col4.z

#############################################################################
##
#W  col4.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 204 ] :=
[ 6947933953, 103249150223, 21064099889183, 33620464, 21028749246735,
4277295094235167, 116876378143, 13794025216, 505413663, 35651825,
103250133023, 31 ]; 

PROPERTIES_SMALL_GROUPS[ 204 ] := 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[ 208 ] :=
[ 405875911603295243, 178093707863616, 84199750798033327115, 1951325512058891
, 405864781769705483, 84422156641025329163, 84422156694024554507,
17559808592400732312587, 1951325511810059, 405864781769456651,
1951325511312395, 405875752608605195, 405864781768958987, 1951325515044875,
99608431659956269067, 20718553785301445852171, 20718553785301446101003,
4309459187342731227878411, 1951325514796043, 856142080560, 1700056306224,
354462900693552, 856143573552, 177237569499696, 36865417387845168,
7668006789843644976, 1594945412260598745648, 84199739668960416779,
17513545840007998952459, 404806494252524555, 84199739668963402763,
404806494253022219, 84199739668963900427, 404806494256008203,
405864728774212619, 9380895731723, 1951272520298507, 1951272519800843,
11068779921419, 478886637522327563, 478886637515360267, 99608420636113913867,
9380894985227, 9380902699019, 4077112452, 4080844932, 177233491141764,
852069445764, 1946186624388107, 44877348875, 11 ]; 

PROPERTIES_SMALL_GROUPS[ 208 ] := 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[ 210 ] :=
[ 421562939, 153467195, 29973535547, 829499, 3359291, 2032197, 710726459,
705163, 701436791, 421417917, 149262777275, 59 ]; 

PROPERTIES_SMALL_GROUPS[ 210 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 216 ] :=
[ 6943541992240246220487, 685784004821973, 6974364470109941032696,
1499808718914112934964935, 32146027741836273287, 6943558883861625630343,
32146027741836273223, 32146105943795494407, 3175121683787, 28193977273611,
1315418334585425355, 148792994395374931, 685784004854229, 146767217235902803,
31702373179148518739, 31998594038353683143, 148138872226734279, 3160424841946
, 6276960551514, 1355765885502170, 640411811114423328535542172,
1362057342222748, 148824202500171271, 14696842759, 6943117270994597077191,
7131565632752355789511, 152853840944316999, 33016429645639860935,
33016507559030966855, 152853840944317063, 152854201654462983,
33016507559030966919, 1479263540836628821625031, 31705751475408519303,
31705751475408521223, 6848442318688097059015, 6848442318688097060999,
32288724398658053816, 6974369204126510771896, 32288724398658053752,
6974369204126510771832, 32288746315406405176, 32143998861428444363,
152177638474025419, 688856449991819, 148814809540906123, 3175121715595,
704526101285259, 31701718793034189003, 679477854126219, 146767216633759883,
6847717318768052980939, 146770246196315275, 31702394994295884939,
688856449991755, 3175121715531, 688957448834059, 3261692152075,
679477854126155, 679477854128139, 146770246196315211, 146770347195157515,
6911713141187294587591, 148141639049732743, 31998671949932849799,
31997996009598773447, 685828103757959, 148138870414796935, 148141639049732679
, 148141999759878663, 685828103757895, 685828103759879, 14696841549,
14697889869, 3145729048909, 43553655053, 14697891853, 3174585862413,
2032082909923789, 685739512694989, 148113472655198669, 3174920389209,
685827491414355, 148138872218378439, 14629733468,
138975360681987652375843102919, 322465254535911458532665351,
69972125047958294525946259655, 63547442898835398812,
2964901048765953792405788, 13726247666201523187996, 13726393744286558580764,
2964869495899934048450844, 2964869495887467905874076, 13726393744404127799324
, 35503867621567611923, 3950287436814468115, 6096132967399577,
164369757440032787, 32144061439784542279, 707656663319047, 146785886460887047
, 6305818083612, 1362056805417244, 6305818083484, 1362056805417116,
6305818148892, 3189147485191, 14696874503, 3145736437767, 679491886171143,
685840913195527, 3175130095623, 67109383, 75497479, 14571012615,
31996564866833891667, 20730854387464337285319, 9408193265803,
2032170285957323, 9408193267723, 2032170285959307, 438948782307313867,
2057103779201159, 2057103779201095, 444334418027774151, 2057103779203079,
444334418027776135, 444334418027776071, 95976234295719528647,
444334157108519047, 444334157108520967, 20730854434427992713415,
149484835184862776, 685739511679181, 14696874125, 3174719064205, 14696874061,
14696876045, 148138608279210187, 3175121731723, 685826887436427,
3175121731659, 3175121733643, 31997996009590417607, 685828095402119,
148138870406441095, 685828095402055, 685828095404039, 67108942, 67110926,
3145593784526, 701877802289202019676077281529158051,
1492831727010882911256915, 967273359933665699058606279, 95981597375214289031,
31995227828971653131, 20732017637464760051719, 967314632016603712576743559,
322458626810434058164422859, 208939960514703826854576842951, 28222835425287,
294201124553023516, 63547442898816528412, 13726247666145414674460,
28222834507801, 18288367695544339, 148132244773453899, 95976177719728726087,
43553947655, 9523620642823, 2057102571249671, 29193142300, 67141639,
14696890375, 3175121739783, 7 ]; 

PROPERTIES_SMALL_GROUPS[ 216 ] := rec(
isNilpotent := [ 2, 9, -11, 18, -20, 24, 73, -81, 85, 114, -116, 150, -152,
177 ], 
isSupersolvable := [ 1, -2, 4, -20, 23, -24, 26, -37, 43, -85, 101, -102, 108
, -116, 119, -133, 135, -152, 162, 170, -172, 174, -177 ], 
isAbelian := [ 2, 9, 18, 24, 73, 85, 114, 150, 177 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6 ], pos := [ [ 162, 171, -172,
176, -177 ], [ 101, -102, 110, 112, -116, 124, -134, 145, -152, 156, 158,
-159, 161, 165, 169, -170, 173, -175 ], [ 23, -24, 26, -42, 49, -51, 59, -60,
63, -81, 84, -85, 87, -88, 92, -95, 99, -100, 103, -109, 111, 118, -123, 135,
-144, 153, 155, 157, 160, 163, -164, 166, -168 ], [ 3, -11, 14, 16, -22, 25,
43, -48, 52, -58, 61, -62, 82, -83, 86, 89, -91, 96, -98, 117, 154 ], [ 1, -2
, 12, -13, 15 ] ] ),
frattFacs := rec( frattFacs := [ 10, 19, 29, 38, 47, 30, 39, 48, 112, 121,
130, 139, 86, 95, 104, 113, 122, 131, 114, 123, 132, 141, 358, 367, 376, 385,
394, 403, 412, 421, 430, 439, 448, 457, 332, 341, 350, 359, 368, 377, 386,
395, 404, 413 ], pos := [ 1, 2, 3, 8, 11, 15, 17, 20, 21, 22, 23, 24, 25, 37,
42, 62, 72, 81, 82, 83, 84, 85, 86, 87, 88, 92, 95, 99, 100, 102, 107, 111,
113, 116, 117, 118, 123, 130, 133, 134, 139, 144, 149, 152 ] ) );

SMALL_GROUP_LIB[ 220 ] :=
[ 1992659530309, 3436810309, 3405130903, 10194250309, 2267725290039, 5130390,
9060160039, 17920039, 744578890903, 1801341415530039, 37218240039, 46400039,
15680093, 10307040039, 39 ]; 

