751558199809, 77481450943288438, 1878809745402,
  109983448268097608421160, 6423685989354203428275, 34628001835861283126,
  12818888231957908059433, 3913591444806991201680, 1252700082366483104237,
  434843142009055993450, 144947714003018664759, 48315904667672888564,
  169053992548666036, 5368433851963654782, 18783776949852326, 41909769765783,
  163640729309495217752465, 10719488067352231985350, 13577150146802511738182,
  3535661493807879868087, 362421533298955354032, 392851277089764430097,
  130950425696588143642, 43650141898862714859, 8613773481515780996,
  4850015766540302149, 957085942390642878, 2566407243186,
  119359389976798056921882, 50115629690708409731681, 9935032709245012522494,
  1801937193708744682484, 205183014971498722336, 200215243745416076142,
  66738414581805358991, 22246138193935119976, 372951000118912356,
  2471793132659458274, 41439000013213030, 36628804260, 181771679957974575248899,
  26738629107794883139752, 15082666661601090469618, 6256329134123045505831,
  524612484307706178524, 695147681569227278737, 231715893856409093190,
  77238631285469698043, 8706480774688506736, 8582070142829966949,
  967386752743167962, 288416705886, 63533182282113925012988,
  19841955611552682784921, 5294479636998357792830, 6825773682987881044921,
  439761212513556492984, 758419298109764560859, 252806432703254853898,
  84268810901084951613, 54962350075779356, 9363201211231661791,
  6106927786198254, 564719472, 132932978909982318393237,
  25209302866327237172798, 11165525372814931838196, 2834957966603193372977,
  1486774692421514524006, 314995329622577041755, 104998443207525680864,
  34999481069175227269, 1149764384468391420, 3888831229908359087,
  127751598274266262, 226568682792, 75192953404210043490490,
  39058801802205177596961, 6266079450035993240326, 3870669375260239595976,
  370317863250131082488, 430074375028915510978, 143358125009638503939,
  47786041669879501628, 10326732882481287724, 5309560185542167350,
  1147414764720143630, 12625954596, 150322159822139682658007,
  63447918523342829532364, 12447373658756056007006, 2736152969329299254491,
  1652462530425150266664, 304016996592144361925, 101338998864048120922,
  33779666288016040623, 10659132453963921332, 3753296254224005017,
  1184348050440436254, 31419609642, 151053952389518404062924,
  28432576502415778922177, 12687486676498507712358, 3842840842809198480461,
  1689609212702858553364, 426982315867688720367, 142327438622562907070,
  47442479540854302673, 1311011824901657901, 5271386615650478579,
  145667980544629207, 9535183596, 513214470665644075873, 403598751195438550518,
  146203537798199443720, 1450717505525704773477, 1509713970952568570570,
  161190833947300530703, 53730277982433510516, 17910092660811170489,
  11369733271582323724, 1990010295645686115, 1263303696842480966, 3759233580,
  335226983236454931074, 480524504906065184575, 27977071658161421975,
  264882034043190405688, 202946521747298385, 29431337115910045394,
  9810445705303348747, 3270148568434449900, 2186178951583493,
  363349840937161606, 242908772398719, 443583, 340477383048009355035,
  21445613960924914579808, 28373115254000779770, 3570814561675805982959,
  195547161618213834532, 396757173519533998425, 132252391173177999758,
  44084130391059333571, 28700605723346424, 4898236710117704237,
  3188956191483490, 344677738378770958780, 21955611983819083953111,
  28723144864897580083, 3129367706523577221360, 202611248012726399525,
  347707522947064136026, 115902507649021378959, 38634169216340459972,
  25152453916888825, 4292685468482273838, 2794717101877091,
  359322220477912766429, 22800991423257084324502, 29943518373159397388,
  3315756378698962698481, 209588262761908495014, 368417375410995855707,
  122805791803665285520, 40935263934555095493, 26650562457393146,
  4548362659395011119, 2961173606377572, 490017505230826878, 236656181503524413,
  40834792102569093, 973145067357802070258, 158389496640267559,
  108127229706422452572, 36042409902140817809, 12014136634046939590,
  7821703537791483, 1334904070449660464, 869078170866277, 376747300443980233759,
  24132666623901120445332, 31395608370331686334, 4708766454957106790643,
