col5.z

#############################################################################
##
#W  col5.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 225 ] :=
[ 30147447, 132191, 146073203039, 131453, 649211999, 95 ]; 

PROPERTIES_SMALL_GROUPS[ 225 ] := rec(
isNilpotent := [ 1, -2, 4, 6 ], 
isSupersolvable := [ 1, -2, 4, 6 ], 
isAbelian := [ 1, -2, 4, 6 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 5, -6 ], [ 2, -4 ], [ 1
] ] ),
frattFacs := rec( frattFacs := [ 5, 10, 11, 15 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 228 ] :=
[ 16973490603365, 74561618789, 12419191189, 209350802789, 47734261882163,
53853318, 74470814243, 233758877219, 349360163, 24675249996, 17232866044505,
917070371, 57107251, 209352377123, 35 ]; 

PROPERTIES_SMALL_GROUPS[ 228 ] := rec(
isNilpotent := [ 6, 15 ], 
isSupersolvable := [ 1, -9, 12, -15 ], 
isAbelian := [ 6, 15 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -15 ], [ 1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 232 ] :=
[ 459478374564635, 73643800496, 106291983751627547, 106596869733174043,
1980452364827, 459469252454939, 1980451750171, 1980456052763, 315319284,
319621876, 17011953970676, 458155200905499, 8516673563, 27 ]; 

PROPERTIES_SMALL_GROUPS[ 232 ] := 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[ 234 ] :=
[ 1190139609767, 5109392039, 591294921277, 27466449575, 155315908533013,
10658581, 5088780455, 5109682343, 1190139900071, 23888039, 117448871,
11280661, 27466739879, 2517186109, 6427399403687, 167 ]; 

PROPERTIES_SMALL_GROUPS[ 234 ] := rec(
isNilpotent := [ 6, 16 ], 
isAbelian := [ 6, 16 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, 10, -11, 14, -16 ], [ 1,
-6, 8, -9, 12, -13 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 243 ] :=
[ 238031142927, 8711159827, 979550512, 238030750001, 57841472225587,
238030799154, 57841484169523, 57841472192819, 57841472209203, 979550215,
236072042519, 8711159833, 1003339825, 243803652147, 243807633459,
243803652153, 236095832369, 57371279278387, 57371279278393, 57371283259705,
2116835770395, 27823197465625143, 979550221, 236072042525, 57841468293238,
57841468309622, 14055476799225975, 13939818045407606, 3387375785033974135,
3387375785033990519, 4030467, 11960337, 2914336787, 2914336789, 2906374165,
706256896023, 4030512, 979451953, 979451954, 979451956, 238006829107,
238006829109, 238006829110, 238006878262, 238018773046, 238018822198,
237998899254, 4030473, 971489305, 971489545, 4030544, 979419218, 979435602,
238002847827, 979419220, 971489616, 236071911762, 236071928146,
57365478474067, 236071911764, 16385, 16400, 3997713, 3997716, 971456848,
236063949137, 0 ]; 

PROPERTIES_SMALL_GROUPS[ 243 ] := rec(
isAbelian := [ 1, 10, 23, 31, 48, 61, 67 ], 
lgLength := rec( lgLength := [ 1, 2, 3, 4, 5 ], pos := [ [ 67 ], [ 2, 31, -47
, 61, -66 ], [ 3, -22, 48, -60 ], [ 23, -30 ], [ 1 ] ] ),
frattFacs := rec( frattFacs := [ 6, 12, 28, 79 ], pos := [ 1, 30, 60, 66
] ) );

SMALL_GROUP_LIB[ 248 ] :=
[ 742915335870029, 103684076100, 184239820788750029, 2995550100029,
742902485220029, 2995549290029, 2995554960029, 415530870, 421200870,
25610213070870, 12052800029, 29 ]; 

PROPERTIES_SMALL_GROUPS[ 248 ] := 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[ 250 ] :=
[ 1569423493840447, 33424959, 25100825663, 98968127, 8292298815,
2073100842047, 6269370907199, 8693372991, 131647, 147519, 131220031, 401471,
100282431, 25077364799, 63 ]; 

PROPERTIES_SMALL_GROUPS[ 250 ] := rec(
isNilpotent := [ 2, 9, -11, 15 ], 
isAbelian := [ 2, 9, 15 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 14, -15 ], [ 5, 7, -13 ]
, [ 1, -4, 6 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14, 17 ], pos := [ 1, 2, 6, 8, 11
] ) );

SMALL_GROUP_LIB[ 252 ] :=
[ 6157125006986243, 8317956119555, 2071242470317471, 40680091520003,
544541660789550115, 32487529645, 24433057966511, 2217288596976067,
33028995503, 16277898194892, 2152760247760973, 161419340207, 8219213151163,
2160879576223171, 127433155, 24433034055521, 8317956601667, 2079495069132611,
33005084513, 161419317089, 32488509421, 40680092002115, 8187999611551,
10251390834356879, 127410042, 24497017712687, 170126118901229, 96985755695,
33029462063, 8251987249199, 519954516293446303, 917110114314167898767,
225379086383, 57308604420143, 96448278715, 170062669228079, 14441769240763439
, 159252527, 64594300572, 8542686976493, 638005295, 128397379, 161419806767,
32488999099, 40680092242991, 47 ]; 

PROPERTIES_SMALL_GROUPS[ 252 ] := rec(
isNilpotent := [ 6, 15, 25, 46 ], 
isSupersolvable := [ 1, -9, 12, -26, 28, -30, 33, -38, 41, -46 ], 
isAbelian := [ 6, 15, 25, 46 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 27, -28, 34, -41, 44,
-46 ], [ 7, -16, 19, -20, 23, -26, 29, -33, 42, -43 ], [ 1, -6, 17, -18, 21,
-22 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 21, 25, 30, 34, 38, 42, 46, 50
, 54, 58, 62, 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
] ) );

SMALL_GROUP_LIB[ 260 ] :=
[ 8334898995, 30502843067, 8003022061871, 10638132, 7914142921403,
2055594971365679, 2155912984371, 7285423268544815, 540962632798454063,
540962668683346223, 107773452335, 117448751, 32514183, 30779191343, 47 ]; 

PROPERTIES_SMALL_GROUPS[ 260 ] := 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[ 264 ] :=
[ 115497382909001, 1032503309301009, 272585736211500019, 435815301900,
1260036160200019, 1260036160100019, 332649583475500019, 1260036161600019,
332649583477000019, 332649583476900019, 87819490074689900019,
8110111577098819000, 272576130267500109, 3910873800109, 1032485288200109,
3910873700109, 3910875200109, 30490012891500901, 437465800901,
115492469000901, 437465700901, 437467200901, 71962620135035500019,
1032521337800019, 272585682145800019, 1032521337700019, 1032521339200019,
1638500190, 1640000190, 114624104300190, 16007944517040009100,
4226097366243915201900, 3773040320001009, 4772723200019, 870144001900,
14758400019, 1651200091, 3910880000019, 19 ]; 

PROPERTIES_SMALL_GROUPS[ 264 ] := rec(
isNilpotent := [ 4, 28, -30, 39 ], 
isSupersolvable := [ 1, -11, 13, -30, 34, 36, -39 ], 
isAbelian := [ 4, 28, 39 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 34, 36, -39 ], [ 5, -33,
35 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32 ],
pos := [ 1, 2, 3, 4, 11, 12, 17, 22, 27, 30 ] ) );

SMALL_GROUP_LIB[ 270 ] :=
[ 90496594138607829, 3692078176343, 24439090044681316469, 4580190325,
13673566295, 22699966551, 6128969060439, 1241212199029, 4580313205,
1227639947381, 331467155251317, 341305985306717, 3692078237783,
1654821791170647, 89502310468128861, 333940451938517, 1236801781973,
92151592257833053, 341302177022045, 16779357, 17039453, 4546889821, 50462807,
16908381, 13673627735, 4580376693, 3692078268503, 1236799815893,
996861825761367, 87 ]; 

PROPERTIES_SMALL_GROUPS[ 270 ] := rec(
isNilpotent := [ 4, 20, -22, 30 ], 
isAbelian := [ 4, 20, 30 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 23, 28, -30 ], [ 5, -7,
10, 14, 16, -22, 24, -27 ], [ 1, -4, 8, -9, 11, -13, 15 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32 ],
pos := [ 1, 2, 3, 4, 7, 11, 15, 17, 19, 22 ] ) );

SMALL_GROUP_LIB[ 272 ] :=
[ 5207592252484878351, 1280450023714816, 1414714719124166017039,
19145555596804111, 5207512228669947919, 1416464854902544269327,
1416464855194602045455, 385278440613172097318927, 19145555595755535,
5207512228668899343, 19145555593658383, 5207591376324132879,
5207512228666802191, 19145555609387023, 1603824455406474756111,
436240251870729296936975, 436240251870729297985551,
118657348508838536647016463, 19145555608338447, 4707287305984, 9363046534912,
2551433932050176, 4707293597440, 1275742752083712, 347002039244427008,
94384554521165565696, 25672598829603432173312, 384799270341373093478415,
1414714639103556583439, 384802381756109509623823, 5201157055736446991,
1414714639103569166351, 5201157055738544143, 1414714639103571263503,
5201157055751127055, 5207511936627900431, 70386062458895, 19145263570485263,
19145263568388111, 79697815797775, 5896413146299498511, 5896413146270138383,
1603824375966744969231, 70386059313167, 70386091819023, 17180918000,
17196646640, 1275725565919472, 4690125258992, 104665396325262080852623375,
1414703199793169039375, 19121907501629455, 257832255503, 15 ]; 

PROPERTIES_SMALL_GROUPS[ 272 ] := rec(
isNilpotent := [ 2, 20, -27, 46, -49, 54 ], 
isAbelian := [ 2, 20, 23, 46, 54 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 53, -54 ], [ 11, -14,
19, -22, 31, -32, 35, -49, 52 ], [ 4, -10, 15, -18, 23, -27, 29, -30, 33, -34
, 51 ], [ 1, -3, 28, 50 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 22, 51, 55, 59, 63 ], pos := [
1, 2, 3, 19, 27, 28, 35, 45, 49 ] ) );