PROPERTIES_SMALL_GROUPS[ 220 ] := rec(
isNilpotent := [ 6, 15 ], 
isAbelian := [ 6, 15 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -8, 11, -15 ], [ 1, -6,
9, -10 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 224 ] :=
[ 619725958093328559557, 554812850654461584, 2766633729281914757,
619708620203977686917, 31095369553240112659558277, 31096231732338796621328261
, 6965362779925785570394416581, 2766633729281588165, 619708620203977360325,
623557634379844436933, 138814730696924241008261, 864945809123606545541,
193751693075421989772485, 193755542089597856849093, 193747861014899250923141,
43399520867337746259655877, 2766633729281868101, 619708620203977640261,
2766633729281774789, 623557787115458151365, 619708620203977546949,
138826260939219240604613, 138818562604711369129157, 138818562681421632519365,
31095358006120189878932933, 2783740118019050885, 619760093475628195205,
43400379197499307068487109, 193747861014899247750533,
43399520867337746256483269, 43399520867108642839224197,
9777057539449301965935182597, 2190060888836643640672193100101,
2190060888836643640672193146757, 490573639099408175510873956263365,
2783740118019004229, 2766633729282894533, 193747861014899250876485,
193747861014899202914117, 864945809123561709125, 43399520867108642839084229,
43399520867108642791121861, 43399520867108642839177541, 9829970169360120,
2476841336559864, 552336009319063800, 9829970170013304, 552357828889059960,
123728142766094550648, 27715103968699957342968, 123728142765998625912,
27715103968699861418232, 27715103968699862071416, 2201935332635857656,
125370388960387907832, 125370399918996963576, 28082959784954890102008,
2476841337213048, 552336009319716984, 6235404074453019464254008,
1396730512677476340413233272, 312867634839754700232974230776,
619725725565343777733, 139676909871291090457541, 139676892764902354441157,
12427405149914501, 2766632701914928517, 2766632701913435525,
623557633352477777285, 623557556984670920069, 627406571160537996677,
3861441581064720197, 864962991537643757381, 864980174294186537669,
17238577029601541, 3861365213259309317, 3861441923524192517,
3861441923524099205, 3861518633787489413, 864980097926381126789,
864962915169838346501, 1727159349688408898501, 193751710028390152539077,
193751692921658959989701, 193755559042566019615685, 3861441581064766853,
864945808096187864453, 864945808096186371461, 864962914827380413829,
864962991195187271045, 864980097926379820421, 864963067905450661253,
193751692845291154578821, 12351037343337221, 2766556334108351237,
2766556334106858245, 619725725907808008965, 619725726250264541957,
138818562603684001163141, 138818562680394264506693, 3861365213258189573,
864945731728379794181, 193747861014214291667717, 43399520867184325686732677,
866062610904524861957, 193998024842748192539141, 43455557564775729084860933,
193998024842748189739781, 43455557564775729083554565,
43455557564775729083461253, 9734044894509763448630698757,
43455557564775729080661893, 9734044894509763448629299077,
2180426056370187012626856660869, 12351037343197253, 2766556334108211269,
12351037343010629, 2766632701914881861, 623557556642214247109,
2766556334108024645, 2766556334107931333, 12351037345949957,
12351037344456965, 2783739090652344581, 2783739090652251269,
864945808096910565893, 43454450165594514237247109, 193747861013872551630917,
17238577029461573, 3861441581067519557, 1727159349688411697861,
17238577032400901, 3861441581067566213, 3861441581068965893,
864962914484925187205, 193747861013872551770885, 9733796837093171343053563781
, 43399520867107616139931973, 386875996378888528202693, 864945731728378067909
, 864962914484923880837, 193751692844948698045829, 3861365213258049605,
193993081096403394224645, 193747861013872551677573,
43454450165594514237200453, 12351037345809989, 12427405154113541,
11056453919604, 21966142013172, 4931422999079796, 4931422999173108,
4920464390117364, 1107104487389774964, 11056458258612, 2476743495894324,
554790639905438580, 2476743495987636, 554790590983216692,
124273092477024031860, 554790688827940404, 554779681296522804,
124270648707204600948, 11056454572788, 2465784884552436, 2465784930835188,
552335862755257524, 123723233260321186548, 27714004250315078930292,
123723233260321326516, 123720789490504694964, 27713456845875529345332,
2206867000911646608, 2766555991654664261, 55135526072837, 12350694892589573,
12350694892402949, 76955663499269, 3861364871523891461, 17238234578853893,
3861364871518292741, 864945731386644376325, 864945731385927460229,
17238234620844293, 3861364870807441925, 193747843830772832835461,
55135525746245, 55135531671557, 48922408542, 48923854878, 2465735961537246,
11007533097246, 2465736015144990, 123720778531742887326, 9852088426169400,
244635697157, 5 ]; 

PROPERTIES_SMALL_GROUPS[ 224 ] := rec(
isNilpotent := [ 2, 44, -62, 149, -172, 189, -194, 197 ], 
isSupersolvable := [ 1, -172, 174, -194, 196, -197 ], 
isAbelian := [ 2, 45, 58, 149, 164, 189, 197 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6 ], pos := [ [ 196, -197 ], [ 37,
44, 63, -93, 117, -125, 129, -135, 139, -142, 147, -163, 174, -195 ], [ 8,
-16, 19, -31, 36, 38, -43, 45, -57, 94, -116, 126, -128, 136, -138, 143, -146
, 164, -173 ], [ 3, -7, 17, -18, 32, -35, 58, -62 ], [ 1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 6, 11, 17, 22, 63, 68, 209, 214, 219 ],
pos := [ 1, 2, 43, 62, 148, 172, 173, 188, 194 ] ) );