col6.z

#############################################################################
##
#W  col6.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1272 ] :=
[ 10102655932966547393, 514441841964170832243, 654370444847068440910951,
1261836861697711207, 654127711280674714118515, 832050449168906363240406119,
534584020343390005351, 534584020343009801319, 679990874557005615225959,
534584020348712861799, 679990874557011318286439, 679990874557010938082407,
864948392437190878559575143, 16384356150349887323106496,
654369603292325554792131, 404434940630725315, 514441511818181751491,
404434940250521283, 404434945953581763, 12850554530279533295281,
7942359573529265, 10102637250113585841, 7942359193325233, 7942364896385713,
832359204586511329080810599, 514442172138294732903, 654370443856621349185639,
514442172137914528871, 514442172143617589351, 990453174989927,
990458878050407, 1603797621133681073255, 654369413787435955614823,
25670832889330228852304, 32653301018255958076227568, 1069618023800499610995,
514251347989750841027, 654127711610848457815143, 420269920725631079,
23777680331390960, 317741071990887, 6277928979037, 404434964203372647, 103 ];


PROPERTIES_SMALL_GROUPS[ 1272 ] := rec(
isNilpotent := [ 4, 30, -32, 44 ], 
isSupersolvable := [ 1, -13, 15, -33, 37, -39, 41, -44 ], 
isAbelian := [ 4, 30, 44 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 39, 41, -44 ], [ 7, -38,
40 ], [ 1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35, 38
], pos := [ 1, 2, 3, 4, 5, 6, 13, 14, 19, 24, 29, 32 ] ) );

SMALL_GROUP_LIB[ 1274 ] :=
[ 86714197375601, 148923008279, 111100389712354649, 138061079, 117449495,
53748569, 149475373847, 68001805937, 190435189046039, 791 ]; 

PROPERTIES_SMALL_GROUPS[ 1274 ] := 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 ] ) );

SMALL_GROUP_LIB[ 1275 ] :=
[ 570561343, 214315310899, 4927 ]; 

PROPERTIES_SMALL_GROUPS[ 1275 ] := rec(
isNilpotent := [ 1, 3 ], 
isSupersolvable := [ 1, 3 ], 
isAbelian := [ 1, 3 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 2, -3 ], [ 1 ] ] ),
frattFacs := rec( frattFacs := [ 3 ], pos := [ 1 ] ) );

SMALL_GROUP_LIB[ 1276 ] :=
[ 3617541313465, 10851324501163, 13939527009800727, 100391150103,
13839045358034091, 17658714913095422487, 104816274727191, 8516673815,
2852004605, 10924345012503, 279 ]; 

PROPERTIES_SMALL_GROUPS[ 1276 ] := 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[ 1278 ] :=
[ 20156722784858171, 1084905535705039, 29819424061982669731, 872859545039,
848993605039, 13061449731, 1084905871845039, 15748639538171,
1386510851121205039, 5039 ]; 

PROPERTIES_SMALL_GROUPS[ 1278 ] := 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 ] ) );

SMALL_GROUP_LIB[ 1284 ] :=
[ 83194329146773, 8721526279819613, 11198455149153916643, 20749187580899,
8887397446436563, 249059437076460, 6791116063443, 68678757755,
8721528173523923, 211 ]; 

PROPERTIES_SMALL_GROUPS[ 1284 ] := rec(
isNilpotent := [ 4, 10 ], 
isSupersolvable := [ 1, -5, 7, -10 ], 
isAbelian := [ 4, 10 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -10 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1287 ] :=
[ 27466431719, 1518229703, 85600199, 1991 ]; 

PROPERTIES_SMALL_GROUPS[ 1287 ] := 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[ 1288 ] :=
[ 701144625346136669, 2944110311506686189, 3804913646051303781027,
17536742703491747, 16111087077047514947, 16111087077042361315,
20751080164573369359011, 16111087077119665795, 20751080164573446663491,
20751080164573441509859, 26727391251979829349093539, 3792011580915667949993,
2285797585125449, 2944108369520178761, 2285797579971817, 2285797657276297,
903073515869561681881, 544366696799865, 701144034353173625, 544366691646233,
544366768950713, 4900728758616826405496995, 2954125481482374979,
3804913632457006908739, 2954125481477221347, 2954125481554525827,
13594379330531, 13594456635011, 22569828622715986083, 981079303367441608,
12508600720191619, 1773838905475, 422845198803, 2293566118463619, 131 ]; 

