col7.z

#############################################################################
##
#W  col7.z                 GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 328 ] :=
[ 5517221649920039, 432550462400, 1808221028113920039, 1809631099072000039,
16820556800039, 5517167928320039, 16820554240039, 16820572160039, 1313281560,
1331201560, 141443755521560, 593094364378979840039, 5512869399040039,
51200000039, 39 ]; 

PROPERTIES_SMALL_GROUPS[ 328 ] := rec(
isNilpotent := [ 2, 9, -11, 15 ], 
isAbelian := [ 2, 9, 15 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 14, -15 ], [ 4, -11, 13
], [ 1, -3, 12 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14, 17 ], pos := [ 1, 2, 3, 8, 11
] ) );

SMALL_GROUP_LIB[ 330 ] :=
[ 13565760139, 5126560319, 1687968480319, 17920139, 46400139, 15680193,
15375840139, 5440391, 15263200319, 5094880913, 5074150960139, 139 ]; 

PROPERTIES_SMALL_GROUPS[ 330 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 340 ] :=
[ 34395459331, 171700192015, 58768074276927, 33620976, 58320876536591,
19794572304515135, 11648272240387, 67318567295582271, 6793306052855136319,
6793306246799753279, 582343458879, 505413695, 102760691, 172842025023, 63 ];


PROPERTIES_SMALL_GROUPS[ 340 ] := 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[ 342 ] :=
[ 38032811728775, 111325158791, 6360187216087, 313513973639, 2471679376042519
, 53958295, 21600890373844871, 37775491198343, 111220812647, 111326628455,
38032813198439, 335923559, 917070695, 57107575, 313515443303, 18548005015,
107223627699431, 359 ]; 

PROPERTIES_SMALL_GROUPS[ 342 ] := 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[ 344 ] :=
[ 7753496574923609, 551258800596, 2667179286507686873, 22538941413449,
7753428089606345, 22538938301753, 22538960083625, 1596301770, 1618083642,
189081221034090, 65420296745, 41 ]; 

PROPERTIES_SMALL_GROUPS[ 344 ] := 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[ 348 ] :=
[ 110481363889, 2966104278059, 1032224639127863, 315320068, 1030235228767275,
358712384770150711, 3184547487799, 220007553136, 8516673591, 334373621,
2966113497143, 55 ]; 

PROPERTIES_SMALL_GROUPS[ 348 ] := rec(
isNilpotent := [ 4, 12 ], 
isSupersolvable := [ 1, -7, 9, -12 ], 
isAbelian := [ 4, 12 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -12 ], [ 1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 350 ] :=
[ 247573973001, 1165905059, 87406124508717, 666285, 3359363, 2032269,
1175212931, 706745289, 411372452867, 131 ]; 

PROPERTIES_SMALL_GROUPS[ 350 ] := rec(
isNilpotent := [ 4, 10 ], 
isAbelian := [ 4, 10 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, 8, -10 ], [ 1, -4, 6, -7
] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 351 ] :=
[ 2664868026983, 3758465533, 7591741799, 2664592134503, 2664730153319,
7591721063, 2664592113767, 7591866215, 10639573, 10784725, 3737313493,
31485469262557, 21899111, 1895 ]; 

PROPERTIES_SMALL_GROUPS[ 351 ] := rec(
isNilpotent := [ 2, 9, -11, 14 ], 
isSupersolvable := [ 1, -11, 13, -14 ], 
isAbelian := [ 2, 9, 14 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 12, -14 ], [ 3, -11 ], [
1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14 ], pos := [ 1, 2, 8, 11 ] ) );

