col1.z

#############################################################################
##
#W  col1.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1012 ] :=
[ 371056384339497, 1823463935017, 1093732138189, 2551711491625,
2604688172664555, 30344819691, 1823261299419, 659665115, 25127857768155,
2526216923, 1086948311, 2573783790555, 219 ]; 

PROPERTIES_SMALL_GROUPS[ 1012 ] := rec(
isNilpotent := [ 6, 13 ], 
isAbelian := [ 6, 13 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -13 ], [ 1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1014 ] :=
[ 90954183275028624671, 88459862344991, 10798024885, 121628381967647,
123332868528602399, 10700063, 23599405566330698015, 86243844383,
89687489290039583, 88836026922823967, 88450604716319, 87610898239775,
1135403096961311, 1119727411487, 23888159, 21810954527, 22639067423,
117448991, 119939346719, 11282101, 118559159879, 121619283425567, 287 ]; 

PROPERTIES_SMALL_GROUPS[ 1014 ] := rec(
isNilpotent := [ 6, 23 ], 
isSupersolvable := [ 1, -6, 8, -23 ], 
isAbelian := [ 6, 23 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, 9, -14, 16, -17, 19, -20
, 22, -23 ], [ 1, -6, 8, 15, 18, 21 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1020 ] :=
[ 263144191562511, 52656434323203, 269004195771715647, 17575141457665,
268407813792870431, 53709682930413587, 274384283861825618239, 4380867690815,
[ (1,2,3,4,5), ( 3, 4, 5)( 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,
     22) ],
268319620867298063, 53639425788223235, 279870660572382743236671,
279870660870281674887231, 930070553867783770175, 273686601647583662143,
273686005265604816927, 54712205666470129683, 285468073783828003087712575,
285468074087684913371283775, 948671964947124224786751,
279160333680330218144063, 893955164078399, 298157300777759,
913060484146528575, 52657439903507, 911835043842752831, 1519548280059461951,
931321693748324204863, 52587780980480, 257832255807, 51673825779,
263728373170495, 17314087921, 263144257618719, 52656500379411,
269004195804217663, 319 ]; 

PROPERTIES_SMALL_GROUPS[ 1020 ] := rec(
isNilpotent := [ 8, 37 ], 
isSupersolvable := [ 1, -8, 10, -28, 30, -37 ], 
isSolvable := [ 1, -8, 10, -37 ], 
isAbelian := [ 8, 37 ], 
lgLength := rec( lgLength := [ 4, 5, false ], pos := [ [ 22, -37 ], [ 1, -8,
10, -21 ], [ 9 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17 ], pos := [ 1, 2,
3, 4, 5, 6, 7, 8 ] ) );

SMALL_GROUP_LIB[ 1026 ] :=
[ 334922502662007301871, 326499891649550063, 34473882123830466313759,
554626121513019119, 35340449988572418898677151, 605273205315311,
205937729786229900584687, 200719099590968317679, 326435188242021551,
334987616882143501487, 334987617470358461615, 326435188238242415,
334987616882139722351, 326498654016522287, 1003138093162428031423,
1029251232024540671377855, 1029217795236886815441343, 326499891762924143,
334987681585721091119, 1029219424678236350065087,
1055977457654138962009999807, 1056011763798271818200861119,
334922502662120675951, 343697294920109273134127, 318226235911343,
326498715699580079, 326499303914540207, 318226232132207, 326498715695800943,
318226712082479, 540569797786799, 604035572287535, 619740341649218735,
32748311026773343, 31856729548447, 32621319465092191, 66906323619706105183,
35100692549656766911, 554626121626393199, 635853591545429603375,
34341244825406331357631, 33600020865978378655, 32685035153944735,
36013315923617917909951, 35100666018330736447, 588218745455, 588698695727,
604097251566191, 334857259050531607151, 334857323746316618351,
343563547769501048642159, 326371676260024943, 318164552853551,
318226349285423, 326435188355395631, 326499891819611183,
334922502662177362991, 311521744943, 526539466799, 31200553279,
540569911160879, 31856846701663, 554626121683080239, 32685031525974175,
569046405706954040879, 6191 ]; 

PROPERTIES_SMALL_GROUPS[ 1026 ] := rec(
isNilpotent := [ 6, 46, -48, 66 ], 
isAbelian := [ 6, 46, 66 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 53, 58, -59, 64, -66 ],
[ 9, -14, 19, 24, -33, 36, 40, 42, -49, 52, 54, -57, 60, -63 ], [ 1, -8, 15,
-18, 20, -23, 34, -35, 37, -39, 41, 50, -51 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 35, 38
, 41, 44, 47, 50, 53, 56 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 14, 19, 24, 30,
33, 37, 41, 43, 45, 48 ] ) );

