sml1176.z

#############################################################################
##
#W  sml1176.z              GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1176 ] :=
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79769662524631389637, 471112369129438837848179, 554031962035763808633054983,
76130142024206087, 459518014740916038476817267888059,
332267526505955349433913723, 390746611174248332040692193659,
332267526505955349433867067, 332267526508714570643991803,
6341403258215956783974632197895, 4585331377123783065309383,
5392349699497575921028843271, 5392349709367310184472926407,
4585331377123783065262727, 4585331385516414243105863,
5392349709367310184472879751, 240255224087871017339, 240257983309081095419,
332271024721335163572998075, 110599917807559143812505192,
1065655634626170335772233568292505, 554031962030113618290741179,
400605756058407768443, 471115613971183049267579, 400605756058407721787,
400608515279617846523, 95241113064923386628119, 67832077796559319,
80987341040753545687, 67832077796512663, 68866785751213399,
651541598960857282595902336775, 471115613975977445208263,
554031971905490880489945287, 471115613975977445161607,
471115622368608623004743, 64724285528711, 8457355463371847,
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557303017267049506920, 187378798393140020701740,
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9181558135057355294452019, 390759898750039756716252670259,
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282550021656028561697075, 340363732233102407, 57679488889555,
400270223262683317319, 48923108423, 132160349573476370902436283143,
79905035592505422221, 557305495575602664563, 655390312764015725139059,
95243279750080424694899, 94129350991245893555315, 110693728825474340200010867
, 112003709045863748820161651, 203378771108983181, 240122671145914700915,
239175452813572412531, 338695675370992013, 400202569311223960691,
67831343961277897, 398306518991355930779, 470638224343442359583495,
8471689713296135, 182769288750311095001463951979184903,
765431194923034705420667734611059, 214226306849283830532316694840027491079,
154902403837292787823024099391111, 182165226912656318479861147988672135,
154902403837292787823024099437767, 154902403837292787823024100837447,
559332715310548643195, 559332715310548596539, 657775273205553308017595,
559332715310550042875, 657775273205553309463931, 657775273205553309417275,
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110696113785915880458331067, 94129348457414223415547,
110696113785915880459777403, 130178629812237072174311631803,
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239174644962636003131, 239174644962637449467, 390526534019827633461474864059,
282381280672861426822523, 332080386071282003824276859,
282381280672861426775867, 282381280672861428222203,
388985997280649688924177542075, 281267351914026895682939,
330770405850892595204126075, 281267351914026895636283,
281267351914026897082619, 553469667923776473684923507,
650880329478363961103334769415, 340308303554784635, 400202566914386453435,
340308303556184315, 400202566914387899771, 470638218693252375587771,
473897857243541699, 473897857243495043, 557303880893049513731,
473897857244941379, 557303880893050960067, 557303880893050913411,
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4585330979572843044856583, 3899090969018543867975, 4585330979572843046302919,
4585330979572843046256263, 5392349231977670457800108807,
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400202571708785240135, 470638224336251132155079, 470638224336251132108423,
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470637271479714620249735, 470637271479714621696071,
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172943608301969, 239173031990826429521, 204185945361182075,
204185945362581755, 282384258450220805319611, 203380487595584891,
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338695332915623441, 288005968181201, 288005969627537,
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340308303196419899, 340308303197866235, 79769488018567950253, 57679488610669,
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470638224336250773836999, 400202571708425475719, 400202571708426922055,
7191587239559, 7191588685895, 9954256987721624327,
[ ( 1, 2)( 4, 5)( 8, 9,10,11,12,13,14), (2,3,4)(5,6,7) ],
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187378799314432182651612, 220357468000220080022602236,
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1421230472318585165, 332091685436236387506046259, 330781705215846978885895475
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1976669898105414845842739, 1680841750088540456243, 7807447393707261543731,
470637472724314023491387, 553469667923778870886438535, 289376164528199,
402973709598911, 3315553539099770951, 340308303560663111,
400201761456817791047, 158997676103, 173643808112711, 172958895046727,
172647588301308, 204183886704281933, 240128306953221244211,
239181088620878955827, 244635697223, 289375806210119, 48946249939,
288005980078271, 340308303202345031, 71 ]; 

PROPERTIES_SMALL_GROUPS[ 1176 ] := rec(
isNilpotent := [ 6, 39, -41, 56, 73, 209, -211, 279 ], 
isSupersolvable := [ 1, -21, 24, -41, 46, 49, -50, 53, -56, 58, -73, 81, -97,
103, -137, 140, -179, 184, -211, 226, -228, 237, 244, -250, 262, -269, 274,
-279 ], 
isSolvable := [ 1, -211, 213, -279 ], 
isAbelian := [ 6, 39, 56, 73, 209, 279 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6, false ], pos := [ [ 220, -221, 225
, -228, 237, -239, 245, -250, 262, 264, -266, 268, -269, 275, -276, 278, -279
], [ 42, -43, 46, 49, -50, 53, -56, 76, -102, 108, -137, 140, -144, 152, -170
, 174, -180, 182, -183, 189, -198, 204, -211, 214, -219, 222, -224, 231, -236
, 240, 242, -244, 253, -261, 263, 267, 270, 272, -274, 277 ], [ 7, -41, 44,
-45, 47, -48, 51, -52, 57, 59, -64, 66, -67, 69, -70, 72, -75, 103, -107, 138
, -139, 145, -151, 171, -173, 181, 184, -188, 199, -203, 213, 229, -230, 241,
251, -252, 271 ], [ 1, -6, 58, 65, 68, 71 ], [ 212 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 31, 37, 44, 50, 56, 62, 68,
74, 80, 86, 92, 261, 267, 273, 279, 285, 291, 297, 303, 309, 315, 321, 327,
333, 339, 345, 46, 52, 58, 64, 70, 76, 82, 88, 94, 100, 106, 112, 118, 124,
130, 136, 142, 203, 209, 215, 221, 227, 233, 239, 245, 251, 257, 263, 269,
275, 281, 287, 293, 299, 305, 311, 317, 323, 329, 335, 341, 347, 353, 359,
365, 371, 377, 383, 389, 395, 401 ], pos := [ 1, 2, 3, 4, 5, 6, 11, 18, 21,
22, 23, 28, 33, 38, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54,
55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73,
74, 75, 80, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132, 137, 138, 139, 144
, 151, 158, 165, 170, 173, 176, 179, 180, 181, 182, 183, 188, 193, 198, 203,
208, 211 ] ) );