col23.z

#############################################################################
##
#W  col23.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1980 ] :=
[ 16315936316391939013019, 96705043830490010249030191,
191475921808271688602505030191, 32909571457027013019, 37020408742403013019,
12342908682755019013, 73390893579633411010139, 8160014226162449039011,
16336035994747798409030191, 16189451756450612105090131,
32345872877105735271365001391, 114708971525001139, 96705043884367980808003191
, 65251344147030401131009, 32905396224516001319, 195351174395757192003191,
386795292487425491848003191, 4164157444001319, 24422495095620099019013,
531905483155927237379010139, 287205519273424139092873090131,
6255017012515956427959831493001391, 135676375863812001139,
8283393318988040003191, 16922615540992716036001391, 73259267717599880009131,
1595504798897518152516001391, 17467387966990067076001391,
33506778771366946549124001391, 12334592426753139100, 18697159172001319,
6233784836001913, 37066107781892001139, 4121219302160003911,
8250523229619080003191, 8176490786063240009131, 16336299430806291396001391,
57671684001139, 32905396224513011309, 32909571457281013019,
65152684039144193013019, 65160951458963841030119, 129002314397478036353030119
, 4164157441011309, 18697159169011309, 6233784833011903, 37066107781889011039
, 2079326721013901, 37020408742657013019, 12342908683009019013,
73390893579633537010139, 4117075329793039011, 73300409412748161030119,
24438959238022017090113, 145313969288191673281001139, 519045121001139,
[ ( 2, 3, 4)( 5, 6, 8)( 7, 9,11), ( 1, 2)( 4, 5)( 6, 7)( 8,10)(12,13,14) ],
[ ( 1, 2, 3, 4, 5)(17,18,19), ( 3, 4, 5)( 6, 7, 8, 9,10,11,12,13,14,15,16) 
 ],
351541138061771909685633030119, 696051453077698508183626625030119,
32909546492416001319, 65160951364655616003119, 32909571461248003119,
65160901561488000003119, 129018683701909854848003119, 8290200256896113009,
4162322944001139, 4164157696001319, 8240372122368001319, 8244547355008003119,
16315936316392320003119, 8912896001139, 12334593999361011903,
268639132907078401011039, 24422495095620353019013,
531905483155927237505010139, 48356540288854983553090113,
1053172856648736382653377001139, 16140561567804949249039011,
351541146201229863469953030119, 189704781319487314927403905090113,
4131770137104501674684495962049001139, 159791421212059442922369090113,
3480256765690889841719381953001139, 68523397632001139, 22847427072001319,
135771831933440001139, 6233792768001913, 135676375863936001139,
226114774502144001139, 268828227249642240001139, 45287734254080003119,
268828551108632064001139, 12342908690816009113, 268639224374235840001139,
448348494341607168001139, 532280531195110891264001139, 6229594624003911,
135676329724672003119, 89669713844509312003119, 12363660011776009113,
269280419381253760001139, 447707253681687360001139,
1053915451766319722012480001139, 24480042655427328009113,
533175230329252747136001139, 887730018796547608384001139, 6229590784113900,
9437696001139, 3146240001193, 18720228096001139, 1049088001391,
18697159424001319, 6233785088001913, 37066107782016001139, 2079326976003911,
37020408742784003119, 12342908683136009113, 73390893579633600001139, 1139 ];


PROPERTIES_SMALL_GROUPS[ 1980 ] := rec(
isNilpotent := [ 12, 38, 56, 120 ], 
isSupersolvable := [ 1, -13, 15, -29, 31, -56, 61, -65, 67, -78, 85, -107,
109, -120 ], 
isSolvable := [ 1, -56, 59, -120 ], 
isAbelian := [ 12, 38, 56, 120 ], 
lgLength := rec( lgLength := [ 4, 5, 6, false ], pos := [ [ 62, -67, 70, -72,
85, 92, -111, 116, -120 ], [ 13, -18, 23, -39, 42, -47, 52, -56, 59, -61, 68,
-69, 73, -74, 77, -84, 86, -91, 112, -115 ], [ 1, -12, 19, -22, 40, -41, 48,
-51, 75, -76 ], [ 57, -58 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49
, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126,
130, 134, 138, 142, 146, 150, 154, 158, 162, 55, 59, 63, 67, 71, 75, 79, 83,
87, 91, 95, 99, 103, 107, 111, 115, 119, 123 ], 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, 26, 27,
28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46,
47, 48, 49, 50, 51, 52, 53, 54, 55, 56 ] ) );

