col14.z

#############################################################################
##
#W  col14.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1628 ] :=
[ 12609698689593, 49032588160691, 80239719397315175, 350006780519,
79815195432119987, 129939552129567838823, 466237053886823, 30152466791,
7793419509, 49287162507623, 359 ]; 

PROPERTIES_SMALL_GROUPS[ 1628 ] := 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[ 1638 ] :=
[ 21950318453301671, 22311243161968535, 35954968778371014551,
426671588772257687, 35976484979993845655, 36260883487121579927,
32848630698059009, 698887888892992200599, 35976845586707160983,
36261244093834895255, 58929482223296839196567, 59395326977972067934103,
13409059316135, 6706695742721, 21963992348991383, 22137617811218327,
73509957902759, 33418082362625, 120756880021692311, 10971797758904317,
18278347083148808917, 18081335606740384525, 29941618859414897746453,
370995077015, 426611162138150807, 426611382272853911, 698789082543818344343,
86821649254295, 13400936941463, 13621071644567, 21950530465630103,
260483198093207, 22137291693492119, 21963666231265175, 20054378153945,
426671482789234583, 22137511828195223, 21963886365968279,
36260883381138556823, 35976484874010822551, 13409074743719, 21950318468729255
, 22311243169433495, 35954968778378479511, 20062515956993, 426671588779722647
, 22137617818683287, 21963992356456343, 36260883487129044887,
35976484980001310615, 32848630713486593, 698887888892999665559,
36261244093842360215, 35976845586714625943, 59395326977972075399063,
58929482223296846661527, 32869713815, 4331669465, 53476600579991,
53582599030679, 44877350807, 20416169945, 73721970231191, 4108716565,
73509973330343, 33418097790209, 120756880029157271, 6690180769789,
120409417107808871, 54738851588131553, 197799770509500434327, 1943 ]; 

PROPERTIES_SMALL_GROUPS[ 1638 ] := rec(
isNilpotent := [ 24, 72 ], 
isAbelian := [ 24, 72 ], 
lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 25, -40, 57, -63, 68, -72 ]
, [ 1, -24, 41, -56, 64, -67 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25,
27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49 ], 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 ] ) );

SMALL_GROUP_LIB[ 1640 ] :=
[ 125981808976527872192039, 40724547817164992039, 13550974154037696003,
176096548186214592039, 289168694922202624000159, 564737868083200159,
473451437880954808422592039, 109517757958072580812804839,
40718976431104004839, 66779120706533990404839, 40718976431001604839,
40718976432537604839, 46844084428804839, 46844085862404839,
125990833708074905604839, 288753102330908364992039, 22205534250113948096003,
777746832539723220825190400159, 777746832724731621454950400159,
1493084581679528483532800159, 473555458177898768281600159,
555132852961484800159, 555132852961382400159, 910417879093018931200159,
555132852962918400159, 910417879093020467200159, 910417879093020364800159,
1493085321712787064729600159, 288798226261857382404839, 107375873433604839,
176096479400960004839, 107375873331204839, 107375874867204839,
22223583841368780862403, 8262792192062403, 13550965766758462403,
8262792089662403, 8262793625662403, 474236659108673508454400159,
176322374552985600159, 289168694578271232000159, 176322374552883200159,
176322374554419200159, 343933030400159, 343934566400159,
925606397085593600159, 776630166167400351282483392039,
288653801947988070404839, 46841161318400159, 473555020023308131225792039,
1273674758988951532062972620800159, 1273674758989136540463602380800159,
776630233208579168947712000159, 777747513325061954778009600159,
910426447150330880000159, 289168215824099020800159, 15938355200159,
176068965603840004839, 13539960750182462403, 474235873499831461580800159,
474235873612641461964800159, 910417427853181030400159,
288753328157275033600159, 338495497830400159, 65444249600159, 5046272001563,
107513452953600159, 159 ]; 

PROPERTIES_SMALL_GROUPS[ 1640 ] := rec(
isNilpotent := [ 6, 44, -46, 68 ], 
isAbelian := [ 6, 44, 68 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 49, 57, 64, -68 ], [ 8,
-15, 22, -46, 48, 54, -56, 58, -63 ], [ 1, -7, 16, -21, 47, 50, -53 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 35, 38
, 41, 44, 47, 50, 53, 56, 59, 62 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 12, 15, 16,
17, 18, 19, 20, 21, 28, 33, 38, 43, 46 ] ) );

SMALL_GROUP_LIB[ 1644 ] :=
[ 288493606283713, 38898181865887943, 63948664433745006863, 71989553533199,
63937674162904389831, 105113536233326408306959, 39473766797279503,
864062119312320, 23657038610703, 186103515065, 38898186997399823, 271 ]; 

PROPERTIES_SMALL_GROUPS[ 1644 ] := 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[ 1650 ] :=
[ 13405980685201339, 13411423136203319, 22119867487149003319, 10831872401339,
24348275601339, 13432997498401933, 22280866044336401393, 2708288203931,
40174687046603319, 22164510721661609133, 36763429705734578001393, 18022801339
, 8125248001339, 8164563201339, 13406016736001339, 8128211203319,
13405980384003319, 13470933104003139, 22119926997116803139,
242972312855880316809133, 220519916201503170737601933, 1079540873715201339,
88323239878828801933, 1603066696387977315201339, 13516801339, 13536614401933,
14758401339, 4928001393, 24384326401339, 8134675201933, 40234377238401339,
1651203391, 24348281603319, 8118291203913, 40234197014403139,
13422223382409133, 66386722856984001339, 1339 ]; 

