sml1404.z

#############################################################################
##
#W  sml1404.z              GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1404 ] :=
[ 97425194623479552922714535, 17411210928889806553511,
17142357426274934844996619165, 95399828553006715339175,
24068868531384051055179511422205, 80407745051122227047,
187992559384621297028600005031, 17398752512247328851815,
133889206063744218765296039, 3333461719816013816373835977283132669,
17131093008574758310840323325, 12401147320037721959, 26002395434875644223056,
24670479839384986483741643, 67948595576119150439, 12209656286520551396985565,
17130902505514328810110799101, 57269690961151847, 17398752512076079704023,
24445166872784324935296983, 24445166929931905645422551,
17398752512076073732055, 24445166872784324929325015, 17411087597577018664919,
73006264552402826066813461, 102512615286212566970051748373,
102500449061863201154833474069, 17411210928890547077543,
24445179331201142836552103, 102500726354725864757806653973,
143927711792765596314332896059925, 143910630413779086709766438937109,
24427848527284662353592743, 34321014289389517769160384935,
49432779448949942231, 69403565286518266537943, 69403508138937556412375,
49432779448943970263, 69403508138937550440407, 49432779451995645911,
67948595576098269143, 80283681077037230039, 112718174052670037567447,
8696266075970599332685, 6185154800752610125, 8671587113051501767501,
24341144964807613266471757, 12452435668237346833326613,
95399828553007455863207, 158256316370308611784958375,
34175210408687446485862867477, 12209606911085962575612829,
8683957423027933219741, 17483220393641289032549144533,
12452423835024880942290901, 58246572661790567, 58246621572208487,
80293449938600449895, 133845841907781959464265687,
187919613993790680471947192279, 187919613993847828052657317847,
133845841907781959458293719, 187919613993790680471941220311,
133845878913038456189741015, 791516951825326733596344997536277,
1111289800119269838373088607908028949, 1111289817200648824882693174365151765,
187919562038525102138030883239, 263839138047282114609377614094759,
73006264692710709395228629, 102512615286352874896187230165,
102500449062003509080968955861, 17411087597757428811623,
24445179330869486294140775, 338030920529358656324555,
338030920529358653338571, 474595412423354474126169035,
338030920529358745904075, 474595412423354474218734539,
474595412423517287838991307, 474595412423354474215748555,
666331959042389816589691048907, 666331959042618406912531551179,
49423906279411976039, 69403499265813883160423, 69403499306517288224615,
49423906279400032103, 69403499265813871216487, 49432692001741997927,
207975999174331371653077, 292006721540872714809804757,
291998056138914477049677781, 49432779620939614055, 69403508139155781060455,
291998253640953363085690837, 409977436994185415072176965589,
409965270769836049256958691285, 69391164261674630137703,
97442512968979434469590887, 95362682382107443210199, 95399687638604168685527,
133941161329322553422129111, 563697855005661689284641579541,
133889206063744219505820071, 188053390506368126087462248871,
791448626309386862720822000378389, 791431788419999050110083561560021,
17483046604700836693493258197, 17130121952773168264565558173,
24649853613425787461784973187029, 34463169608886861152998073504995285,
8912424580134578456533, 80283681086219110247, 112730632137660168144743,
12175136773945998719092693, 12513562689598410903554005,
8906621999798088107989, 26002426172220386888413, 12174908271564780068162269,
474491619219933146972309461, 12513044616007496520206293,
17093883167852713719291447253, 17569042016701663167077451733,
17556875594481357221472241621, 8832834612266855, 12401065962138011495,
12401106665543075687, 8832834600322919, 12401065962126067559,
8832883510740839, 18520224644251748304, 26002395409827481356240,
