col22.z

#############################################################################
##
#W  col22.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1940 ] :=
[ 253311921773571, 8018791033236575, 15572836857695699327, 21091058712959,
15550041753620868191, 491082475424799747, 58609852849160774589874559,
58609852857344072415707519, 92411535562182264619391, 30167097342106625114495,
24554032852894079, 4133939577215, 133177549731, 8027228696740223, 383 ]; 

PROPERTIES_SMALL_GROUPS[ 1940 ] := 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[ 1950 ] :=
[ 31092048834934943, 302342420407200954615, 589565489016586190305527,
15953022630047, 87501753890975, 46657872158223639, 91542482698062903543,
7962146747029, 170628515079695879, 90983041412830931703,
178507843813041095211255, 53000222879, 1179340922221622105131767,
1264952504715469310154722583, 63644202567839, 63758338820255,
124105795327035551, 124329028040296607, 242006301092983507103,
4433960286689036447, 242844353243721107615, 362768724051655462167,
9196186719395523639806111, 480225380009111462119583,
928775543312260803894610079, 32869714079, 39798723579159, 124535566188677279,
44877351071, 12262443255, 87607767271583, 23910852136215, 170835848056703135,
4108719733, 87501768824327, 23870083504767, 170835318064452863,
46626170473728759, 333129904926917347487, 2207 ]; 

PROPERTIES_SMALL_GROUPS[ 1950 ] := rec(
isNilpotent := [ 12, 40 ], 
isSupersolvable := [ 1, -12, 15, -19, 26, 29, -40 ], 
isAbelian := [ 12, 40 ], 
lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 13, -15, 18, -29, 32, -35,
38, -40 ], [ 1, -12, 16, -17, 30, -31, 36, -37 ] ] ),
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[ 1953 ] :=
[ 812877983135, 19451638921559, 38039305368358079, 37989088582438079,
89995078079, 25118424028079, 1684828079, 440668775, 3252687868079,
3278400508079, 28079 ]; 

PROPERTIES_SMALL_GROUPS[ 1953 ] := rec(
isNilpotent := [ 5, 11 ], 
isAbelian := [ 5, 11 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 6, -11 ], [ 1, -5 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11 ], pos := [ 1, 2, 3, 4, 5
] ) );

SMALL_GROUP_LIB[ 1956 ] :=
[ 77013984100564419893, 39373967188083509, 690842021482261,
111109083795111221, 217329495920001669203, 172441031841107, 39373371421438787
, 112487944653449027, 20276727460163, 2069669824215948, 77127909614920426409,
56796876809027, 374678685667, 111109094126298179, 323 ]; 

PROPERTIES_SMALL_GROUPS[ 1956 ] := rec(
isNilpotent := [ 6, 15 ], 
isSupersolvable := [ 1, -9, 12, -15 ], 
isAbelian := [ 6, 15 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -15 ], [ 1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1960 ] :=
[ 1106028717428748424647, 3625057373758066695193235,
7105166224510783926336972623, 211456635427456847, 2166341889970531686520263,
407726319279843313578626380556111, 407726319352042399787397045358415,
106134506263590102846509327, 208023632276636613306111641423,
208023632322470612130445416719, 106134506263590102846462671,
106134506286974796125629583, 208023632322470612130445370063,
7105130124948857958716346731, 1849519068241502114603,
3625066390280028385860395, 1849519068241502067947, 1849523668509033557675,
2178866223649204558383129, 564301587371051481, 1111666440636501299673,
564301587371004825, 567176754578728281, 13926125889875750710696017538895,
3625084808423857162203407, 7105166270344770764692093199,
3625084808423857162156751, 3625084831808550441323663, 107873808685775,
23492567087852687, 90249069220595260215119, 208055386620072081334452982031,
2579479070044005066024, 1105276475708326024089,
208023632285634343651140827855, 54150257818549534860431, 943152981953356943,
287908123783893, 1848593365034385097871, 48923108495, 940372626272091053,
1848396032382664597139, 564300364312151499, 1845763526548945004711,
3622874655723674801275727, 23516490120700751, 7100794131169004779561442963,
1105276474485267170763, 15163651238723412256254119,
208023630075481643468111086415, 27278564994133417083757079002219343,
13917556497109681612603708408655, 943059198143344427, 1848396029985827087723,
943059198144744107, 1848396029985828534059, 3622856218773845873995115,
3947224203070140623, 3947224203070093967, 7736559439308406302479,
3947224203071540303, 7736559439308407748815, 7736559439308407702159,
15163656501045767193587471, 54150257734354149453071, 54150257734354149406415,
106134505159345861343765327, 54150257734354150852751,
106134505159345861345211663, 106134505159345861345165007,
208023630112317899962105834319, 1848405436581881236751,
1848405436581881190095, 3622874655711689180939087, 1848405436581882636431,
3622874655711689182385423, 3622874655711689182338767,
7100834325194921996507564879, 3622853597018407833619727,
3622853597018407833573071, 3622853597018407835019407,
7100793050156090181482288399, 13917554378305936766529946667855,
1843129676573322866177, 479781626703809, 940372283816720321, 479781626657153,
479781628103489, 3622856218773845515677035, 943059197785026347,
1848396029985470215979, 943059197784979691, 943059197786426027,
1106028234809650016175, 287908123505007, 564300119701502319, 287908123458351,
287908124904687, 3617696508681499805724431, 941716083262632143,
1845763524836663687375, 941716083262585487, 941716083264031823,
7100834325194921996149246799, 1848405436581522918671,
3622874655711688824067343, 1848405436581522872015, 1848405436581524318351,
11985978701519, 11985980147855, 46068840104115891023,
27278396596993923711617385871335059,
104792699195292391511010805652918466642767,
53465662854668809277968755546968032079, 7736932442970256437455,
106150707459136249055816975, 106134505140551847846221519,
208023630072831675434535884495, 27278565072837414298382666137900751,
7100834286269641273071990479, 7100793767127598508967561899,
13917554328907363697004734097551, 27278375377679187731651659625239823,
53465615740241779305902047497145527659,
104792585042078963579706269195085684067151, 27627682512570826895,
1316060750491318440, 3622854148555630616738027, 563916592844192559,
7736556754455123688079, 106134505140551847487903439,
13917635201088478103950855149263, 7100794131178408978419717839,
481151823003791, 2013889240793291, 27627682511543648399, 943063992540684431,
1848394692350806155407, 244635697295, 481151464685711, 146790973653,
480466551619787, 943063992182366351, 143 ]; 