SMALL_GROUP_LIB[ 352 ] :=
[ 145387483243217423000009, 45994142072861090000, 413032622588430000009,
145386045926539822000009, 18014090713775743173358000009,
18014267791218848039662000009, 6340959931249061608293103000009,
413032622588423000009, 145386045926539815000009, 145889106855985703000009,
51175888154007700202000009, 177490479787543138000009,
62477150517016398379000009, 62477653577945844267000009,
62476648873080130218000009, 21991780403324216412843000009,
413032622588429000009, 145386045926539821000009, 413032622588427000009,
145889114953089575000009, 145386045926539819000009,
51177395927923032679000009, 51176389789846864555000009,
51176389793906950827000009, 18014089204588871680687000009,
414457712869926000009, 145390329340625510000009,
21991956977710463453743000009, 62476648873080130150000009,
21991780403324216412775000009, 21991780403312070757038000009,
7767024997182377754103532000009, 2733992799008196969454636781000009,
2733992799008196969454636782000009, 962365465250885333248042340079000009,
414457712869925000009, 413032622588451000009, 62476648873080130217000009,
62476648873080129189000009, 177490479787542177000009,
21991780403312070757035000009, 21991780403312070756007000009,
21991780403312070757037000009, 520062238755009000, 130665152523009000,
45863476920363009000, 520062238769009000, 45864213024929009000,
16144202616279217009000, 5682759320561782963009000, 16144202616277161009000,
5682759320561780907009000, 5682759320561780921009000, 183062648324147009000,
16281012390592683009000, 16281012759691435009000, 5730915972460576955009000,
130665152537009000, 45863476920377009000, 2005949511420011878840009000,
706094228019844180089273009000, 248545168262985151390161339009000,
145387470982218279000009, 51352965601138049639000009,
51352964176047768167000009, 1177436553734000009, 413032587985478000009,
413032587985446000009, 145889106821382758000009, 145889102772830822000009,
146392163702276710000009, 504238366000645000009, 177491908914841157000009,
177493338053674563000009, 1432495326724000009, 504234317448740000009,
504238377535044000009, 504238377535042000009, 504242437621314000009,
177493334005122658000009, 177491904866289252000009, 354570785218627079000009,
62477151933986506311000009, 62477150508884690503000009,
62477654994915952199000009, 504238366000646000009, 177490479752939078000009,
177490479752939046000009, 177491904854754886000009, 177491908903306822000009,
177493334005122630000009, 177491912963393094000009,
62477150504836138598000009, 1173388001804000009, 413028539433548000009,
413028539433516000009, 145387470993752780000009, 145387471005287116000009,
51176389789812261582000009, 51176389793872347853000009, 504234317448716000009
, 177490475704387116000009, 62476648873057060556000009,
21991780403316096239310000009, 177583369728577032000009,
62509346144463638088000009, 22003289842851205107304000009,
62509346144463638028000009, 22003289842851205107276000009,
22003289842851205107274000009, 7745158024683624202260076000009,
22003289842851205107214000009, 7745158024683624202260046000009,
2726295624688635719200034414000009, 1173388001801000009,
413028539433545000009, 1173388001797000009, 413032587985477000009,
145889102761296483000009, 413028539433541000009, 413028539433539000009,
1173388001860000009, 1173388001828000009, 414457678266980000009,
414457678266978000009, 177490479752954568000009,
22003080662399329519306000009, 62476648873045541577000009,
1432495326721000009, 504238366000705000009, 354570785218627139000009,
1432495326784000009, 504238366000706000009, 504238366000736000009,
177491904843220578000009, 62476648873045541580000009,
7745084393164563995969230000009, 21991780403312036168397000009,
124807910279168919111000009, 177490475704387079000009,
177491904843220550000009, 62477150504824604262000009, 504234317448713000009,
62508751881816262344000009, 62476648873045541578000009,
22003080662399329519305000009, 1173388001857000009, 1177436553824000009,
371195907000900, 739246113000900, 260584767523000900, 260584767525000900,
260215668773000900, 91856131063847000900, 371196000000900, 130663055458000900
, 45993397583971000900, 130663055460000900, 45993396535398000900,
16189675582521447000900, 45993398632550000900, 45993028485222000900,
16189546028859495000900, 371195921000900, 130293956657000900,
130293957649000900, 45863473778992000900, 16143942769709361000900,
5682667854937198899000900, 16143942769709364000900, 16143813216047472000900,
5682622252048191858000900, 413028527899273000009, 3333423624000009,
1173376467592000009, 1173376467588000009, 4069540352000009,
504234305929860000009, 1432483792512000009, 504234305929740000009,
177490475692868236000009, 177490475692852870000009, 1432483793412000009,
504234305914504000009, 62476647443895158414000009, 3333423617000009,
3333423744000009, 1048577000090, 1048608000090, 130292908067000090,
370147364000090, 130292909216000090, 16143812846945446000090, 9437696000009,
9 ]; 

PROPERTIES_SMALL_GROUPS[ 352 ] := rec(
isNilpotent := [ 2, 44, -62, 149, -172, 188, -193, 195 ], 
isAbelian := [ 2, 45, 58, 149, 164, 188, 195 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6 ], pos := [ [ 194, -195 ], [ 37,
44, 63, -93, 117, -125, 129, -135, 139, -142, 147, -163, 173, -193 ], [ 8,
-16, 19, -31, 36, 38, -43, 45, -57, 94, -116, 126, -128, 136, -138, 143, -146
, 164, -172 ], [ 3, -7, 17, -18, 32, -35, 58, -62 ], [ 1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 6, 11, 17, 22, 58, 63, 209, 214 ], pos := [
1, 2, 43, 62, 148, 172, 187, 193 ] ) );