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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346############################################################################# ## #W col10.z GAP library of groups Hans Ulrich Besche ## Bettina Eick, Eamonn O'Brien ## SMALL_GROUP_LIB[ 450 ] := [ 1542428603656437, 4640860222466143, 932270914644434212983, 7633639543, 10313021988959, 7600214141, 4641018414866527, 3420186675445, 2088458822682402911, 16785503, 6813009225418855336031, 3458209759522130015, 74765567527007, 22733260919, 10305824557151, 3427618988277, 1559521113903325, 701883584067389565, 16779389, 33644490004791391, 15140020500511244383, 7684910577549407, 17077949202527, 3458209759522160735, 166146343007, 50462815 , 22901096543, 16908413, 22733324407, 10305824587871, 7600275701, 10230159343831, 4637622219817055, 95 ]; PROPERTIES_SMALL_GROUPS[ 450 ] := rec( isNilpotent := [ 4, 10, 19, 34 ], isSupersolvable := [ 1, -10, 14, -19, 26, -34 ], isAbelian := [ 4, 10, 19, 34 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 21, -22, 25, 27, 31, 33, -34 ], [ 5, 8, -13, 15, -16, 18, -20, 23, -24, 26, 28, 30, 32 ], [ 1, -4, 6, -7, 14, 17, 29 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 23, 27 , 31, 35, 39, 43, 47, 51, 55 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 ] ) ); SMALL_GROUP_LIB[ 456 ] := [ 17722499118221185145, 38893951537954937, 6479962004274409, 109705619604951161, 50026034180936587139, 14179093424748, 8081459329282147377845, 38865135045852053, 17722498535835536789, 38865135043962485, 38865135072306005, 122552823510891107, 122552823509001539, 55884088733651390339, 122552823537345059, 55884088733679733859, 55884088733677844291, 25483144463756887630211, 85298912668565, 85298939122517 , 17735373384642843317, 1353294709785538463448, 626678610257804180125698, 50025494787727450805, 240580164336533, 109705031414549909, 240580162446965, 240580190790485, 2954820300982089445, 14210280738757, 6479869152698821, 14210278849189, 14210307192709, 22811870783426041457027, 109706207935169123, 50026032416320050275, 109706207933279555, 109706207961623075, 30960572310, 30988915830, 6451572677268438, 2685970363004816392332, 1224802486430563681352268, 85244973060131, 367201951860000473, 17858220836570695385, 268753528737827, 201231433763, 28330096520268, 39162767216473817, 526539460643, 31200547123, 240580281489443, 35 ]; PROPERTIES_SMALL_GROUPS[ 456 ] := rec( isNilpotent := [ 6, 39, -41, 54 ], isSupersolvable := [ 1, -21, 24, -41, 44, 47, -48, 51, -54 ], isAbelian := [ 6, 39, 54 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 44, 47, -48, 51, -54 ], [ 7, -43, 45, -46, 49, -50 ], [ 1, -6 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 35, 38 , 41, 44, 47 ], pos := [ 1, 2, 3, 4, 5, 6, 11, 18, 21, 22, 23, 28, 33, 38, 41 ] ) ); SMALL_GROUP_LIB[ 459 ] := [ 15502483217, 33624561, 34083313, 15435633137, 4383 ]; PROPERTIES_SMALL_GROUPS[ 459 ] := rec( isAbelian := [ 1, -2, 5 ], lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 5 ], [ 2, -4 ], [ 1 ] ] ), frattFacs := rec( frattFacs := [ 4, 8 ], pos := [ 1, 4 ] ) ); SMALL_GROUP_LIB[ 460 ] := [ 166123355335, 1161377766097, 536781930956391, 120175242, 76193162284231, 806068389331815015, 3809407354455, 2526216791, 367313873, 1166898475863, 87 ] ; PROPERTIES_SMALL_GROUPS[ 460 ] := rec( isNilpotent := [ 4, 11 ], isAbelian := [ 4, 11 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -11 ], [ 1, -6 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) ); SMALL_GROUP_LIB[ 462 ] := [ 26066880159, 7123520195, 12042737760159, 6400195, 46400159, 25920195, 21571040159, 5440591, 21345760519, 11863520915, 9965993520159, 159 ]; PROPERTIES_SMALL_GROUPS[ 462 ] := rec( isNilpotent := [ 12 ], isAbelian := [ 12 ], lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ), frattFacs := rec( frattFacs := [ ], pos := [ ] ) ); SMALL_GROUP_LIB[ 464 ] := [ 762318208315179156507, 60970819020322624, 353206847199146209461275, 1642927104900573211, 762314397709756229659, 353715637290769283475483, 353715637298946548885531, 164124055706717925716624411, 1642927104883362843, 762314397709739019291, 1642927104848942107, 762318183783589450779, 762314397709704598555, 1642927105107097627, 379797930563934439452699, 176226239781670282966092827, 176226239781670282983303195, 81768975258695015991375922203, 1642927105089887259, 131400247551664, 261954760388272, 121677991603201712, 131400350813872, 60839419030376112, 28229490522745336496, 13098483598054777982640, 6077696389492909974603440, 353206843388593398629403, 163887975328495726317929499, 761221653448647365659, 353206843388593605153819, 761221653448681786395, 353206843388593639574555, 761221653448888310811, 762314389532748975131, 3540758194319387, 1642918928151474203, 1642918928117053467, 3801871075115035, 818530014579389020187, 818530014578907129883, 379797926769683048245275, 3540758142688283, 3540758676209691, 281991880436, 282250035956, 60839136952424180, 131118565438196, 1640564016098352155, 7615518998555, 27 ]; PROPERTIES_SMALL_GROUPS[ 464 ] := rec( isNilpotent := [ 2, 20, -27, 45, -48, 51 ], isAbelian := [ 2, 20, 23, 45, 51 ], lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 50, -51 ], [ 11, -14, 19, -22, 30, -31, 34, -49 ], [ 4, -10, 15, -18, 23, -29, 32, -33 ], [ 1, -3 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 22, 51, 55, 59 ], pos := [ 1, 2, 3, 19, 27, 34, 44, 48 ] ) ); SMALL_GROUP_LIB[ 468 ] := [ 845630571242678999, 1810824787880663, 421467260423206477, 9847203102288599, 209399455186277465365, 1920203452657, 2152148447785966987991, 1806903641714855, 4603084003697846999, 3020634793798072870468885, 453671893455483157, 3869963661479, 1791602169046992, 859074195514368971, 21040725307559, 900571040540221, 447434732341408021, 4077859093, 1806902876558171, 1810824803308247, 845630571258106583, 3869198504795, 21040724562779, 1920234805489, 9847203117716183, 898691604747853, 4608491513663868071, 4077114324, 4598607796397265755, 2154655797889639174871, 7168297250193575, 34849119009396683, 3861840789671, 3869978591399, 1806903656644775, 9835651309097819, 4600405210867487447, 2152989638663818595495, 196833237507908638285, 1197499997138368455134375, 472385228902601320215235751, 24848642212007, 11682558312579239, 5728152454717 , 34845347799171239, 5467437345173373095, 9172943015, 3828222615024, 1835628225550283, 44877349031, 4108714261, 21040740237479, 1920250480189, 9847203125428391, 167 ]; PROPERTIES_SMALL_GROUPS[ 468 ] := rec( isNilpotent := [ 6, 18, 28, 55 ], isSupersolvable := [ 1, -12, 15, -31, 33, -38, 42, -47, 50, -55 ], isAbelian := [ 6, 18, 28, 55 ], lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 32, -33, 43, -50, 53, -55 ], [ 8, 11, -19, 22, -23, 26, -29, 31, 34, -36, 38, -42, 51, -52 ], [ 1, -7, 9, -10, 20, -21, 24, -25, 30, 37 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 21, 25, 30, 34, 38, 42, 46, 50 , 54, 58, 62, 66, 70, 74, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 , 23, 24, 25, 26, 27, 28 ] ) ); SMALL_GROUP_LIB[ 472 ] := [ 73738818487282025, 2746434555476, 34804561128792224233, 156225245764697, 73738476717786329, 156225234448201, 156225313663673, 5805365754, 5884581226, 1293561441590426, 330622747193, 57 ]; PROPERTIES_SMALL_GROUPS[ 472 ] := rec( isNilpotent := [ 2, 8, -10, 12 ], isAbelian := [ 2, 8, 12 ], lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 11, -12 ], [ 3, -10 ], [ 1, -2 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 11, 14 ], pos := [ 1, 2, 7, 10 ] ) ); SMALL_GROUP_LIB[ 476 ] := [ 80096595717, 240151233807, 115401043279967, 33621488, 114231687054607, 