PROPERTIES_SMALL_GROUPS[ 1960 ] := rec(
isNilpotent := [ 4, 29, -31, 40, 46, 109, -111, 144 ], 
isSupersolvable := [ 1, -32, 34, -46, 48, -50, 53, -111, 115, -118, 126, 129,
-131, 134, -144 ], 
isAbelian := [ 4, 29, 40, 46, 109, 144 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 126, -127, 134, 136,
-138, 140, -141, 143, -144 ], [ 33, 36, -40, 53, -57, 65, -83, 89, -98, 104,
-111, 116, -125, 128, -129, 131, -133, 135, 139, 142 ], [ 7, -32, 34, -35, 42
, -43, 45, -48, 50, -52, 58, -64, 84, -88, 99, -103, 112, -115, 130 ], [ 1,
-6, 41, 44, 49 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 32, 38, 44, 50, 56, 62, 68,
195, 201, 207, 213, 219, 225, 231, 237, 243, 34, 40, 46, 52, 58, 64, 113, 119
, 125, 131, 137, 143, 149, 155, 161, 167, 173, 179, 185, 191, 197, 203, 209 ]
, pos := [ 1, 2, 3, 4, 5, 6, 13, 18, 23, 28, 31, 32, 33, 34, 35, 36, 37, 38,
39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 57, 64, 71, 78, 83,
88, 93, 98, 103, 108, 111 ] ) );

SMALL_GROUP_LIB[ 1962 ] :=
[ 11812828591880974439, 6020962799226983, 268824266727620509,
14630977176088679, 612210397743414310069, 7592888897639,
23157999528529532661863, 11803261925203087463, 6020827566624359,
6020964703911527, 11812828593785658983, 3082323799655, 7457656295015,
74010622645, 14630979080773223, 136882604882845, 28705990929382041191, 11879
]; 

PROPERTIES_SMALL_GROUPS[ 1962 ] := rec(
isNilpotent := [ 6, 18 ], 
isAbelian := [ 6, 18 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 9, 12, -13, 16, -18 ], [ 1,
-8, 10, -11, 14, -15 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1972 ] :=
[ 9314310804415, 16765239668491, 33313129773241023, 155149623999,
33049851179085579, 18364683412624319, 129546976272087134393023,
129546976110111569105599, 1049846570272440570559, 65174558292084396735,
269967831491007, 8516673983, 4740227843, 16893018649023, 447 ]; 

PROPERTIES_SMALL_GROUPS[ 1972 ] := 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[ 1974 ] :=
[ 212793209761623, 4537489734239, 420053486797885527, 2865576031,
103303867223, 11605570143, 204177939663959, 2435748715, 203746957667503,
22642817464103, 403047583113272535, 2391 ]; 

PROPERTIES_SMALL_GROUPS[ 1974 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1976 ] :=
[ 1330481870630829299, 2056132451266966601, 4085897824102703847479,
15125359490400311, 2628306098253023034611, 98649402606121696728487991,
25265077789781293847, 25265077789779404279, 49923793717858754842679,
25265077789807747799, 49923793717858783186199, 49923793717858781296631,
98649416386494146783781431, 4062916561482537135965, 1040552510113853,
2056131863076510269, 1040552508224285, 1040552536567805,
2629031381005843724015, 673320622903247, 1330481468192432591, 673320621013679
, 673320649357199, 8073734085323796011264567, 2067762049358856983,
4085897816455937709335, 2067762049356967415, 2067762049385310935,
7646796371447, 7646824714967, 29872607922763846199, 49937801788912049290007,
1330114437504531119, 49923786743985207094775, 12785967880261847, 526539460823
, 340787368253, 1046434776864983, 215 ]; 

PROPERTIES_SMALL_GROUPS[ 1976 ] := rec(
isNilpotent := [ 4, 29, -31, 39 ], 
isAbelian := [ 4, 29, 39 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 35, -39 ], [ 7, -34 ], [
1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35 ],
pos := [ 1, 2, 3, 4, 5, 6, 13, 18, 23, 28, 31 ] ) );