#############################################################################
##
#W  sml720.z               GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##
Revision.sml720_z :=
    "@(#)$Id: sml720.z,v 1.1 1998/07/18 16:57:48 gap Exp $";

SMALL_GROUP_LIB[ 720 ] :=
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[ ( 1,12, 3,39,41)( 2,75,58,10, 9)( 4,47,72,46,59)( 5,45,54,30,44)
    ( 6,28,21,77,61)( 7,52,20,74,19)( 8,63,15,70,62)(11,26,42,64,40)
    (13,31,48,67,57)(14,71,79,23,43)(16,69,34,35,25)(17,56,38,65,37)
    (18,53,24,36,49)(22,76,80,60,68)(27,66,50,33,78)(29,73,51,32,55), 
  ( 1,72,50,22, 6,80,42, 4)( 2,26,64,74,20,66,33,75)( 3,32,29,77,21,63,70,
     39)( 5, 8,25,11,23,51,17,27)( 7,49,15,31,10,67,55,24)( 9,38,19,76,52,
     69,58,47)(12,54,61,48,28,14,41,36)(13,57,16,34,53,18,56,65)
    (30,59,46,43,71,68,60,45)(35,62,44,78,37,73,79,40) ],
[ ( 1,27, 2,28, 3,25, 4,26)( 5,36,23,31,15,48,11,43)( 6,35,21,29,18,47,13,
     39)( 7,34,24,33,19,44,12,41)( 8,38,22,32,16,46,14,40)( 9,37,20,30,17,
     45,10,42)(49,51,50), ( 1, 8,15)( 2,14,20)( 3,16, 5)( 4,22,10)
    ( 6, 9,21)( 7,12,11)(13,18,17)(19,24,23)(25,32,39)(26,38,44)(27,40,29)
    (28,46,34)(30,33,45)(31,36,35)(37,42,41)(43,48,47)(49,50,51) ],
[ ( 1, 3,10, 7,22,23,32,19)( 2,31,40,33,18, 9,28, 6)( 4,38,14,20,24,15,13,
      5)( 8,21,16,12,34,30,37,25)(11,39,29,27,35,17,26,36)(41,43,42), 
  ( 1,36,31,11, 7,25)( 2,28,26,24,38,17)( 3,16,34,10,14, 5)( 4,15,39,18,40,
     29)( 6,33)( 8,32,13,20,23,37)( 9,35,19,12,22,27) ],
[ (1,2,4,5,3)(6,7)(8,9), ( 1, 5)( 6, 9, 7, 8)(10,12,11) ],
[ ( 5, 7, 6)( 8,10, 9), ( 1, 3, 2, 4)( 5, 6)( 9,12,10,11) ],
[ ( 1, 2)( 4,43, 5,49,41,32,46,19)( 6,21,45,30,11,31,18,16)( 7,12,15,42,36,
     48,23,44)( 8,10,20,26,40,51,50,33)( 9,35,24,47,17,22,34,37)
    (13,38,14,39,28,27,29,25), ( 1, 2, 3)( 4,46,28,10, 6,41, 5,13,51,11)
    ( 7,29, 9,18,23,36,14,17,45,15)( 8,50,39,44,21,40,20,25,42,31)(12,48)
    (16,47,35,38,32,30,37,22,27,43)(19,49)(24,34)(26,33) ],
[ ( 1, 3)( 4,37,32,16,30,39)( 5,26, 8,17,35,19)( 6,28,38)( 7,15,21,24,27,23
     )( 9,40,34,18,33,11)(10,31,20,29,41,42)(12,25)(13,36)(14,22,43), 
  ( 1, 2)( 4,26, 5,11,33,10,42,37)( 6,40,12,29,43,16,36,35)( 7,20,13,34,24,
     17,25,30)( 8,15,22,19,31,27,38,41)( 9,14,23,18,32,28,21,39) ],
[ ( 1, 2, 3, 4)( 5, 6)( 8,12,11, 9,10), ( 1, 4, 3, 2)( 5, 7)(10,11,12) ],
[ ( 1, 2, 3)( 4, 9,23)( 5,13,25)( 6,24,19)( 7,18,15)( 8,26,16)(10,12,27)
    (11,22,20)(14,17,21), ( 1, 2)( 4,20,26, 7,25,21)( 5,23,27,11,15,24)
    ( 6,16,13,12,14,22)( 8,10,18,17,19, 9), 
  ( 1, 3, 2)( 4,15,12,22,24, 7,23, 6,13,27)( 5,20,17, 9,26,11,25, 8,18,21)
    (10,19)(14,16) ],
[ ( 1, 2, 3)( 4,19,23,21,26, 8, 9,13,27,17)( 5,11)( 6,22,24,15,18,14,12,25,
     7,16)(10,20), ( 2, 3)( 4,23, 5,26,19, 7, 6,10,24,16, 8,13,11,17, 9,15,
     14,20,25,18)(12,21,22,27) ],
[ ( 1, 2, 3)( 4, 7, 6, 5)( 8,11,12,10, 9), ( 4, 6)( 5, 7)( 8,10,12, 9,11) ],
[ ( 1,19, 4,13)( 2,11, 7, 5)( 3,22, 8,17)( 6,16,12,10)( 9,14,15,20)
    (18,23,24,21), ( 1,21,12, 5,15, 3,24, 2,10,20, 4,23, 6,11, 9, 8,18, 7,
     16,14)(13,17,19,22)(25,26,27) ],
[ ( 1, 2)( 3, 5, 4)( 6,21,22)( 7,20,23)( 8,16,24)( 9,17,25)(10,15,29)
    (11,14,28)(12,19,26)(13,18,27), 
  ( 1, 2)( 3, 5, 4)( 6,28,25,16,14, 7,29,24,17,15)( 8,27,22,20,18, 9,26,23,
     21,19)(10,11)(12,13) ],
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1538180453854488452065623375895, 1107489926775231685576337421090839,
1107489926775231614426939988738071, 797392747278166762387485879727931415,
343836419272078474163038347293859299351,
343836419272078474163038347293860315159,
247562221875896501397387538978899468795927,
343836419272078474163038347293859332119,
247562221875896501397387538978899467812887,
247562221875896501397387538978899468828695,
178244799750645481006119027993734937551421463, 307634317886618546601825698565
, 221496708878365353423706929545989, 159477630395956516822329067339645701,
114823893885088692112076798777382568709,
82673203597263858320695294990008263557893, 1107483525493258076509203114000407
, 1107483525493258076509203113984023, 797388138355145815086715697879891991,
574119472471130385714257288159671943191,
413366020179213877714265247564369816027159,