54306940455551071, 1358121926751, 505413727, 169869557, 242433917023, 95 ]; PROPERTIES_SMALL_GROUPS[ 476 ] := rec( isNilpotent := [ 4, 11 ], isAbelian := [ 4, 11 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -11 ], [ 1, -6 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) ); SMALL_GROUP_LIB[ 484 ] := [ 5344510449170099, 2534430909, 11042376200099, 5160099, 22359370909, 11040466410099, 5130990, 2586271600565610099, 245376960099, 46400099, 22810080099, 99 ]; PROPERTIES_SMALL_GROUPS[ 484 ] := rec( isNilpotent := [ 2, 4, 7, 12 ], isSupersolvable := [ 1, -7, 9, -12 ], isAbelian := [ 2, 4, 7, 12 ], lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 9, 11, -12 ], [ 3, -4, 6 , -8, 10 ], [ 1, -2, 5 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 15, 19, 23 ], pos := [ 1, 2, 3 , 4, 5, 6, 7 ] ) ); SMALL_GROUP_LIB[ 488 ] := [ 93430683364320059, 3251469812400, 45513385872899040059, 45593976139596000059, 191455099200059, 93430278688320059, 191455086240059, 191455176960059, 6648483540, 6739203540, 1583454186723540, 93265137067680059, 391910400059, 59 ]; PROPERTIES_SMALL_GROUPS[ 488 ] := rec( isNilpotent := [ 2, 9, -11, 14 ], isAbelian := [ 2, 9, 14 ], lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 13, -14 ], [ 4, -12 ], [ 1, -3 ] ] ), frattFacs := rec( frattFacs := [ 4, 7, 11, 14, 17 ], pos := [ 1, 2, 3, 8, 11 ] ) ); SMALL_GROUP_LIB[ 490 ] := [ 978783477, 808303282127, 396114424016975, 668879, 3359375, 1648989071, 2032341, 1639699403, 808071707663, 143 ]; PROPERTIES_SMALL_GROUPS[ 490 ] := rec( isNilpotent := [ 4, 10 ], isAbelian := [ 4, 10 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 6, -7, 9, -10 ], [ 1, -5, 8 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) ); SMALL_GROUP_LIB[ 492 ] := [ 648890942401, 25203919361639, 12400448104960079, 1313283160, 12393892497921639, 6090497509747200079, 26491207680079, 1293803646400, 51200000079, 1392641561, 25203957760079, 79 ]; PROPERTIES_SMALL_GROUPS[ 492 ] := rec( isNilpotent := [ 4, 12 ], isSupersolvable := [ 1, -7, 9, -12 ], isAbelian := [ 4, 12 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -12 ], [ 1, -6 ] ] ), frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) ); SMALL_GROUP_LIB[ 495 ] := [ 7660811319, 5131391, 17921139, 1139 ]; PROPERTIES_SMALL_GROUPS[ 495 ] := rec( isNilpotent := [ 2, 4 ], isAbelian := [ 2, 4 ], lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 3, -4 ], [ 1, -2 ] ] ), frattFacs := rec( frattFacs := [ 3, 5 ], pos := [ 1, 2 ] ) ); SMALL_GROUP_LIB[ 496 ] := [ 1411913184690179700029, 98343184291083000, 2846599066398600029, 1411907038341078600029, 700308921264394566600029, 700308921276736633800029, 347353224953271523269300029, 2846599066374300029, 1411907038341054300029, 2846599066325700029, 1411913147664269700029, 1411907038341005700029, 2846599066690200029, 748401611735438895600029, 371207199420784789883100029, 371207199420784789907400029, 184118770912709262867678900029, 2846599066665900029, 198269410526100, 395344694726100, 196288635341726100, 198269556326100, 98144915244326100, 48679878072564026100, 24145219517172799526100, 11976028880510877603326100, 1411907025999375900029, 5739064455600029, 2846586725060400029, 2846586725011800029, 6133220467200029, 1508874204851731800029, 1508874204851051400029, 748401605613773224200029, 5739064382700029, 5739065136000029, 398155500870, 398520000870, 98144516967300870, 197871692400870, 11548915200029, 29 ]; PROPERTIES_SMALL_GROUPS[ 496 ] := rec( isNilpotent := [ 2, 19, -26, 37, -40, 42 ], isAbelian := [ 2, 19, 22, 37, 42 ], lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 41, -42 ], [ 10, -13, 18, -21, 27, -40 ], [ 3, -9, 14, -17, 22, -26 ], [ 1, -2 ] ] ), frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 47, 51 ], pos := [ 1, 2, 18, 26, 36, 40 ] ) );