  223584657192841789736, 523196272773011865949, 174398757591003955602,
  58132919197001318855, 37846952602214908, 6459213244111258161,
  4205216955802214, 389137127218467591776, 24427767811164162673,
  32428093934872299503, 1402820006372638064884, 252912260764298025,
  155868889596959785310, 51956296532319928723, 17318765510773309896,
  11275237962743549, 1924307278974812722, 1252804218083175,
  400245148671354077217, 25640704836758620569686, 33353762389279506624,
  2868423565478037553397, 237413933673690931498, 318713729497559728479,
  106237909832519909780, 35412636610839970249, 23055101960182782,
  3934737401204441651, 2561677995576424, 105888385655847938949154,
  6618024103490496184407, 8824032137987328245953, 5882688091991552164086,
  488554957056205025579, 653632010221283574112, 217877336740427858325,
  72625778913475953098, 47282408146794751, 8069530990386217524,
  5253600905199977, 217403747225369620512803, 13587734201585601282136,
  18116978935447468376258, 23543832274785534199, 125812353718385197356,
  2615981363865059681, 871993787955020182, 290664595985007051,
  97077433424680448, 32296066220556853, 10786381491631722,
  7404535250420050427940, 27222556067720773721, 617044604201670869187,
  24215735248798734491, 4285031973622714669, 2690637249866526381,
  896879083288842416, 298959694429614463, 199353566310970113, 33217743825513233,
  22150396256775019, 2236664066104625725477, 57286558393104726392922,
  186388672175385477316, 24861303174825942765, 8542814141371834670,
  2762367019425105079, 920789006475035316, 306929668825012097,
  409283253265780738, 34103296536112971, 45475917029531756,
  4131942564224861208614, 117559504761314280357979, 344328547018738434245,
  25515937183117369966, 2391170465407906095, 2835104131457485880,
  945034710485828917, 315011570161943298, 839902726061059331, 35001285573549772,
  93322525117896045, 588595806869638348839, 36787237929352396892,
  49049650572469862598, 26183763663344182331, 35152249576936735024,
  2909307073704909477, 969769024568303450, 323256341522768143,
  1722667125944125956, 35917371280308089, 191407458438236782,
  512814096735172411432, 32050881045948275805, 42734508061264367815,
  26836721169907058316, 71782801122515964209, 2981857907767451254,
  993952635922484043, 331317545307495008, 3531252090816472837,
  36813060589722186, 392361343424053103, 556223037491808239657,
  34763939843238015070, 46351919790984020168, 27474510327497328061,
  18597992508728156466, 3052723369721925671, 1017574456573975516,
  339191485524658833, 7234539607294788614, 37687942836073723,
  803837734143865968, 508169707946591671338, 31760606746661979551,
  42347475662215972809, 28135531009040378942, 300945365844217795,
  3126170112115597992, 1042056704038532957, 347352234679511314,
  14813355070239858951, 38594692742168444, 1645928341137762673,
  518470134566810342443, 32846979866763167520, 43205844547234195402,
  28803896364822797055, 302089644801800372, 3200432929424755561,
  1066810976474918814, 355603658824973267, 30315472112628071944,
  39511517647219773, 3368385790292008562, 530770867249437550124,
  33561169603125985537, 44230905604119796043, 29487270402746530816,
  315541575338032749, 3276363378082948202, 1092121126027649695,
  364040375342550228, 236543453764361, 40448930593617214, 26282605974387,
  541937805763070264013, 34901891985473086562, 45161483813589188868,
  30201300472278058241, 2567463084507124556086, 3355700052475340139,
  1118566684158447008, 372855561386149333, 333419496720768, 41428395709572671,
  37046610747322, 554098969676795582962, 34850159932134934755,
  46174914139732965448, 30977919939675497730, 320185219014734135,
  3441991104408388972, 1147330368136129953, 382443456045376982, 295309718058817,
  42493717338375744, 32812190895995, 565483075039337413295,
  35867556981118586980, 47123589586611451310, 31882272872105410819,
  1339709455969393508664, 3542474763567268205, 1180824921189089698,
  393608307063030231, 303564098997452, 43734256340337217, 33729344333622,
  74410281904459680055344, 4650642619028730003557, 6200856825371640004815,
  33047202073201570052, 337884952541759971, 3671911341466841454,
  1223970447155614115, 407990149051871704, 378305259735333, 45332238783541826,
