col20.z

#############################################################################
##
#W  col20.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 812 ] :=
[ 3119380439765099, 3842298867819, 1279920952245, 6908714389611,
5639566112952743, 315323204, 4552305128478150763, 3841767186599, 4877910183,
5606546900815979, 4551508155251167655, 37061789900967, 8516673703, 1593189113
, 6945229254823, 167 ]; 

PROPERTIES_SMALL_GROUPS[ 812 ] := rec(
isNilpotent := [ 6, 16 ], 
isAbelian := [ 6, 16 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 8, -9, 12, -16 ], [ 1, -7,
10, -11 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 819 ] :=
[ 8770190849, 17529076391, 14356718258327, 14582793078935, 10640149,
113060636567, 21899159, 11282393, 17529386903, 17805424535, 1943 ]; 

PROPERTIES_SMALL_GROUPS[ 819 ] := 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[ 820 ] :=
[ 7973924129284839, 9727183364839, 3231009342403, 41970649604839,
34504265034240159, 1313286360, 28192838859901444839, 9724968960159,
12451840159, 34405169973764839, 2645066467902403, 23200514417918568960159,
23200514461984975360159, 88925215188871680159, 28192056626833920159,
132250583040159, 51200000159, 4014081563, 42078167040159, 159 ]; 

PROPERTIES_SMALL_GROUPS[ 820 ] := rec(
isNilpotent := [ 6, 20 ], 
isAbelian := [ 6, 20 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 8, -9, 16, -20 ], [ 1, -7,
10, -15 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 824 ] :=
[ 3805265025146215829, 45777897231876, 3135533679660783191573,
4618029899601029, 3805259317589679365, 4618029791357813, 4618030549060325,
55528780110, 56286482622, 37674930588453870, 5600936968805, 101 ]; 

PROPERTIES_SMALL_GROUPS[ 824 ] := rec(
isNilpotent := [ 2, 8, -10, 12 ], 
isAbelian := [ 2, 8, 12 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 11, -12 ], [ 3, -10 ], [
1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14 ], pos := [ 1, 2, 7, 10 ] ) );

SMALL_GROUP_LIB[ 825 ] :=
[ 12729621339, 5141393, 16641339, 92943841933, 1339 ]; 

PROPERTIES_SMALL_GROUPS[ 825 ] := rec(
isNilpotent := [ 2, 5 ], 
isSupersolvable := [ 1, -3, 5 ], 
isAbelian := [ 2, 5 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 3, -5 ], [ 1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5 ], pos := [ 1, 2 ] ) );

SMALL_GROUP_LIB[ 828 ] :=
[ 48221382224765366255, 1217277163478565859, 42711404488851263072403,
70167251139437, 52046372355693103411, 173736440722631116, 1470135144824719,
58238384441117387, 51583821826503050547, 84457722163, 1470135129374449,
70167900497069, 1217277163798091043, 58099232053433583,
1007905508280880175471, 84442271914, 39831787589212835255535,
758549860372286938389920111, 1609796737331727, 1336266613662667279,
209829508454347, 3995792462032792079, 1106428758120213265935, 140082149747804
, 1773838905871, 85096772531, 1470135454042639, 70168225165259,
1217277163957843471, 527 ]; 

PROPERTIES_SMALL_GROUPS[ 828 ] := rec(
isNilpotent := [ 4, 10, 16, 30 ], 
isSupersolvable := [ 1, -5, 7, -16, 19, -23, 25, -30 ], 
isAbelian := [ 4, 10, 16, 30 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 20, -25, 28, -30 ], [ 5,
-11, 14, -19, 26, -27 ], [ 1, -4, 12, -13 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 23, 27
, 31, 35, 39, 43 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
15, 16 ] ) );

SMALL_GROUP_LIB[ 836 ] :=
[ 404992479645, 764887156613, 646283832073667, 53855910, 7684481705651,
917070515, 487088955, 773058380723, 179 ]; 

PROPERTIES_SMALL_GROUPS[ 836 ] := 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[ 837 ] :=
[ 6983758753497959, 348368903131, 8343779247959, 6983733046527959,
6983745902847959, 8343778437959, 6983733045717959, 8343784107959, 415558771,
421228771, 347542678771, 1684827959, 27959 ]; 

PROPERTIES_SMALL_GROUPS[ 837 ] := rec(
isNilpotent := [ 2, 9, -11, 13 ], 
isAbelian := [ 2, 9, 13 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 12, -13 ], [ 3, -11 ], [
1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14 ], pos := [ 1, 2, 8, 11 ] ) );

