col15.z

#############################################################################
##
#W  col15.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 675 ] :=
[ 7678344568285, 11408512375, 56639902071, 38232003728759, 25890915562491231,
11374962165, 16785759, 38356910279007, 25890914723645791, 38356910277983,
25890914723644767, 38356910293343, 16778621, 16793981, 11341415805,
56824627551, 351 ]; 

PROPERTIES_SMALL_GROUPS[ 675 ] := rec(
isNilpotent := [ 1, -4, 6, -7, 13, -15, 17 ], 
isSupersolvable := [ 1, -4, 6, -7, 13, -15, 17 ], 
isAbelian := [ 1, -2, 6, -7, 13, 17 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 16, -17 ], [ 7, -15 ]
, [ 2, -6 ], [ 1 ] ] ),
frattFacs := rec( frattFacs := [ 7, 14, 15, 21, 34, 35, 41 ], pos := [ 1, 4,
5, 6, 7, 12, 15 ] ) );

SMALL_GROUP_LIB[ 676 ] :=
[ 36828788627785103, 7315061051, 16829891845252534732175, 54480454972559,
10699919, 79085467451, 54396114796943, 10639284, 53396863547195,
24856918345893429647, 24856918625795588495, 469052109032898959, 1026426691727
, 117448847, 80465965199, 143 ]; 

PROPERTIES_SMALL_GROUPS[ 676 ] := rec(
isNilpotent := [ 2, 5, 8, 16 ], 
isAbelian := [ 2, 5, 8, 16 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 13, 15, -16 ], [ 4, -5,
7, -8, 10, -12, 14 ], [ 1, -3, 6, 9 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 22, 15, 19, 23 ], pos := [ 1,
2, 3, 4, 5, 6, 7, 8 ] ) );

SMALL_GROUP_LIB[ 680 ] :=
[ 23890498025484291, 119358756203016207, 81434647873218150463, 11716680236800
, 81124036254918258703, 55115998238434707636287, 16213704441089552387,
187419213353855837274175, 37654985623304012206964799,
37654985758351527888551999, 405319242672504895, 405319242671456319,
275617086020500062271, 405319242687184959, 275617086020515790911,
275617086020514742335, 187419618494942542823487, 81163755816133591823,
175526859768591, 119358464158860047, 175526858720015, 175526874448655,
16245480236952588035, 35132968800003, 23890412139712259, 35132967751427,
35132983480067, 55375559562113372389439, 119756831015829567,
81434646412944998463, 119756831014780991, 119756831030509631, 17180918768,
17196647408, 7955671021519856, 55164272956583252602895,
25508117712539356851870892095, 25508117712674404367552479295,
37478608436018267181547583, 37655196185615621547884607, 275632156203894702143
, 81433793608985608255, 119300061175743247, 23843691467640579,
55374978857802365141055, 55374979056401652908095, 275616490224312385599,
81052938586133889087, 596056232427583, 257832255551, 51673825523,
176111040331839, 63 ]; 

PROPERTIES_SMALL_GROUPS[ 680 ] := rec(
isNilpotent := [ 4, 33, -35, 53 ], 
isAbelian := [ 4, 33, 53 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 49, -53 ], [ 11, -35, 40
, -48 ], [ 1, -10, 36, -39 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35, 38
, 41, 44, 47 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 17, 22, 27, 32, 35
] ) );

SMALL_GROUP_LIB[ 684 ] :=
[ 59689813645188769355, 87309336687351371, 9979638822520805755,
246635591954409035, 7282643905859800967191, 21268620290989, 87265814828803559
, 10762844443569176311, 127650393576935, 43473915472759740,
60269182438774211081, 360576019981799, 14590115207616151,
10647140205935842039, 30966241015, 67923984755560865179211,
59487034787931559499, 87265809018387773, 87309336804504587,
59689813645305922571, 127644583161149, 360576014318909, 21268858376557,
246635592071562251, 14548011386810491, 168698750021858710151, 30960578142,
59486991266073011687, 145244926061236583, 86969369726375399,
40709495773187644686857, 551607001314730217, 127588710519143, 127650506951015
, 87265814942177639, 6806345318952113090683, 88454116180570393436664455,
402866539647335, 276407443474477415, 63559383704983, 825960271774021991,
189062691944892503399, 193491763559, 42444716088924, 87711674202860777,
526539460967, 31200547447, 360576133355879, 21268977413527,
246635592130133351, 359 ]; 