18520224644248762320, 26002395409827478370256, 18520224644341327824,
17571566836823581213643, 24670479839059359335793611,
24670479839222172956050379, 17571566836823578227659,
24670479839059359332807627, 17571566836823670793163, 48396350174037863,
57182072504059751, 80283599716112697191, 6193921688800398589,
4405362381180157, 6176344177671933181, 17336997838262165376253,
8869251780863286609877, 67948595576859674471, 112718174052717033949031,
12175093601146727427246037, 8696301218664704723677, 6185155191740320477,
12452430005870820388800469, 8869247745011683690453, 40703417010023,
40752327427943, 57188333049497447, 576001411971036970958670675905437,
104071243913370723748765, 12392273808001460315, 12401147149541042135,
17398752512076832171991, 17411210928890923311527, 24427848527284662729826727,
35208469844715611, 48396350153156699, 4405362372242929, 67948595576850737111,
6185154801511050061, 95399828553007832097191, 8683957422638083148701,
133941359289518230528956263, 1098991939721063, 410257415933787016637217000157
, 74124817884329822941, 95331796232117890705499, 133845841907781960216733655,
187919562038525102138407117223, 222532427226052369984774332839,
370694398690422358113698692905427367, 312435527470577058482198117999015,
12401059664888858471, 17411210597191573833575, 12401147332614686567,
17411087597757799073639, 24445339678276643744909159, 240762763813696316363,
35202380536481639, 35208641834387303, 49423906280152500071,
49432779621309876071, 69391164261675000399719, 67922139928310179931,
95362682382108195678167, 133889206063744219882054055,
187980445313497705225145390951, 12192245247420718733208397,
264027349538207395085710136828327, 222532505214669994101683118503,
51353641718151601464946527133, 371319269757391330911453951050749799,
937306643069544883110405565159271, 57182035812288359, 80406680520364132199,
4405386066005245, 80283681086589372263, 112890979544817618913127,
112891445429732596778855, 6185154824822606557, 112718288592061619504999,
338672841597485879134055, 222533423494342374955300947815,
8720962622802246519517, 159174836634004389567924071, 25243938719591,
13191036565465584, 49546993181759644619, 34442871572327, 3132559984597,
48396350914561895, 4405363133648125, 67948595577229936487,
6185154801890249437, 95399828553008020195175, 1895 ]; 

PROPERTIES_SMALL_GROUPS[ 1404 ] := rec(
isNilpotent := [ 6, 18, 56, -58, 157, -159, 175, 227 ], 
isSupersolvable := [ 1, -12, 15, -74, 84, -108, 112, -130, 142, -159, 162,
-175, 178, -180, 184, -188, 190, -198, 205, -217, 220, -227 ], 
isAbelian := [ 6, 18, 56, 157, 175, 227 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 176, -177, 189, -190,
210, -220, 225, -227 ], [ 74, -89, 94, 99, 114, 116, -144, 147, 151, 153,
-162, 167, -168, 173, -175, 178, 184, -188, 191, -195, 198, 202, -209, 221,
-224 ], [ 8, 11, -24, 29, 34, -43, 46, 50, 52, -64, 69, -73, 90, -93, 95, -98
, 100, -102, 105, 107, -113, 115, 145, -146, 148, -150, 152, 163, -166, 169,
-172, 179, -183, 196, -197, 199, -201 ], [ 1, -7, 9, -10, 25, -28, 30, -33,
44, -45, 47, -49, 51, 65, -68, 103, -104, 106 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 31, 37, 44, 50, 56, 62, 68,
74, 80, 86, 92, 98, 104, 110, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99, 178,
184, 190, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262, 268,
274, 280, 286, 292, 298, 304, 310, 316, 322, 328, 334, 287, 293, 299, 305,
311, 317, 323, 329, 335, 341, 347, 353, 359, 365, 371, 377 ], pos := [ 1, 2,
3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 24, 29, 34, 40, 43,
47, 51, 53, 55, 58, 64, 69, 74, 83, 89, 94, 99, 102, 106, 108, 109, 110, 111,
115, 117, 119, 122, 124, 130, 135, 141, 144, 148, 152, 154, 156, 159, 160,
161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175
] ) );