SMALL_GROUP_LIB[ 840 ] :=
[ 87162325125931134941, 29722833292934370407, 24502751583197796914279,
34807967309000669, 172886441053056989, 103764818744504715,
145708751538570548327, 34643196435954601, 145224900182410681979,
87162654666590152857, 122395352740960141312763, 41192629478028,
[ ( 1, 7,12, 6,21)( 2,10,14, 3,19)( 4,13,17, 5,16)( 8,11,15, 9,18)
    (25,26,27,28,29,30,31), ( 1,16,23)( 2,18,20)( 3,10,17)( 4,21,22)
    ( 5,13,15)( 6, 7,14)( 8,19,24)( 9,11,12)(25,26,27,28,29,30,31) ],
511527139023470832243815, 429682738060407880628982887, 87714557863008529775,
87714557863008483119, 73680228603893625562031, 87714557863009929455,
73680228603893627008367, 73680228603893626961711, 61891392027269611894959023,
73216352818122732170249, 103764675034738121, 87162324786151208393,
103764675034691465, 103764675036137801, 24967178529131503496111,
35384324341083503, 29722831583328499055, 35384324341036847, 35384324342483183
, 20582311328449195998423983, 29169942359965969775, 24502751581488191042927,
29169942359965923119, 29169942359967369455, 87024164278419779979,
511643366579046147576935, 73129294670084681656473,
429780224952489110334079739, 725119175455010159, 725119175454963503,
609100108914035434415, 725119175456409839, 609100108914036880751,
609100108914036834095, 511644091489321554111407, 241843831183634195,
241843831183587539, 203148819041166206291, 241843831185033875,
203148819041167652627, 203148819041167605971, 170645007995426489068883,
610134468050945305787, 610134468050945259131, 512512953167670281544443,
610134468050946705467, 512512953167670282990779, 512512953167670282944123,
430510880660847912684317435, 172722111030358209, 172722111030311553,
145086573818879846145, 172722111031757889, 145086573818881292481,
145086573818881245825, 121872722008412412014337, 609100112338606689467,
609100112338606642811, 511644094369381001052923, 609100112338608089147,
511644094369381002499259, 511644094369381002452603,
429781039270284992228657915, 1015050250872522419387, 1015050250872522372731,
852642210737945371403003, 1015050250872523819067, 852642210737945372849339,
852642210737945372802683, 716219457019879138479942395,
512512950291035410336955, 512512950291035410290299,
430510878244474615897244411, 512512950291035411736635,
430510878244474615898690747, 430510878244474615898644091,
361629137725358682224861809403, 41440298233289, 41440299632969,
29238404900181306377, 24473270428384358475720, 20509443450069209836923054,
145224323143142042633, 205816400309705, 172886098597688777, 205816400263049,
205816401709385, 87162242495680965711, 123528987667983, 103764574133859855,
123528987621327, 123528989067663, 122395349855763846376367,
173462795409698159, 145708749826289235311, 173462795409651503,
173462795411097839, 29100161848219889149, 41241575026621, 34643049670031293,
41241574979965, 41241576426301, 121988915291231618837843, 172886783521206035,
145224899155042432787, 172886783521159379, 172886783522605715,
73216629304217541783297, 103765063367930049, 87162653932756072641,
103765063367883393, 103765063369329729, 102812096298096668045658875,
145708753250859044027, 122395352735823294764219, 145708753250858997371,
145708753250860443707, 48922408866, 48923855202, 34560762233547810,
[ ( 1, 3, 7, 4)( 5, 6)( 8,10,12, 9,11), 
  ( 1, 5, 7, 3, 4, 6, 2)( 8,12,11,10, 9) ],
[ ( 2, 5, 3, 4)( 6, 9,12, 8,11, 7,10), (1,5,2)(3,4) ],
[ ( 2, 7)( 3, 6)( 4, 5)( 8,12,11, 9), 
  ( 1, 5)( 2, 4)( 6, 7)( 8,12, 9)(10,11) ],
[ ( 1, 7)( 2, 6)( 3, 5)(10,12,11), ( 2, 3)( 4, 5)( 6, 7)( 8,11,12, 9,10) ],
[ ( 1, 2)( 3, 6, 9, 5, 8, 4, 7)(10,13)(11,12), (10,13,12,11,14) ],
511585130748045492874607, 68806843723387209770686194120,
608960879794952009519, 511527069119538320865071, 104422103097311291,
609167915313683098991, 511702083219027220753595, 87162078618188855937,
511701048863314882137275, 512512949428046290843259,
429829749901109824103320763, 726350552736104507, 138202057339318728,
48801178784356189991820, 40992990179502644930511036,
40992990179173495279946388, 51579521340845819590125437004, 41351650246715,
42134396092475, 34726132081410107, 725199897447532445, 29480617456624633757,
517999898881329483, 2033378335751559562535, 32622478852031595815,
26390421167410785928487, 103600219457664975, 609099245929508337455,
87058684141568752257, 511643124943428756870779, 863235289940027,
287908314513527, 726350551398383675, 205620901871805, 725119175460888635,
1208393149816553531, 610134464626385854523, 61152952379, 82336908314700,
35095973539481501, 244635697211, 146790973509, 206501325226043, 48946249867,
205816412160119, 123528999518397, 173462795415576635, 59 ]; 

PROPERTIES_SMALL_GROUPS[ 840 ] := rec(
isNilpotent := [ 12, 131, -133, 186 ], 
isSupersolvable := [ 1, -12, 14, -93, 96, -133, 139, 141, -150, 156, -158,
165, -176, 179, -186 ], 
isSolvable := [ 1, -12, 14, -133, 139, -186 ], 
isAbelian := [ 12, 131, 186 ], 
lgLength := rec( lgLength := [ 4, 5, 6, false ], pos := [ [ 140, 143, 150,
-151, 156, -158, 169, -176, 179, -186 ], [ 16, -37, 42, -133, 139, 141, -142,
144, -149, 152, -155, 159, -168, 177, -178 ], [ 1, -12, 14, -15, 38, -41 ], [
13, 134, -138 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37
, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95,
98, 101, 104, 107, 110, 113, 116, 119, 122, 125 ], pos := [ 1, 2, 3, 4, 5, 6,
7, 8, 9, 10, 11, 12, 13, 14, 15, 22, 27, 32, 37, 38, 39, 40, 41, 48, 55, 62,
69, 76, 83, 90, 93, 94, 95, 100, 105, 110, 115, 120, 125, 130, 133 ] ) );