SMALL_GROUP_LIB[ 1032 ] :=
[ 11860858522553703916721, 79911915605199328433, 2287119629227236553,
93594780304513197233, 96589908828680677952051, 285612125314781747,
85103302991370434467590893, 79907404419498424397, 82464440883575522443853,
79907404419367733165, 79907404421328101645, 98151407853401141651,
98151407853270450419, 101292253094425944662579, 98151407855230818899,
101292253094427905031059, 101292253094427774339827,
104533605193637158075968563, 77434383754487885, 77434385584165133,
82469001838497729061613, 2442888516030276153333816,
2676904824453970935991143306, 96589718328517581730541, 90692455110064205,
93594688232670872141, 90692454979372973, 90692456939741453,
2360300816569195497061, 2216205715098565, 2287113207187822021,
2216205584407333, 2216207544775813, 99680785626388723867194419,
93594872386026527123, 96589908552462014604179, 93594872385895835891,
93594872387856204371, 276220754407667, 276222714776147, 294466929459666197555
, 4713749148399838403724, 4864589474237928284307948, 77430653042577491,
196406209960415023505, 82665122896296960971153, 95107769251762259,
76014202650707, 6631636956216300, 80101863420492349841, 87807779426387,
2157973624507, 90692463212918867, 83 ]; 

PROPERTIES_SMALL_GROUPS[ 1032 ] := 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[ 1035 ] :=
[ 13793238755, 11219 ]; 

PROPERTIES_SMALL_GROUPS[ 1035 ] := rec(
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 2 ], [ 1 ] ] ),
frattFacs := rec( frattFacs := [ 3 ], pos := [ 1 ] ) );

SMALL_GROUP_LIB[ 1036 ] :=
[ 4460685586997, 31214146673267, 32469877803831767, 222732198359,
32331594373585523, 33495663347638882775, 164850843672791, 30152466647,
4353565937, 31341446443223, 215 ]; 

PROPERTIES_SMALL_GROUPS[ 1036 ] := 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[ 1044 ] :=
[ 322394022909421651805, 8306588864762489335, 360991539179149240930821,
8610660562833223, 8666529704755543026167, 28327151588691252032946934277,
347926321962932860421, 922298542289980240, 7956481515746119,
308806536361816781, 345777042212341872133, 8177334252359, 7956481464136939,
295229698950257, 8306588865829532151, 308220028929746781,
8672078846057518145351, 73595405901639, 8301273783198872811,
8666529704756610068983, 9047857011762454633324359, 335938565455906446026589,
9867899329883171319226580541255, 10170847504878381347102728007,
8544689418797895, 8938314775966909255, 295246203671245, 8920668797306241863,
9331600634558228562759, 883429944002928, 7615518999367, 284177597957,
7956482548368199, 295230783181517, 8306588866363032391, 839 ]; 

PROPERTIES_SMALL_GROUPS[ 1044 ] := rec(
isNilpotent := [ 4, 12, 18, 36 ], 
isSupersolvable := [ 1, -7, 9, -21, 25, -29, 31, -36 ], 
isAbelian := [ 4, 12, 18, 36 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 26, -31, 34, -36 ], [ 7,
-13, 16, -19, 21, -25, 32, -33 ], [ 1, -6, 14, -15, 20 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 46, 50
, 23, 27, 31, 35, 39, 43 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
13, 14, 15, 16, 17, 18 ] ) );

SMALL_GROUP_LIB[ 1050 ] :=
[ 422051823299291, 2212691789271807717, 2323314594078724181733, 402216057563,
669753256667, 423923860618401, 445976862720200421, 134155300879,
703242518333375, 445123262675127153, 468275728729886225637, 891845339,
3099075866323304814705, 1790004327090818279717793, 401962217819, 404000151899
, 422053607393627, 424204661744987, 443156291221460315, 21633755711164763,
447378526748528987, 1769945524664076705, 13009097347587731469659,
487289169086352196955, 500811506962947739432283, 390168923, 670401184161,
426074800693595, 638005595, 383201637, 671537351003, 403228772769,
705126029497691, 128398099, 669753723647, 401954753349, 705117111359171,
423391830120561, 740382351440509787, 347 ]; 

PROPERTIES_SMALL_GROUPS[ 1050 ] := rec(
isNilpotent := [ 12, 40 ], 
isSupersolvable := [ 1, -12, 15, -19, 26, 29, -40 ], 
isAbelian := [ 12, 40 ], 
lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 13, -15, 18, -29, 32, -35,
38, -40 ], [ 1, -12, 16, -17, 30, -31, 36, -37 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 ]
, pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ] ) );

SMALL_GROUP_LIB[ 1060 ] :=
[ 11923439864755, 202574821314787, 215150672207987151, 992047370703,
214634019500118243, 12622738540121011, 241742302426684652093903,
241742302636997144576463, 709136079707904213455, 227512480048595419599,
631129100280015, 191154888911, 11464616543, 202971747004623, 207 ]; 

PROPERTIES_SMALL_GROUPS[ 1060 ] := rec(
isNilpotent := [ 4, 15 ], 
isAbelian := [ 4, 15 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 11, -15 ], [ 1, -10 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1062 ] :=
[ 6565552729388159, 351079011133879, 8058478989508710319, 341871347639,
330622750615, 6156180495, 351079169564823, 6171202322495, 372846527384307991,
3479 ]; 

PROPERTIES_SMALL_GROUPS[ 1062 ] := rec(
isNilpotent := [ 4, 10 ], 
isAbelian := [ 4, 10 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, 8, -10 ], [ 1, -4, 6, -7
] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );