col17.z

#############################################################################
##
#W  col17.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 738 ] :=
[ 718713784382441, 37778969601679, 610484710425603161, 1315843161,
51200001679, 1392643161, 37779005441679, 971366462441, 27880976691201679,
1679 ]; 

PROPERTIES_SMALL_GROUPS[ 738 ] := 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[ 740 ] :=
[ 1913474019891, 22304925929555, 16552854939619727, 861648156,
16501181862432851, 1413389018559027, 9064270351600065352079,
9064270375145863025039, 38697565726388130191, 12199148571144114575,
70667652980879, 30152466575, 2633639151, 22368588411023, 143 ]; 

PROPERTIES_SMALL_GROUPS[ 740 ] := 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[ 744 ] :=
[ 3941504647356678327029, 5298326053292727029, 221270972781483001,
6400225791135927029, 4761777242755714500059, 297006093953100,
2932479448442398196100929, 5297721369687000929, 3941504635089576600929,
5297721369662700929, 5297721370027200929, 6840405630192600059,
6840405630168300059, 5089261814298274500059, 6840405630532800059,
5089261814298639000059, 5089261814298614700059, 3786410789863333517700059,
7121472355800929, 7121472696000929, 3941945394990336900929,
122645630761007477193000, 96635056341858517889010870, 4761758816048218500929,
8602423997400929, 6400213449384600929, 8602423973100929, 8602424337600929,
164624713913434526101, 297407165426101, 221269778703026101, 297407141126101,
297407505626101, 3542762241096263482500059, 6400238134685400059,
4761777205729877400059, 6400238134661100059, 6400238135025600059,
398155501770, 398520001770, 220676560128901770, 244469024218445328783900,
181884954051633083745653100, 1196586432000059, 13691116080806427029,
669541853029132827029, 9194059353600059, 1791590400059, 593650944053100,
899921873433627029, 11548915200059, 401241600871, 8602425504000059, 59 ]; 

PROPERTIES_SMALL_GROUPS[ 744 ] := 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[ 748 ] :=
[ 226259701513, 377053317391, 285453965131935, 33622512, 281909357775119,
210702640608247967, 3840613023903, 505413791, 304087289, 381617701023, 159 ];


PROPERTIES_SMALL_GROUPS[ 748 ] := 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[ 750 ] :=
[ 9475184531709, 16060662165883039871, 12045497794572667056255, 12666810495,
3213157684548636511289471, 6038089844866777215, 10344616165503,
28550644310143, 37832757375, 9475186688127, 7106438646407295,
21376215827058815, 9627188166783, 12633379069, 37765906685, 28324185641213,
21413285085815007, 28374718417143, 7106388715864287, 5329829285086339295,
16032163430417027199, 7220391577763967, 16781439, 18874495, 50350526591,
155742137384861919, 116806603665049305215, 661672478769279, 35502724210163839
, 318540377941554987135, 276875968639, 50462847, 38000590975, 28501554200703,
16908541, 37832818935, 28500715339999, 21376167575797887, 127 ]; 

PROPERTIES_SMALL_GROUPS[ 750 ] := rec(
isNilpotent := [ 4, 23, -25, 39 ], 
isSupersolvable := [ 1, -4, 8, -25, 32, -39 ], 
isAbelian := [ 4, 23, 39 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 28, 30, 34, -35, 38, -39
], [ 5, -7, 10, 12, -16, 19, 21, -27, 29, 31, -33, 36, -37 ], [ 1, -4, 8, -9,
11, 17, -18, 20 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35, 38
, 41 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 11, 13, 16, 20, 22, 25 ] ) );

SMALL_GROUP_LIB[ 752 ] :=
[ 64666522618170423814221, 1913380521761212216, 85992715431504767341,
64666403032734695151469, 48629224651355781399819117,
48629224651514382777561965, 36569176937938946298878784077,
85992715431298804365, 64666403032734489188493, 85992715430886878413,
64666522142368762141389, 64666403032734077262541, 85992715433976323053,
50784558276042756605679021, 38189987823584244129361286285,
38189987823584244129567249261, 28718870843335351676287105716813,
85992715433770360077, 2544371656667284, 5078622086635732, 3821662176502455956
, 2544372892445140, 1910836153189799892, 1436948786824629244148,
1080585487602688906465236, 812600286677132470904491412,
64666402874136406853261, 114351620539706285, 85992556836305913773,
85992556835893987821, 119420167535349805, 67532657123245440084461,
67532657123239673121133, 50784558156774517659575661, 114351619921817357,
114351626306669613, 3374703363830, 3377792808470, 1910832777456530102,
2541000660545942, 151878746206253, 45 ]; 

PROPERTIES_SMALL_GROUPS[ 752 ] := 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 ] ) );

SMALL_GROUP_LIB[ 756 ] :=
[ 48047856079566737791487, 21334939611280955903, 12161638446653264305833403,
105888674012252625407, 9194647603665871461315929299, 28072287224565775,
63555365183616781319, 12162781152271742350024339, 28220818572479495,
63443410220329895916, 16424759673393466320653, 140064379561643015,
16086823342132243135075, 12162232279981299271839379, 37132073582227,
63555365180941014323, 48090076505136421737779, 48090076764033560679731,
63555365180940921011, 48090076505136421644467, 63611212992388938803,
36260129795974914401111443, 36276110451776765768764819,
47963748979715203009939, 21334939611292526591, 16128821343064756591487,
27424739333048615474541776275, 27412657957262415840595824019,
36260425734045318972460435, 16086544475864014055423,
12193346265486606267358079, 28220815896712499, 21334419762311370035,
21334678659450311987, 28220815896619187, 21334419762311276723,
28220815944301619, 140064379561317683, 195912191009242163,
148109099581936571699, 21278275481004598159, 28072287247707151,
21166505887783157647, 31982589879183931007887, 16298375446416943500691,
105888674012264196095, 111970479286971939199871, 24179049947845684930956691,
16044378710759679746491, 21222650468136791995, 12321531347837158492667995,
16298321823888837683035, 37132072790365, 37132120472797, 27998023126296925,
108764365169489333002302235, 108748384513687481634648859,
143847684305586297893659, 63611212995207846407, 48090132943933631791367,
296525287471217643725, 296525287471217597069, 224173117329375827904269,
296525287471219043405, 224173117329375829350605, 224173117330745655482573,
224173117329375829303949, 169474876701009261151096589,
169474876702044849706864397, 84067945083450119, 63611212310868275975,
63611212653324808967, 84067945083263495, 63611212310868089351,
84141818613891335, 47963134650758714970907, 47984273084359047467803,
63444112404512592667, 28220818584050183, 21334419765721129223,
36276110228900283277349659, 36260129573098431909696283,
47963526103232042734363, 21278497982963358215, 16128764901437096190215,
12145489018913310730497979, 9400349423716440336989071195,
21782088922460189467, 195912191152708103, 148165538376471183623,
16002437890774592254747, 16426380920202766064155, 21727943120458432795,
21446114406724662883, 16002045920609453261923, 1006802874214312620888859,
17355074175978853186075, 12098688191835005455884571,
12450263012702525148922651, 12418301307874087258509595, 37330820117255,
28220134423638791, 28220476880171783, 37330819930631, 28220134423452167,
37331584155911, 83919854048138316, 63443409828952349772, 83919854048091660,
63443409828952303116, 83919854049537996, 21725872578459824333,
16424759670653815503053, 16424759672023641635021, 21725872578459777677,
16424759670653815456397, 21725872578461224013, 185269008610055,
259142539051271, 195911506813137671, 28145866492487059, 37132096723603,
27998024643035539, 21166579468353807763, 21558697676410950427,
140064379573213703, 148109099582670889223, 16002214499528543015707,
21222723160675423843, 28072293356889187, 16298321888661304396315,
21558626739729395995, 48922548763, 49686774043, 37034992523803,
84067942407683153, 28220815908469811, 21278497980287777843,
21334939611298405247, 16086544475864019934079, 37328144350289,
185269008284753, 37132096584925, 140064379573074995, 28072287259557775,
105888674012270074751, 21222650462045384635, 80051837562490907797319,
48922410090, 84905246001887301153201023, 64188365639994250268994083711,
84141818040582407, 63611803977434431751, 28737928044232967,
21725797583626223879, 16129212201722087055623, 587437657492202573,
37232998908167, 37330831687943, 28146163083559175, 28220818589835527,
21278497982969143559, 16044266903318699409295, 84905330555621702124870527,
36387974651342330436431803, 192565128709833510706111522631, 259141965742343,
196503173379293447, 111005054042515, 587363980236079367,
148556399867661754631, 148558544232668430599, 84215590000165987,
445668827009506984199, 148109619431105704199, 84906556137137366211244295,
63666986245972403299, 336925633222134126563591, 51980009735, 74117414053116,
28479712695026765, 244635697415, 48946250011, 185269020180743, 37132108480915
, 140064379578999047, 28072287265481827, 105888674012273012999, 263 ]; 

PROPERTIES_SMALL_GROUPS[ 756 ] := rec(
isNilpotent := [ 6, 15, 53, -55, 133, -135, 149, 189 ], 
isSupersolvable := [ 1, -9, 12, -60, 70, -85, 88, -106, 118, -149, 152, -156,
158, -162, 167, -179, 182, -189 ], 
isAbelian := [ 6, 15, 53, 133, 149, 189 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 157, -158, 172, -182,
187, -189 ], [ 60, -75, 80, 85, 90, 92, -120, 123, 127, 129, -136, 141, -142,
147, -149, 152, -156, 159, -162, 165, -171, 183, -186 ], [ 7, -21, 26, 31,
-40, 43, 47, 49, -59, 76, -79, 81, -84, 86, -89, 91, 121, -122, 124, -126,
128, 137, -140, 143, -146, 150, -151, 163, -164 ], [ 1, -6, 22, -25, 27, -30,
41, -42, 44, -46, 48 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 31, 37, 44, 50, 56, 62, 68,
74, 80, 86, 92, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99, 160, 166, 172, 178,
184, 190, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262, 268,
274, 280, 287, 293, 299, 305, 311, 317, 323, 329, 335, 341, 347, 353, 359,
365 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 21, 26, 31
, 37, 40, 44, 48, 50, 52, 55, 60, 69, 75, 80, 85, 86, 87, 91, 93, 95, 98, 100
, 106, 111, 117, 120, 124, 128, 130, 132, 135, 136, 137, 138, 139, 140, 141,
142, 143, 144, 145, 146, 147, 148, 149 ] ) );