PROPERTIES_SMALL_GROUPS[ 1288 ] := rec(
isNilpotent := [ 4, 27, -29, 35 ], 
isSupersolvable := [ 1, -29, 31, -35 ], 
isAbelian := [ 4, 27, 35 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 30, -35 ], [ 5, -29 ], [
1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29 ], pos := [
1, 2, 3, 4, 11, 16, 21, 26, 29 ] ) );

SMALL_GROUP_LIB[ 1290 ] :=
[ 10341883466123, 10482034253963, 13340593483711115, 56159891339, 65420298635
, 4879142817, 84469402598027, 1692769639, 84332388403199, 6173754297777,
108965679382500107, 1931 ]; 

PROPERTIES_SMALL_GROUPS[ 1290 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1292 ] :=
[ 1042547839395, 1181539421981, 1545033400475183, 17360616239,
1346621059441059, 33037915708190188079, 19791906301727, 917070623, 809575233,
1195837883423, 287 ]; 

PROPERTIES_SMALL_GROUPS[ 1292 ] := 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[ 1300 ] :=
[ 27001520737901835879, 75858056263596143, 35425788320387489431095,
70223974825439, 98573858374599932015, 832576227907776126780276279,
45632569916066861527299687, 62047020905311191788010176055,
77830456937294151794125417578039, 77830441811829778951116296912439,
28221319023555392055, 58352179950047, 20770400538945111, 27250590511798530615
, 53000221151, 58352179208699, 15920184026739, 75995854264918127,
20749298691806823, 98795300796920909279, 1324980882911, 75826046769422843,
20675020261549683, 128432594081547732967535, 128432594150446725914735,
349393752299092631663, 98573996172601253999, 35066149376979845846631,
217053273002517778829230624223, 217053273002607692015026720223,
592617906197543161519820255, 35066149403479458518631,
217053273002518123324195360223, 592617906197887656484556255,
134373732547016070759, 168778825535208690765942239,
168778825535553185730678239, 2270665107186783055138271,
128146195713309431713247, 206741983592927, 269739602456740319, 15961191286359
, 268765166797554143, 350661483699141575135, 44877349343, 12262441527,
58458193330655, 15960968332887, 75996384264880607, 479 ]; 

PROPERTIES_SMALL_GROUPS[ 1300 ] := rec(
isNilpotent := [ 4, 15, 21, 50 ], 
isAbelian := [ 4, 15, 21, 50 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 41, -45, 48, -50 ], [ 11
, -16, 19, -22, 28, -40, 46, -47 ], [ 1, -10, 17, -18, 23, -27 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 46, 50
, 54, 58, 62, 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, 19, 20, 21 ] ) );

SMALL_GROUP_LIB[ 1302 ] :=
[ 2172018241079, 2224260001079, 2827863433441079, 16751033281079,
2828891148481079, 2862369005761079, 542168641775, 21809808459361079,
2828943390241079, 2862421247521079, 3683216103562081079, 3726804273740641079,
1762561079, 518401775, 2172873601079, 2198586241079, 12052801079, 2099521775,
15723318241079, 440645371, 15671892964559, 2702769146135, 20471799766321079,
1079 ]; 

PROPERTIES_SMALL_GROUPS[ 1302 ] := rec(
isNilpotent := [ 24 ], 
isAbelian := [ 24 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -24 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1305 ] :=
[ 45632698943, 22847 ]; 

PROPERTIES_SMALL_GROUPS[ 1305 ] := rec(
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 2 ], [ 1 ] ] ),
frattFacs := rec( frattFacs := [ 3 ], pos := [ 1 ] ) );

SMALL_GROUP_LIB[ 1308 ] :=
[ 5253399911050034939, 4016511831154427, 91324863421489, 9756517062164219,
12761541229397615063, 22777986413015, 16684322757766597689083,
4016394148847831, 12754510498903703291, 16682899703939844252119,
9938609122074839, 3099738046679, 273410394256368, 5263528447561298219,
7457656283351, 74010610981, 9756519102886103, 215 ]; 