  42033917748943, 19423661626698065510449, 1213978851668629094502,
  1618638468891505459408, 34743502488832819461, 344946883434050114,
  3860389165425869167, 1286796388475290020, 428932129491763673, 377812460873326,
  47659125499085379, 41979162319832, 39023901995457022525490,
  2438993874716063907943, 3251991832954751877329, 37522982687939444998,
  355662856288271826, 4169220298659938672, 1389740099553313189,
  463246699851104730, 301592903549423, 51471855539012164, 33510322617177,
  1836418917433271648307, 114776182339579478120, 153034909786105970898,
  42509697162807214343, 1062742429070180668, 4723299684756357489,
  1574433228252119462, 524811076084040155, 341673877659408, 58312341787116101,
  37963764184954, 935867332922724974644, 58491708307670311017,
  77988944410227081427, 51992629606818054408, 1805299639125627197,
  5776958845202006386, 1925652948400669095, 641884316133556700, 417893434983313,
  71320479570395718, 46432603887611 ]: Check := false );
  print "A group with factorized order", FactoredOrder( G );
  print "has been constructed";
  Gn :=  \[ 1, 3, 8, 18, 28, 54 ];
  return G, Gn;
end function;


function F2332()
  print "\nIf F denotes the free group of rank 2, then below is a pc-presentation for
the group G = F/(F^2)^3 x F/(F^3)^2 of exponent 6 and order 2^30*3^28. The
subgroup <G.1*G.4*G.28*G.31,G.2*G.6*G.29*G.32*G.58> is a 2-generator subgroup 
of exponent 6 and order 2^28*3^25, and hence it is B(2,6). A pc-presentation
for B(2,6) may be found above in procedure B26. Note that <G.1,...,G.27>
and <G.28,...,G.58> are the two direct factors.\n";

  G := PCGroup( \[ 58, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
  2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 232, 37817, 755, 67920, 85379, 57191,
  31324, 11431862, 214140, 212458, 1027301, 6327, 2292745, 2286539, 2284509,
  69993604246, 11651523668, 71954690, 71932824, 71925574, 71923196,
  2157487420615, 87365399660417, 739778639, 739770345, 739767619, 13699376,
  5034517806, 4993546664, 7490143846, 7490134508, 801765817169049, 22832347,
  8323634645, 74901341819, 74901310557, 1860418, 382627963658624, 18310600822,
  54928081340, 247174324018, 8881249547, 3044373, 29974217311, 539290843083,
  808934150519, 1168816378404, 5258248968562, 292159571780, 876359987286,
  2629035988380, 139859159341, 909693006479279, 69955822879, 209739607553,
  1887517950243, 2619070631386574, 24971326452, 112814295610, 2022386325456,
  6067021982254, 319773692175, 1438372753993, 1080058173251, 3236229101565,
  19414470342545, 27504244135024, 56597839634, 30946440782040, 30943296777142,
  30942248775548, 263712477816449, 393141914781627, 10246497093090,
  53794109738704, 150534957293299, 57324457421357, 3775025244836,
  696492157668630, 439420927989, 1370444019100279, 3016155289054558,
  18605481563816, 1419649176193367, 19654099687377, 4660524993624,
  78687971097382, 3549868624482361, 86552607107, 48536038861946, 12134009715564,
  21778, 98688, 131110, 2763440, 202045, 268919, 5703345, 53276, 552888,
  11761330, 436176447, 1137529, 24233651, 898008640, 2340218, 49890996,
  230917697, 4812411, 102631093, 1944210900546, 20974, 210962102, 3993514280515,
  41333, 433325751, 1024651691588, 83094, 889456312, 64144965, 85526143,
  1824523961, 131495494, 175326848, 3740272314, 33676871, 359204481, 7662995131,
  282436044360, 735512194, 15690892988, 578008647241, 1505232515, 32111593149,
  147786303050, 3078882948, 65682802366, 9222219, 12295813, 134284838591,
  18843724, 25124486, 274408146624, 4812365, 51316359, 560493233857,
  40230717006, 53640955528, 10256, 82103502415, 109471336073, 19131,
  20936394320, 223321523850, 37228, 1304529, 455400752779, 74117, 2657554,
  928316917388, 149286, 678131, 1891664660109, 302407, 5644617300, 7526155918,
  614216, 11494491733, 15325988495, 1248969, 2924938838, 31199331984,
  2540746 ]: Check := false );
  print "A group with factorized order", FactoredOrder( G );
  print "has been constructed";
  Gn :=  [Integers()| ]; /* I'll work this out later */
  return G, Gn;
end function;

print "For a summary of the contents, type
	?solgps\n";
