col19.z

#############################################################################
##
#W  col19.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 792 ] :=
[ 415178136534123285090011, 4695581194715655010109,
337915392985896321931000191, 659401211915019010,
270239803192622856546603000191, 430822990329948425000191,
341211808341414652171000191, 341211872717958031657000191,
430822990329948426000191, 430823071613462824000191,
341211872717958031658000191, 328411631566136148377191000,
3730353400568611367001019, 5928775582214001019, 4710042172391974001019,
5928775582213001019, 5947022901796001019, 328825246268160738099009011,
524214818833170009011, 415183391752717106009011, 524214818833169009011,
524221454222128009011, 267629042230970129843115000191,
426660849729405834000191, 337915457362335892394000191,
426660849729405833000191, 426660931012920232000191, 833617925001901,
2492465188001901, 1563436155666471001901, 5928764047881011009,
660231684617019001, 4695590329910021010019, 522906004095749090011,
3718907568901325699000119, 832569361011900, 518565698156451093119940091100,
410704032939969883507012578019100, 11482069540542978011009,
543968422013192000191, 1974036606978019100, 7485784584000119,
661887386384000911, 538713193972616000191, 1048584000191,
327997495952101442309090011, 2857499784781836878617475000119,
7242582594050001019, 7242582594049001019, 5736125445444099001019,
7242582594080001019, 5736125445444130001019, 5736125445444129001019,
4543011352822682147001019, 5751891198745090000119, 5751891198745089000119,
4555497829504653827000119, 5751891198745120000119, 4555497829504653858000119,
4555497829504653857000119, 3607954280967784372771000119, 1974041842178009011,
1563441144795651009011, 1974041842208009011, 1563441144795682009011,
1238245386683945507009011, 17196464043199234000119, 17196464043199233000119,
13619599522315373315000119, 17196464043199264000119,
13619599522315373346000119, 13619599522315373345000119,
10786722821673877244707000119, 4555497774693489282000119,
4555497774693489281000119, 4555497774693489312000119,
3607954237557341952674000119, 2857499756145414924933795000119,
414661150967464344119000, 4695572001849891001109, 7485784578001109,
5928752513570001109, 7485784577001109, 7485784608001109,
522901005533731001901, 833618434001901, 660228538914001901, 833618433001901,
833618464001901, 3718907513917145891001019, 5928775582466001019,
4695590295307042001019, 5928775582465001019, 5928775582496001019,
414141547778409251009011, 660234830594009011, 522905994658594009011,
660234830593009011, 660234830624009011, 2945374794487736304547000119,
4695590364513154000119, 3718907568797516706000119, 4695590364513153000119,
4695590364513184000119, 1048577001190, 1048608001190, 658565496867001190,
205742001983939041655489285090011, 1792418649409583676394945174403000119,
3607995419522308823554000119, 327998020818822377760009011,
2857518721972306518789024000119, 1792421485339613114971104271266000119,
162947925998396196819091993379009011,
1419600062445556936790585260432291000119, 21714365862400000119,
826710441148679040019100, 654754669416063009728011900,
654754669389454345152091100, 776704275688090553562080011900,
21714365848064011009, 5922098256384019001, 34446193546235648010019,
414140226497544961009011, 3607954237511666025345000119, 9144635904000119,
7262488762880000119, 2492469760000911, 21712706996992000119,
5751891129539200000119, 1664102400011900, 9437696000119, 1049088000191,
7485784832000119, 833618688000911, 5928775582592000119, 119 ]; 

PROPERTIES_SMALL_GROUPS[ 792 ] := 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 ] ) );

SMALL_GROUP_LIB[ 798 ] :=
[ 258274552751, 262465194671, 206094813924527, 815846598575, 206176407990191,
207806253608879, 43176209531, 651042661107887, 206180598632111,
207810444250799, 164528759942385839, 165829376746098863, 335923631, 67185275,
258385407407, 260427820463, 917070767, 272098427, 734252532911, 57108871,
730167708023, 214834649243, 585936654243119, 431 ]; 

PROPERTIES_SMALL_GROUPS[ 798 ] := rec(
isNilpotent := [ 24 ], 
isAbelian := [ 24 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -24 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 804 ] :=
[ 226587403796317013, 281846193586517, 7840683768853, 508360823634773,
408723552418900883, 9734048214, 219342483436163, 523964413159043,
276879347843, 15651880802316, 177409899065706185, 632086405763, 10322260675,
508361108251523, 131 ]; 