PROPERTIES_SMALL_GROUPS[ 1308 ] := rec(
isNilpotent := [ 6, 18 ], 
isSupersolvable := [ 1, -12, 15, -18 ], 
isAbelian := [ 6, 18 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 8, 11, -18 ], [ 1, -7, 9,
-10 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1314 ] :=
[ 1497972507181724879, 1140039763113167, 23847364153368073, 1284676146050255,
36280839707520649273, 1004490994895, 1966720360996307612879,
1496743082017436879, 1140013050500303, 1140040139347151, 1497972507557958863,
870282958031, 977778382031, 14619387961, 1284676522284239, 18122438909449,
1688066270103311567, 5327 ]; 

PROPERTIES_SMALL_GROUPS[ 1314 ] := rec(
isNilpotent := [ 6, 18 ], 
isAbelian := [ 6, 18 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 9, 12, -13, 16, -18 ], [ 1,
-8, 10, -11, 14, -15 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1316 ] :=
[ 15100565219337, 135867224759697, 179369000078956067, 754222986019,
709068988213011, 103303865107, 11605568027, 136298273915923, 275 ]; 

PROPERTIES_SMALL_GROUPS[ 1316 ] := rec(
isNilpotent := [ 4, 9 ], 
isAbelian := [ 4, 9 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -9 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1320 ] :=
[ 19309988562403849013009, 19313673136775429030019,
25489184917580423941030019, 7323403747337013009, 16458597794313013009,
5488047555081019003, 21765589733212933010039, 1831197475337039001,
21725364382335749030019, 7244229724078853090013, 28730578524312699779000139,
228725882883000139,
[ ( 1, 2, 4, 5)( 3, 6, 7, 9)( 8,10,12,14)(11,15,16,20)(13,17,19,22)
    (18,21,23,24), ( 1, 3, 2)( 4, 7, 5)( 6, 8,11)( 9,12,16)(10,13,18)
    (14,19,23)(15,17,21)(20,22,24), ( 1, 4)( 2, 5)( 3, 7)( 6, 9)( 8,12)
    (10,14)(11,16)(13,19)(15,20)(17,22)(18,23)(21,24) ],
[ ( 1, 2, 4, 5)( 3, 6, 7, 9)( 8,10,12,14)(11,15,16,13)(17,19,18,20)
    (21,23,22,24), ( 1, 3, 2)( 4, 7, 5)( 6, 8,11)( 9,12,16)(10,13,17)
    (14,15,18)(19,21,24)(20,22,23), ( 1, 4)( 2, 5)( 3, 7)( 6, 9)( 8,12)
    (10,14)(11,16)(13,15)(17,18)(19,20)(21,22)(23,24)(25,26,27,28,29,30,31,
     32,33,34,35) ],
19313639883346434003019, 19313639883346433003019, 25494004645959373315003019,
19313639883346464003019, 25494004645959373346003019,
25494004645959373345003019, 33652086132666314854947003019,
4221390632761028530380130090, 12755455110473318947001309, 7320624169474001309
, 9663223568794146001309, 7320624169473001309, 7320624169504001309,
12760318718292066595003019, 7323415281922003019, 9666908119957794003019,
7323415281921003019, 7323415281952003019, 16837200786049773667107003019,
9663223591666434003019, 12755455140946838306003019, 9663223591666433003019,
9663223591666464003019, 11084759042001309, 11084759072001309,
19313642628710435001309, 7236907706876425019003, 105074996051821232901010039,
9552718179682288389090013, 138698994788480455807875000139,
60304795898370001039, 60304795898369001039, 79602330637439491001039,
60304795898400001039, 79602330637439522001039, 79602330637439521001039,
105075076441471717923001039, 20109918736898003019, 20109918736897003019,
26545092761227779003019, 20109918736928003019, 26545092761227810003019,
26545092761227809003019, 35039522444849189411003019, 79686310869080578000139,
79686310869080577000139, 105185930347350596099000139, 79686310869080608000139
, 105185930347350596130000139, 105185930347350596129000139,
138845428058502951082531000139, 5488052805890009013, 5488052805889009013,
7244229708357891009013, 5488052805920009013, 7244229708357922009013,
7244229708357921009013, 9562383215036997923009013, 79602330752782978000139,
79602330752782977000139, 105075076593840296579000139, 79602330752783008000139
, 105075076593840296610000139, 105075076593840296609000139,