PROPERTIES_SMALL_GROUPS[ 684 ] := rec(
isNilpotent := [ 6, 15, 27, 51 ], 
isSupersolvable := [ 1, -9, 12, -30, 33, -35, 38, -43, 46, -51 ], 
isAbelian := [ 6, 15, 27, 51 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 32, -33, 39, -46, 49,
-51 ], [ 7, -15, 18, 21, -22, 25, -31, 34, -38, 47, -48 ], [ 1, -6, 16, -17,
19, -20, 23, -24 ] ] ),
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, 71, 75 ], 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, 26, 27 ] ) );

SMALL_GROUP_LIB[ 686 ] :=
[ 743627361519753911, 459849527, 1579988379671, 2280672503, 314564270039,
215793721519127, 1082112192480887, 328359485015, 666359, 746711, 2731929335,
3359447, 2299270103, 1577419111511, 215 ]; 

PROPERTIES_SMALL_GROUPS[ 686 ] := 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[ 688 ] :=
[ 28633802167318602556553, 1016500461958779336, 41618897981185291241,
28633738636577108164073, 19700055701247441708683753,
19700055701339515249922537, 13553638322521662224771105417,
41618897981054600009, 28633738636576977472841, 41618897980793217545,
28633801891099547134985, 28633738636576716090377, 41618897982753586025,
20658128945401708930060457, 14212792714436428671347392841,
14212792714436428671478084073, 9778401387532262978724817887881,
41618897982622894793, 1477459542256740, 2948496786609444, 2030039580961060452
, 1477460326404132, 1015023004373998116, 698335826981031711108,
480455048911220217561636, 330553073650867690428539748,
28633738544505527293769, 60492333845123753, 41618805911564789417,
41618805911303406953, 63434437608665129, 30026350119186870265193,
30026350119183210910697, 20658128882055110728099817, 60492333453050057,
60492337504478249, 2141375838042, 2143336206522, 1015020862344635034,
1475320518791994, 87807779426345, 41 ]; 

PROPERTIES_SMALL_GROUPS[ 688 ] := 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[ 690 ] :=
[ 2526217275, 367314357, 1746204194107, 127437179, 1740686997719,
248884828877, 1204886941093307, 571 ]; 

PROPERTIES_SMALL_GROUPS[ 690 ] := rec(
isNilpotent := [ 8 ], 
isAbelian := [ 8 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -8 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 693 ] :=
[ 3584331915, 5131591, 5441195, 1159 ]; 

PROPERTIES_SMALL_GROUPS[ 693 ] := rec(
isNilpotent := [ 2, 4 ], 
isAbelian := [ 2, 4 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 3, -4 ], [ 1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5 ], pos := [ 1, 2 ] ) );

SMALL_GROUP_LIB[ 696 ] :=
[ 137183498656552769, 3693719851600142811, 2570834755564228629559,
196818474116208, 2568364665425772896731, 1788057156610247353750583,
3966521611704809527, 3966521611687599159, 2760699058599266735159,
3966521611945754679, 2760699058599524890679, 2760699058599507680311,
1921446544801930663924791, 66549086122543358426176, 2570823331923624695595,
5307047488469803, 3693711674558446379, 5307047471259435, 5307047729414955,
95479125556763289265, 197102531218097, 137182652955708081, 197102514007729,
197102772163249, 1789300972820772586427447, 3693728029915363383,
2570834731032690554935, 3693728029898153015, 3693728030156308535,
281991881220, 282250036740, 136789578080950788, 2570819815778493963319,
132621326134380057431632, 92304443009895435096221808, 7939478160660387291,
3691160508445269803, 2568364673604070906935, 5699001056100407,
393381098858608, 7615518998583, 284177597173, 5307048555511863, 55 ]; 

