col12.z

#############################################################################
##
#W  col12.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1508 ] :=
[ 5224419283899, 12822629556939, 19474239741858383, 118643974735,
19327961753232075, 7875550488613819, 44285405621926265508431,
44285405580638376317519, 344287528154416665167, 29146703801035919951,
151397483045199, 8516673871, 3481412351, 12913902891343, 335 ]; 

PROPERTIES_SMALL_GROUPS[ 1508 ] := 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[ 1518 ] :=
[ 366721209535, 366927358511, 556583181863983, 419787455, 2526217407,
1086948795, 3848256370111, 127440083, 3826187584559, 1639938185939,
5841666457636415, 703 ]; 

PROPERTIES_SMALL_GROUPS[ 1518 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1520 ] :=
[ 376152132577594243451475, 2130758680373761874075009,
3243517265304717725488489991, 7838221652457996477959,
571249842855235396121299539, 16497305185628685227664939263495,
7140458237613849992128967, 7140458237613849958116743,
10853496521179589844092675591, 10853496516029650226234388935,
10853496516029650226200376711, 16497314704365074880079061642759,
16512154163914040706035253512519, 16497314712187836549327713796551,
16512154171736802375279620126087, 25098474329149341876265562272039367,
25098474329149341876265562238027143, 16497314712187833161209543459271,
25075918362525506408183284145847815, 16512154179564710596026871838087,
25098474352938354962504576252374535, 38149680980306999651926746527069699591,
25075918362525511558122903058513415, 25098474341039934466968753650134535,
7140463384165350632420615, 7140458237613850944471239,
7140463384165351652787335, 10853504354234362093039058183,
10853496521176201726874680583, 10853504343934482855213726983,
10853504349084422474126392583, 1401814919533050109673,
2130757649030591809464041, 3238753191079482405477435113,
3238753191080160029111502569, 4922904850441843886637889831721,
1401814919533016097449, 2130757649030591775451817, 1402844229832960489769,
2130758678340891719844137, 2132324259985041170186537, 1401814919533866403049,
3619250589321231036981464681, 5501260895768271712894525590185,
5501260895768271712894559602409, 8361916561567773004136309965800233,
1402844229833980856489, 247468507823207341515, 376151861171497583207883,
571751240705124411912324555, 571751240705302733921289675,
869061885872060298647017128459, 247468507823173329291,
376151861171497549195659, 247739378954587273227, 376152132042628963139595,
376564127212141976387595, 247468507824023634891, 952249791774908511323000139,
1447419683497860974591910381963, 1447419683497860974591944394187,
2200077918916748681417033100198411, 247739378955607639947,
2133892937691582395492807, 3243517260148001871289528775,
4930146243247727860085298119111, 4930146243247731248203468456391,
7493822289736551500612442083573255, 2133892937691582361480583,
3243517260148001871255516551, 2133898084243083035784455,
3243517265294553371929820423, 3243525093202774119181532423,
2133892937691583347835079, 27493354230151259093624265132359,
41789898429829913825599251842286983, 41789898429829913825599251876299207,
63520645613341469014914153117486759431, 2133898084243084056151175,
5156715855355376903, 10303267357118071943, 15666119708851689520391,
5156715855423401351, 7833064936603763504519, 11906258707023964079360327,
18097513234679755447857218951, 27508220116713231610738571771399,
10853740587114622349346960647, 10853740581968070849659011271,
16497685684591469146828402916615, 10853740581968070848706668999,
16497685684591469146827450574343, 16497685684586322595327762624967,
25076482240571210346353339237461511, 571249842583835985482013195,
868299760727146434546838692363, 375822265044801946581003,
571249842583835986298306571, 375822265044802150654347,
571249842583835986502379915, 375822265044802966947723,
16497305185623528512784884409863, 25075903882147758194536658206273031,
10853490253703074611148207367, 16497305185623528512785836752135,
10853490253703074611216231815, 16497305185623528512785904776583,
10853490253703074612168574087, 10863259318361110308934085063,
10853496516026262109152442823, 16512154163908890766415320480199,
10853496516026262109118430599, 16512154163908890766415286467975,
16497314704359921552343067031047, 25098474329141513968044813965948423,
7140458234225732842158407, 10863259318361110309954451783,
16512154163908890766414232089031, 4697669888865717481799,
7146881130498693008027975, 7140458234225733930549575,
10863259318361110311042842951, 4697669888865649457351,
7140458234225733862525127, 10863259318361110310974818503,
4697669888865615445127, 7146881130498692905991303, 7140458234225731719755015,
4697669888866669824071, 7140458234225732774133959, 7140458234225732740121735,
10853496516026262107962014983, 4701895478553651019847, 4697669888867758215239
, 7146881130498695048761415, 2130757648352969093710109, 922245783516116189,
1401814241911388734685, 1401814241911320710237, 1030594270855791581,
2381085913349110669675613, 2381085913349108628942173,
3619250588291243075037199709, 922245783414079517, 922245785556849629,
376151860993176492479175, 162808011735467655, 247468329503170991751,
247468329503102967303, 271156499075143047, 626480125989318068444679,
626480125989316027711239, 952249791503859019534208775, 162808011633430983,
162808013776201095, 3243517260144613754173570439, 1403876928260020416839,
2133892934303466333913415, 2133892934303466265888967, 7828831821821435560007,
18087733046148753856499206343, 18087733046148753854458472903,
27493354230146109154004332100039, 1403876928259918380167,
1403876928262061150279, 3388118204349575, 3388119258728519,
7833061548485525142791, 5153327738307443015, 7140618803926518360340679,
1504030324905366585059952, 247251507770191483335, 7140454114278363964882055,
3090570222906409031, 606312244740167, 107010619638069, 923601039355330631, 71
]; 