SMALL_GROUP_LIB[ 1988 ] :=
[ 1410628381562914569, 1149495869154569, 122280457308105, 1687145460514569,
3360990308366250419, 6109704650419, 1149475100480419, 583923200419,
8676597039040419, 848993600419, 62233924835, 1690637066720419, 419 ]; 

PROPERTIES_SMALL_GROUPS[ 1988 ] := rec(
isNilpotent := [ 6, 13 ], 
isAbelian := [ 6, 13 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -13 ], [ 1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1989 ] :=
[ 133917908763, 7415599551, 270537211, 4543 ]; 

PROPERTIES_SMALL_GROUPS[ 1989 ] := rec(
isNilpotent := [ 2, 4 ], 
isAbelian := [ 2, 4 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 3, -4 ], [ 1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5 ], pos := [ 1, 2 ] ) );

SMALL_GROUP_LIB[ 1992 ] :=
[ 241391565851755419113, 19533337661785961990073, 38910418694387601217819651,
30158775362477046787, 20015157122307870401251, 20015157122304163002819,
39870192998023165269380099, 20015157122359773979299,
39870192998023220880356579, 39870192998023217172958147,
79421424452072523778215943683, 959296600974212172109362136,
38910398583495601705613301, 9805887820374572245, 19533332620246837104341,
9805887816667173813, 9805887872278150293, 480851635382868477914341,
121180803702567365, 241391383673859752901, 121180799995168933,
121180855606145413, 77509554009105261240840398339, 19533342703599433263843,
38910418679262894867234019, 19533342703595725865411, 19533342703651336841891,
15124765668960707, 15124821279937187, 60046167098903834250755,
960979581055960334728844, 1914271364156952719375300428,
40040815748081883568665, 10047764418500939939, 363060723658488140,
4920577835700387, 61216562915827, 9805888050233268387, 163 ]; 

PROPERTIES_SMALL_GROUPS[ 1992 ] := rec(
isNilpotent := [ 4, 28, -30, 39 ], 
isSupersolvable := [ 1, -11, 13, -30, 34, 36, -39 ], 
isAbelian := [ 4, 28, 39 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 34, 36, -39 ], [ 5, -33,
35 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32 ],
pos := [ 1, 2, 3, 4, 11, 12, 17, 22, 27, 30 ] ) );

SMALL_GROUP_LIB[ 1995 ] :=
[ 540843263, 57114059, 1073293106687, 1075335519743, 6911 ]; 

PROPERTIES_SMALL_GROUPS[ 1995 ] := rec(
isNilpotent := [ 5 ], 
isAbelian := [ 5 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -5 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1998 ] :=
[ 71253522082021083616151, 35666455530440790935, 15827112486078121918341109,
138490991587355693975, 31609139236785516286547693461, 73346814683681687,
142348725723552804409349015, 71245612502560160125847, 35662423479301262231,
71261427629678537034647, 71261427666333616655255, 35662423479180329879,
71261427629678416102295, 35666380261782109079, 213349271731293256273981,
426279303874391130635096125, 426271402204269978211700797,
35666455534068761495, 71261431661735118519191, 426271813500436027350896701,
851690261572712697656049586237, 851706049109614760197993451581,
71253522082024711586711, 142380332404037187354770327, 17851085934513047,
35666382235639958423, 35666418890719579031, 17851085813580695,
35666382235519026071, 17851101171989399, 69314763544152983, 73271546024999831
, 146396539244809112471, 3964687724695357333, 1982354193690517,
3956772239327913877, 15807304930060500830101, 8317144747363907850301,
138490991590983664535, 292500285474247942618007, 15795854046809921331056701,
7921461885777959817205, 3960737019066740725, 16617655860380432031092797,
8317143095912434532413, 36655200600983, 36670559009687, 73273519761916823,
71245608470756569121687, 71245612502563788096407, 142348725723552808037319575
, 35658465218180547479, 17849112076663703, 17851089562483607,
35662423482929232791, 35666455535882746775, 71253522082026525571991,
8978017860503, 34681463683991, 998417547325, 69314767172123543,
1982357942593429, 138490991592797649815, 3960736902971682805,
276705001505258078894999, 48023 ]; 

PROPERTIES_SMALL_GROUPS[ 1998 ] := rec(
isNilpotent := [ 6, 46, -48, 66 ], 
isAbelian := [ 6, 46, 66 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 53, 58, -59, 64, -66 ],
[ 9, -14, 19, 24, -33, 36, 40, 42, -49, 52, 54, -57, 60, -63 ], [ 1, -8, 15,
-18, 20, -23, 34, -35, 37, -39, 41, 50, -51 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 35, 38
, 41, 44, 47, 50, 53, 56 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 14, 19, 24, 30,
33, 37, 41, 43, 45, 48 ] ) );