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#############################################################################
##
#W sml504.z GAP library of groups Hans Ulrich Besche
## Bettina Eick, Eamonn O'Brien
##
Revision.sml504_z :=
"@(#)$Id: sml504.z,v 1.1 1998/07/18 16:57:15 gap Exp $";
SMALL_GROUP_LIB[ 504 ] :=
[ 9501421787565392494841, 6350576275275186425, 3181750786241932151959,
31403534616051679481, 1638450975444718512878851, 12476669944651278,
4788804178780744443249827, 18852027697741219427, 9501595592819976146531,
18852027697741172771, 18852372209014809059, 836894317678362782835072259,
3294650480195605538947, 1660503842021420769481987, 1660504598568174500016259,
3294650480195605585603, 3294651981280435812931, 1660504598568174500062915,
12600691189368419, 12945202462958051, 3288288290537335407779,
1606790285379554016191688, 805119124488220207245448398,
15914979294466246460579, 62308938832463459, 31577339867959889507,
62308938832416803, 62653450106053091, 1603646151732102055793407,
6312997590039237823, 3181837602642224110783, 6312997590039191167,
6313169845676732479, 825779672922151687965932803, 3250894792536856264387,
1638451731988390134662851, 3250894792536856217731, 3250896293621686491715,
24803637694669, 74019535168141, 18802219935900353869, 18852027352609386029,
6350748873379664987, 3188076458197524567131, 12600346057535021,
62308596376071725, 12501326838821257, 31403707214156158043,
6300743565763307671, 15827468959875063612143, 24754715893980,
1618935394938976949864752762344, 25090387862412521160,
1608473149084949583313658700, 810670467139363351354904915436,
37404827070902831, 131615145384130900589, 9557964700113854788205,
6537004915396833859, 25011557872175, 24928292212405740, 6437737627425665645,
123626832671279, 12525788032017595, 6450188074357068355, 48922735171,
18876832509529812323, 18876832509529765667, 9513923584184210858915,
18876832509531212003, 9513923584184212305251, 9513923584184212258595,
4795017486428223436319651, 1723631032269736490167950, 9501421613257693948865,
37404817897680257, 18852027012829459841, 37404817897633601, 37404817899079937
, 3200776915220744317859, 12600691201125731, 6350747848686859619,
12600691201079075, 12600691202525411, 1606790534414577759398819,
6325548527185571171, 3188076457172831761763, 6325548527185524515,
6325548527186970851, 1600476952502393387772055, 5646343838233566997611152111,
87113750621056355, 87113750621009699, 43905331232194601891, 87113750622456035
, 43905331232196048227, 43905331232196001571, 22128286941945239530403,
44103771779810716847, 44103771779810670191, 22228300979950460379887,
44103771779812116527, 22228300979950461826223, 22228300979950461779567,
11203063693897957868530415, 37306285394358463, 18802368170870089471,
37306285395758143, 18802368170871535807, 9476393558450616495871,
131590342284636728495, 131590342284636681839, 66321532514472887247599,
131590342284638128175, 66321532514472888693935, 66321532514472888647279,
33426052387297351126854383, 22228299944361910537391, 22228299944361910490735,
22228299944361911937071, 11203063171961325767480495,
5646343838668511108914383599, 25002384649601, 25002386049281,
6350401967576640449, 3188075963060016291240, 1597458580333765600976526,
31403360305677691841, 123626832391553, 62308253920703873, 123626832344897,
123626833791233, 6300594890695076941, 24803661442573, 12501180072900109,
24803661395917, 24803662842253, 15827467919149655370659, 62308938844220771,
31403706186787911011, 62308938844174115, 62308938845620451,
3175574535655032336127, 12501473617522879, 6300743125463398591,
12501473617476223, 12501473618922559, 7977044354226710239431407,
31403708241531587759, 15827468956792956261551, 31403708241531541103,
31403708241532987439, 48922408794, 48923855130, 12451768463584218,
[ (1,9,8,6,5,4,2), (1,2,8,9,7,5,3) ],
[ ( 1, 5, 3)( 2, 7, 4)( 8, 9,10), (1,7,3,4)(2,6) ],
3212173402656700297299859368, 3191421241558673351923356,
1608476305745373109654746780, 131615094947564520941, 37454043157659695,
261140965743920621, 406546753535394111788048345239,
1434274517002867117715369947955951, 11203163469354032795217071,
1600464488010168953015359, 5646394244872390523345086511,
1434285787385230693239948507354287, 204900373591478180334518850268927,
722880036842111944446390757540809455, 261141159737327663, 49782520173045672,
6332172576094519421292, 3191414978738254775023260, 3191414978342962091231820,
2407136608664785555836255900, 74227477413935, 25011569442863,
12550701744046127, 261141159068468717, 18964215672802543085,
111917583866956105, 394845185815914333467, 7046662670716060955,
3551517936799282742555, 3175549508949945580159, 11203063171098337321326191,
172842919428143, 87507477884731439, 74019748479163, 261091942993281071,
44103769725077397551, 61152952367, 49461081147036, 12773286892930541,
244635697199, 48946249795, 123626844241967, 24803673292987, 62308938850099247
, 47 ];
PROPERTIES_SMALL_GROUPS[ 504 ] := rec(
isNilpotent := [ 6, 39, -41, 51, 66, 153, -155, 202 ],
isSupersolvable := [ 1, -21, 24, -51, 56, 59, -60, 63, -73, 75, -89, 92, -125
, 128, -155, 162, 172, 178, -180, 189, -194, 197, -202 ],
isSolvable := [ 1, -155, 158, -202 ],
isAbelian := [ 6, 39, 51, 66, 153, 202 ],
lgLength := rec( lgLength := [ 3, 4, 5, 6, false ], pos := [ [ 158, 172, -173
, 178, 190, -194, 197, 200, -202 ], [ 52, -53, 56, 59, -60, 63, -66, 74, -79,
99, -132, 143, -155, 161, -163, 166, -171, 176, -177, 179, -182, 187, -189,
195, -196, 198, -199 ], [ 7, -42, 45, -46, 49, -51, 54, -55, 57, -58, 61, -62
, 67, -73, 80, -98, 133, -142, 159, -160, 164, -165, 174, -175, 183, -186 ],
[ 1, -6, 43, -44, 47, -48 ], [ 156, -157 ] ] ),
frattFacs := rec( frattFacs := [ 7, 13, 19, 25, 31, 37, 44, 50, 56, 62, 68,
74, 80, 86, 92, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99, 262, 268, 274, 280,
286, 292, 298, 304, 310, 316, 322, 328, 334, 340, 346, 161, 167, 173, 179,
185, 191, 197, 203, 209, 215, 221, 227, 233, 239, 245, 251, 257, 263, 269,
275, 281 ], pos := [ 1, 2, 3, 4, 5, 6, 11, 18, 21, 22, 23, 28, 33, 38, 41, 42
, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61,
62, 63, 64, 65, 66, 73, 74, 79, 84, 89, 90, 91, 98, 105, 110, 117, 122, 125,
126, 127, 132, 137, 142, 147, 152, 155 ] ) );
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