138699101103869358248611000139, 132659507704630018000139,
132659507704630017000139, 175110550170280921859000139,
132659507704630048000139, 175110550170280921890000139,
175110550170280921889000139, 231145926224770986150691000139,
105185930164646714114000139, 105185930164646714113000139,
138845427817333826525955000139, 105185930164646714144000139,
138845427817333826525986000139, 138845427817333826525985000139,
183275964718880651178154787000139, 3197906247086113176139000,
21725333874016803001309, 12468617730001309, 16458586260002001309,
12468617729001309, 12468617760001309, 7244215856661027001903,
4157604354001903, 5488042312226001903, 4157604353001903, 4157604384001903,
28730578371771106083001039, 16489083044610001039, 21765589675541282001039,
16489083044609001039, 16489083044640001039, 2417176517542435003901,
1387266562003901, 1831194329634003901, 1387266561003901, 1387266592003901,
28677480939040801571003019, 16458609328898003019, 21725364347732770003019,
16458609328897003019, 16458609328928003019, 9562383215036990243009013,
5488052798210009013, 7244229708350242009013, 5488052798209009013,
5488052798240009013, 37924363651864555684771000139, 21765589790884738000139,
28730578524139684770000139, 21765589790884737000139, 21765589790884768000139,
173015041000139, 173015072000139, 301689958563875000139,
[ ( 1, 4, 3, 9, 5, 7,10,11, 6, 8,12), 
  ( 1,10, 3,12)( 2, 5, 8, 9)( 4,11, 6, 7) ],
[ ( 1, 2)( 4, 5)( 6, 7)( 8,10), ( 2, 3, 4)( 5, 6, 8)( 7, 9,11)(12,13) ],
[ (1,2,3,4,5), ( 1, 2)( 6, 7, 8, 9,10,11,12,13,14,15,16) ],
[ ( 1, 2, 3, 4, 5)( 6, 7, 8, 9,10,11,12,13,14,15,16), 
  ( 1, 2)( 7,16)( 8,15)( 9,14)(10,13)(11,12) ],
[ ( 1, 2, 3, 4, 5)( 7,16)( 8,15)( 9,14)(10,13)(11,12), 
  ( 3, 4, 5)( 6, 7, 8, 9,10,11,12,13,14,15,16) ],
[ ( 1, 2, 3, 4, 5)( 6, 7)( 8, 9,10,11,12,13,14,15,16,17,18), (3,4,5) ],
6374121887932451136031900, 8413840892059675888064031900,
7295381252676096013009, 7323390317056000319, 14661998155776013009,
11082924544000139, 11084759296000319, 14628779459328000319,
79605921045680642001039, 105079899760408697346000139, 7244210330931713009013,
105185930134196095745000139, 105079815780292399746000139,
138705467683587348273794000139, 60368417229312000139, 4828864996311424039100,
6374101838949614016031900, 6374101805705560512091300,
8413814427535393436128013900, 60307515906560013009, 27412506089984019003,
265587510909865728010039, 3670016000139, 5482506355201001903,
79602269736272641001039, 7236907712119553009013, 105074996051878904705000139,
45685412352000139, 15234765312000319, 60368417200640000139, 4157612288000913,
60304795898496000139, 100499626920704000139, 79686310730668800000139,
4153421824013900, 9437696000139, 3146240000193, 12491686656000139,
1049088000391, 12468617984000319, 4157604608000913, 16489083044736000139, 139
]; 

PROPERTIES_SMALL_GROUPS[ 1320 ] := rec(
isNilpotent := [ 12, 130, -132, 181 ], 
isSupersolvable := [ 1, -12, 15, -21, 23, -93, 95, -132, 142, 144, -153, 161,
-172, 174, -181 ], 
isSolvable := [ 1, -12, 15, -132, 139, -181 ], 
isAbelian := [ 12, 130, 181 ], 
lgLength := rec( lgLength := [ 4, 5, 6, false ], pos := [ [ 142, 144, -146,
153, 161, 166, -172, 174, -181 ], [ 15, -40, 45, -132, 139, -141, 143, 147,
-152, 154, -160, 162, -165, 173 ], [ 1, -12, 41, -44 ], [ 13, -14, 133, -138
] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37
, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95,
98, 101, 104, 107, 110, 113, 116, 119, 122 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8
, 9, 10, 11, 12, 13, 14, 21, 22, 27, 32, 37, 40, 41, 42, 43, 44, 51, 58, 65,
72, 79, 86, 93, 94, 99, 104, 109, 114, 119, 124, 129, 132 ] ) );