PROPERTIES_SMALL_GROUPS[ 804 ] := 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[ 808 ] :=
[ 3313425718700000099, 41472500990000, 2674168559325100000099,
2677243804727500000099, 4100765000000099, 3313420548200000099,
4100764900000099, 4100765600000099, 51300009900, 52000009900,
33468058700009900, 3309614569700000099, 5072000000099, 99 ]; 

PROPERTIES_SMALL_GROUPS[ 808 ] := rec(
isNilpotent := [ 2, 9, -11, 14 ], 
isAbelian := [ 2, 9, 14 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 13, -14 ], [ 4, -12 ], [
1, -3 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14, 17 ], pos := [ 1, 2, 3, 8, 11
] ) );

SMALL_GROUP_LIB[ 810 ] :=
[ 1220544986396074341824316245, 6861707161603465559,
988641491113610525154211766741, 2828403468247509, 8505989458321751,
14100141415874903, 11421114563230196055, 8471243172921687,
11421079816944795991, 14141837025476951, 11454887952671326551,
11426750410801545559, 9278459241673418367319, 2296614872549499349,
2285350118241608149, 5548818780622440399317, 1851139203822930436565,
1860303105792673415637, 2828403470279125, 1499422800155587651404245,
2290989453777830357, 1855692982498121744853, 1855701457126244753877,
1503111315830417426776533, 1855701457121949786581, 3000673812880212396376533,
1869433192832076128605, 9251074651913434177879, 22465306883463742041637213,
1499431930242627054117213, 1506868487434523222294901, 6861707161604481367,
1214532491097768448602489205, 1883105831880176173405,
7515551985790391928226135, 1525315723822892121334109,
1235490929493797667426025821, 1525315723822887826366813,
2448516552104131592802025821, 1503134225550625579254613,
1855715630264440603477, 1506827351320952886346581, 1503111313005643382391637,
1217520163534574461598319445, 2996980687103039623660373,
986191332465287835125764899669, 1217568336527236909395501429,
1503170780200247444250997, 1220563456961928925913489781,
1217520163585356878718042485, 986191332504139075228991889781,
2427554356604247400262795637, 798814979328354933457091387351413,
3491808436597, 10441069699445, 8464225198432629, 3491808485749,
2821419855585653, 3491829383541, 2828369129390453, 2828373424357749,
2290982461045236085, 10458247496023, 17407571657047, 14100098529132887,
14100098470396247, 2835326958633333, 3491810525557, 2821419871240565,
10441071788405, 2285357041728946549, 8457275943436661, 2307942213138022749,
8471243173937495, 11421079816950514007, 42279378896290135,
1851150531163510571357, 34246296964481171799, 2291013771339530709,
2828403471294933, 2285350118233735637, 2828404006584789,
1851133602721712079317, 1851133602721720467925, 2291006814027260373,
1869427716817493442909, 6861707161604989271, 9251074651913430237527,
2307935444334805341, 1499431924766612467237213, 1499431924766612471431517,
1869427709859711426909, 1855715616340091618133, 2291006925696664405,
1514236445459448300708189, 1869427710435237167453, 4294975837, 4299161949,
3483222679901, 3483222704477, 10408256018897895357793446418842453,
57013460834100093381449661285205, 77676447726961689429, 12886999383,
4297064797, 10458248511831, 3491811557749, 8471243174445399, 2828403471811029
, 6861707161605243223, 2291006925161890645, 5557982801476886331735, 343 ]; 

PROPERTIES_SMALL_GROUPS[ 810 ] := rec(
isNilpotent := [ 4, 54, -62, 97, -100, 113 ], 
isSupersolvable := [ 1, -100, 104, -113 ], 
isAbelian := [ 4, 54, 57, 97, 113 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 101, -104, 111, -113
], [ 5, -7, 22, 35, 40, -41, 47, -48, 54, -56, 63, -66, 69, 75, 81, 88, 93,
-100, 105, -110 ], [ 8, -13, 15, -16, 21, 23, -26, 28, -29, 34, 36, -39, 42,
-46, 49, -53, 57, -62, 67, -68, 70, -74, 76, -80, 82, -87, 89, -92 ], [ 1, -4
, 14, 17, -20, 27, 30, -33 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 95, 99
, 103, 107, 111, 115, 119, 123 ], pos := [ 1, 2, 3, 4, 13, 26, 39, 46, 53, 62
, 66, 72, 78, 85, 92, 94, 96, 100 ] ) );