PROPERTIES_SMALL_GROUPS[ 1650 ] := rec(
isNilpotent := [ 12, 38 ], 
isSupersolvable := [ 1, -19, 25, 27, -38 ], 
isAbelian := [ 12, 38 ], 
lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 13, 16, -17, 20, -27, 30,
-33, 36, -38 ], [ 1, -12, 14, -15, 18, -19, 28, -29, 34, -35 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 ]
, pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ] ) );

SMALL_GROUP_LIB[ 1652 ] :=
[ 47899751521305, 545932765196541, 904141640925593963, 2392952295019,
2824001701250907, 330622747483, 29332360943, 547300329772123, 347 ]; 

PROPERTIES_SMALL_GROUPS[ 1652 ] := rec(
isNilpotent := [ 4, 9 ], 
isAbelian := [ 4, 9 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -9 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1656 ] :=
[ 896781802064127225341716391, 11345503508495886377704649,
1536965208151130056380466746483, 7539477330154514445007,
2557052140888744487924012200754291, 932435715293650976433938419,
1544113544526308655478693606515, 1544113611647792551504536659955,
932435715293650976547318323, 932435755825948018609610163,
1544113611647792551504650039859, 1485965283462634516267671502216,
18812981907581083850692114819, 6851152186214776366915,
11360496320998178635788099, 6851152186214662987011, 6860203087498655439555,
1485074980844669604255658292303, 541534904626892958523919,
896784408722626019179637263, 541534904626892845144015,
541536478696684269081999, 2545214495851407975953264918895731,
928119087047754231269837363, 1536965275272589342705056322099,
928119087047754231156457459, 928119127580051273332129203, 4552794753889099343
, 40756399879314578447, 111767783385278160416783055, 6851149451803853756669,
326620669924684454089, 11345508036680966678021755, 540884422070349721764775,
18788161322377310341329191119, 40802884866590253263,
2963882210304045695023542785228, 4908188940339193581725182285466348,
37260917463999417798512957, 562739016248689148859827, 978285325678552748780,
4137164299852633103, 327013830739141561291, 560458189124920327550387,
2734412170023951, 1483284117418949458798730019751,
56495262021627777410273033907601615, 7502817078873119571523,
7502817078873006191619, 12424665089952082248517763, 7502817078876520968643,
12424665089952085763294787, 12424665089952085649914883,
20575245388967986215654527107, 12440305063771447338374799,
12440305063771447224994895, 20601145185628877161799655631,
12440305063771450739771919, 20601145185628877165314432655,
20601145185628877165201052751, 34115496427401443940125551749327,
326621027486012128783, 540884421001233232021583, 326621027489413525903,
540884421001236746798607, 895704601177526445245534287,
12424665106358564225660559, 12424665106358564112280655,
20575245416153503003127824591, 12424665106358567627057679,
20575245416153503006642601615, 20575245416153503006529221711,
34072606409150224693640982497487, 20601145158459766867187971727,
20601145158459766867074591823, 20601145158459766870589368847,
34115496382409397268417848082063, 56495262009269961899830302876305615,
897322031076484442377025000, 11345498966638781735375441, 4137164299172364305,
6851146717395425036305, 4137164299058984401, 4137164302573761425,
540883239021346790586381, 197234331550803405, 326620313265179864525,
197234331437423501, 197234334952200525, 18788161295167183852489035907,
6851152186243348102723, 11345508028477736176862787, 6851152186243234722819,
6851152186246749499843, 895704601177525574487871567, 326621026615254466063,
540884421000365989135887, 326621026615141086159, 326621026618655863183,
31113195149816096700790894971087, 11345508044884214639228559,
18788161322352700643477110415, 11345508044884214525848655,
11345508044884218040625679, 24609701480238159, 24609704995015183,
67528848282752005925071, 4067661955508202246928418330169836455,
154929334065470337161062556706660617814223, 34115571961512512086184552208015,
1483284658952473836256550678927, 56495304899258209364930455813958159,
93556293166442906225176485817909313167,
6736058002852874338589677455311006699599,
256562790776890455854540506980409868146526415, 7512261501083378418191,
1080787405490241913904748, 1789783959179097122165609564,
1789783943419377251684002764, 2963882236400599107297402362972,
22500554018303580716221, 2934854665848088525961, 74574321495544061855879995,
895702969455930725290488783, 34115496389871846238194377288783,
4530682210326970895, 7512261497832549810703, 590752242705409995,
22500160500421224350223, 12440305047364994046337551, 590753113463317596,
2496694421062159, 118945496728499, 4137164327970849295, 197234360349288395,
6851152186257633960463, 527 ]; 

PROPERTIES_SMALL_GROUPS[ 1656 ] := rec(
isNilpotent := [ 4, 28, -30, 36, 45, 105, -107, 137 ], 
isSupersolvable := [ 1, -11, 13, -36, 40, 42, -45, 48, -78, 80, -107, 116,
126, -130, 132, -137 ], 
isAbelian := [ 4, 28, 36, 45, 105, 137 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 116, 127, -130, 132,
135, -137 ], [ 40, 42, -45, 55, -84, 95, -107, 110, -115, 119, -121, 124,
-126, 131, 133, -134 ], [ 5, -31, 34, -39, 41, 46, -54, 85, -94, 108, -109,
117, -118, 122, -123 ], [ 1, -4, 32, -33 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 32, 38, 44, 50, 56, 62, 33,
39, 45, 51, 57, 63, 190, 196, 202, 208, 214, 220, 226, 232, 238, 107, 113,
119, 125, 131, 137, 143, 149, 155, 161, 167, 173, 179, 185 ], pos := [ 1, 2,
3, 4, 11, 12, 17, 22, 27, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42,
43, 44, 45, 46, 47, 54, 61, 66, 73, 78, 79, 84, 89, 94, 99, 104, 107 ] ) );