PROPERTIES_SMALL_GROUPS[ 696 ] := rec(
isNilpotent := [ 4, 30, -32, 44 ], 
isSupersolvable := [ 1, -13, 15, -33, 37, -39, 41, -44 ], 
isAbelian := [ 4, 30, 44 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 39, 41, -44 ], [ 7, -38,
40 ], [ 1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35, 38
], pos := [ 1, 2, 3, 4, 5, 6, 13, 14, 19, 24, 29, 32 ] ) );

SMALL_GROUP_LIB[ 700 ] :=
[ 132282846375042477, 312763590610367, 92866925739443956845, 89818422879,
64818593536984360738221, 47300167530455930056150125, 137903411174044173,
446799784451, 188975491824585, 132667036740554253, 127433229, 446799761753,
268182180255, 314012130535679, 188621823863469, 219814755318280931, 127410546
, 187370799583647, 917989878628739327, 92423195158993431213,
452873567560757170524899, 92423195604900375213, 452873567557635821916899,
655671383612844717, 3212087526144623055587, 1873451151491, 1320331105161347,
1338108014793, 6555280662669443, 924231782120168579, 638005379, 383201421,
448583878787, 269456689353, 314021048915075, 131 ]; 

PROPERTIES_SMALL_GROUPS[ 700 ] := rec(
isNilpotent := [ 4, 11, 17, 36 ], 
isAbelian := [ 4, 11, 17, 36 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 27, -31, 34, -36 ], [ 7,
-12, 15, -17, 20, -26, 32, -33 ], [ 1, -6, 13, -14, 18, -19 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 46, 23
, 27, 31, 35, 39, 43 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15, 16, 17 ] ) );

SMALL_GROUP_LIB[ 702 ] :=
[ 2842906272333614951, 4055553978847079, 997175951831028751069,
22137405464956775, 700133418830895147992317, 2874191250685, 4049724095412071,
2846918631750711143, 2846918684749936487, 4049724094914407,
2846918631750213479, 4055439920727911, 5941951743961311918037,
5943362128394618845141, 8464433039005890517, 4055553993776999,
2846924461656541031, 4171250108302403739957205, 4172240198174585202784213,
5942016034989563033557, 2842906272348544871, 1998536879401721562983,
5777171363687, 4055448043599719, 4055501042825063, 5777170866023,
4055448043102055, 5777234069351, 31534571927399, 37250397243239,
26149764882052967, 2023408551816445, 2874221110525, 2011968998280445,
1412407841986145533, 1476801900658669525, 22137405479886695,
18357135038541104999, 991566674082185197525, 1416443202883418845,
2017717734132445, 1036711253748489838549, 1476796649693333461, 4077363157,
4140566485, 2866099232725, 6958385472935437816744669, 48289898084715229,
5769048491879, 5777186293607, 4049724110341991, 4055554001241959,
2842906272356009831, 8408532839, 44877350759, 4108715989, 31534586857319,
2874236538109, 22137405487351655, 2017717256375005, 15540459090043946855,
1895 ]; 

PROPERTIES_SMALL_GROUPS[ 702 ] := rec(
isNilpotent := [ 6, 44, -46, 62 ], 
isSupersolvable := [ 1, -46, 49, -62 ], 
isAbelian := [ 6, 44, 62 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 47, -49, 54, -55, 60,
-62 ], [ 7, -12, 17, 22, -31, 34, 38, 40, -46, 50, -53, 56, -59 ], [ 1, -6,
13, -16, 18, -21, 32, -33, 35, -37, 39 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 35, 38
, 41, 44, 47, 50 ], pos := [ 1, 2, 3, 4, 5, 6, 12, 17, 22, 28, 31, 35, 39, 41
, 43, 46 ] ) );