PROPERTIES_SMALL_GROUPS[ 1520 ] := rec(
isNilpotent := [ 4, 80, -87, 166, -169, 178 ], 
isSupersolvable := [ 1, -170, 172, -178 ], 
isAbelian := [ 4, 80, 83, 166, 178 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6 ], pos := [ [ 171, 174, -178 ], [
25, -31, 39, -42, 47, 55, -58, 63, 71, -74, 79, -82, 88, -90, 97, -98, 101,
104, -105, 108, -170, 172, -173 ], [ 7, -24, 32, -38, 43, -46, 48, -54, 59,
-62, 64, -70, 75, -78, 83, -87, 91, -96, 99, -100, 102, -103, 106, -107 ], [
1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 22, 26, 30, 34, 38, 42, 46,
131, 135, 139, 143, 147, 151, 155, 159 ], pos := [ 1, 2, 3, 4, 5, 6, 31, 47,
63, 79, 87, 94, 101, 108, 135, 145, 155, 165, 169 ] ) );

SMALL_GROUP_LIB[ 1521 ] :=
[ 301442257352314079, 17942551775, 49558895098847, 10701791, 129324318215,
198172523727071, 196912964012255, 1794267359, 1679499880415, 85600223,
130290759647, 129462646751, 2015 ]; 

PROPERTIES_SMALL_GROUPS[ 1521 ] := rec(
isNilpotent := [ 2, 4, 8, 13 ], 
isAbelian := [ 2, 4, 8, 13 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 9, 11, -13 ], [ 3, -4, 6
, -8, 10 ], [ 1, -2, 5 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 15, 19, 23, 27 ], pos := [ 1,
2, 3, 4, 5, 6, 7, 8 ] ) );

SMALL_GROUP_LIB[ 1524 ] :=
[ 5419639024072824977, 3556473415341713, 197065007241733, 24600090311692433,
37490574138764301323, 49167637778699, 3556255394345723, 24993187179996923,
2387392745723, 590149779288300, 5445042146904222197, 16139097580283,
137113788295, 24600094092387323, 251 ]; 

PROPERTIES_SMALL_GROUPS[ 1524 ] := 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[ 1530 ] :=
[ 394570191868703, 78941635223315, 604587342277120319, 40347799161683729,
63342153475211407857, 61893418400195080497, 96917523155045507404785,
1460290982207, 257832259903, 51673829875, 395154372432191, 17314092017,
394570256880415, 78941700235027, 604587342308577599, 26336940801809,
603693061398081823, 120780751250714899, 925018637753867309375, 4415 ]; 

PROPERTIES_SMALL_GROUPS[ 1530 ] := rec(
isNilpotent := [ 8, 20 ], 
isAbelian := [ 8, 20 ], 
lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 9, -11, 16, -20 ], [ 1, -8,
12, -15 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17 ], pos := [ 1, 2,
3, 4, 5, 6, 7, 8 ] ) );

SMALL_GROUP_LIB[ 1540 ] :=
[ 7793985241703509, 7910157625703059, 12002848238918503059, 10110668903509,
22726259303509, 12627161703905, 35109563616103059, 7577612905903,
35054018579305039, 19481190419309035, 54069117132822500359, 630784100359,
7910046579200359, 10107712000359, 10183072000359, 15565316524800359,
13516800359, 11659420480105903, 197502686650592105039, 125680701956320109035,
2128755746886393904100359, 138787289600359, 83278297600539,
214292478451200359, 12650195200935, 213732705961600359, 897603199020800359,
330010416767072000359, 14758400359, 8204800395, 22798355200359, 4928000593,
22762310400539, 12650105600935, 35109815932800359, 359 ]; 

PROPERTIES_SMALL_GROUPS[ 1540 ] := rec(
isNilpotent := [ 12, 36 ], 
isAbelian := [ 12, 36 ], 
lgLength := rec( lgLength := [ 4, 5 ], pos := [ [ 13, -17, 22, -36 ], [ 1,
-12, 18, -21 ] ] ),
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[ 1548 ] :=
[ 278212122760241211409307, 179730406912104739739, 7968561731403607607155,
210516852631935124379, 13273263131202916279749823, 143358504362244695,
179723593888395631031, 8610350391827281483807, 116105271336159671,
15396546156159599676, 278663657391134848932161, 135992637660928439,
5147649710961399727, 8574456074070214794271, 92074064005559,
25791364301871524117, 25798177735558953563, 39925031982413215582811,
116104869460695317, 135992637268928789, 3321088079346829,
210516852640037980763, 5141037545041494643, 325880088676424120845271,
828662001842135, 25797989782617036599, 441700054915521629345,
116101005051582263, 116105279177633591, 179723593896237104951,
12319463120846097806000755, 820031703978468420830629897175,
142617716530976567, 221063872598326261559, 3321213412164271,
220772372019979725623, 342206874877281170901815, 75478891366199,
9946108794908412, 180015282343755589793, 87807779428151, 2157973626271,
135992645502402359, 3321096312820399, 210516852644089336631, 1847 ]; 

PROPERTIES_SMALL_GROUPS[ 1548 ] := rec(
isNilpotent := [ 6, 15, 25, 46 ], 
isSupersolvable := [ 1, -9, 12, -26, 28, -30, 33, -38, 41, -46 ], 
isAbelian := [ 6, 15, 25, 46 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 27, -28, 34, -41, 44,
-46 ], [ 7, -16, 19, -20, 23, -26, 29, -33, 42, -43 ], [ 1, -6, 17, -18, 21,
-22 ] ] ),
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 ], 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
] ) );