413366020179213877714265247564369816010775,
297623534529033991954270978246435673532907543,
797389679474438897290567242463870999, 574120569221596006049137255290296647703
, 413366809839549124318443677652023178788887,
413366809839549124318443677553067132289047,
297624103084475369509279447909545756962439191,
159478240976478176223675363317826309, 574121667503841945696259841985812152343
, 574121667503841945747558656491329208343, 12317420198453628174359,
8868542542982070067626007, 12317420198453628125207, 8868542542982070067609623
, 6385350630947185906449235991, 12317486604557966376983,
8868590355377145369395223, 12317420198453630205975, 8868542542982070069690391
, 8868590355377145371426839, 6385385055871640075497439255,
8868542542982070070673431, 4597477240227580949766180241431,
4597452454281973948101199757335, 8868542542982070069641239,
4597477240227580949766179176471, 6385350630947185906452283415,
4597477240227580949766180192279, 6385385055871640075495374871,
6385350630947185906451300375, 3310183612963858283927057041834007,
3310165767083021242728319322013719, 2383332201333977964427576478109122583,
8868542542982070069657623, 6385350630947185906451316759,
6385385055871640075497406487, 4597477240227580949766179225623,
6385350630947185906452332567, 6385385055871640075498422295,
3310183612963858283927057042866199, 8868590355377145369346071,
6385385055871640075495358487, 6385385055871640075497390103,
4597477240227580949766179209239, 4597477240227580949766177144855,
6385350630947185906451267607, 4597452454281973948101198725143,
4597452454281973948101199740951, 3310183612963858283927057042849815,
159698818616583770569777969227384640, 221803914745255236902843809793856,
852761126867809639828834064, 114983149403949802218189776526093600192,
159698818616596947525263862849603008, 613988011353954934665183773808,
114983149403940333688203606209965346112, 159698818616583796789171959632760128
, 613988011344822426269248408656, 83015766190502179325259459388586155853248,
115299675264586360173971471645315696064, 662034171056234036800600301126000,
319125579825179289245513565452, 443229971979415711184717068,
8224914719589437293827, 314017298048268018635044701956,
436135136178150057559066372, 4934947565116602730241,
248160220059149829649282531279900, 344666972304374763401097970716,
17765808867520059436712967, 1773713518150059861262659,
1277073733059753307842855235, 2463491008944238805315,
1773713518150059862049091, 2463491008944239034691, 1773713518150059862278467,
2463491008944239821123, 1277664706818469956713365767,
919918588909274586498236334343, 1774534315058683738898695,
1277664706818469956714283271, 1774534315058683738996999,
1277664706818469956714381575, 1774534315058683739914503,
919918588943521426892044484631, 662341384039335356299436014813207,
1277664706866100680177795095, 919918588943521426892045467671,
1277664706866100680177827863, 919918588943521426892045500439,
1277664706866100680178810903, 307633722006414862568707506949,
221496279844618686691116898763525, 427269058342262806834889477,
307633722006414862568708424453, 427269058342262806834987781,
307633722006414862568708522757, 427269058342262806835905285,
1107474186519488044226782769037335, 797381414294031391772223845774245911,
1538158592388177937897959243799, 1107474186519488044226782770020375,
1538158592388177937897959276567, 1107474186519488044226782770053143,
1538158592388177937897960259607, 477550580623316945751502365086826519,
343836418048788200941010630762256515095, 663264695310162424753575646248983,
477550580623316945751502365087809559, 663264695310162424753575646281751,
477550580623316945751502365087842327, 663264695310162424753575647264791,
2967126874702510699937863, 2957291182001319498055751,
2136331349785840230848364615, 2957291182001319498039367,
2136331349785840230848348231, 2129249651040982612234584135,
1538158571845804998736205692999, 4107348863845479284807,
2967126874702510700953671, 2136331349785840230847316039, 5704651154542100551,
4121009548152755257415, 4107348863845480333383, 2967126874702510702002247,
5704651154542067783, 4107348863845480300615, 2967126874702510701969479,
5704651154542051399, 4121009548152755208263, 4107348863845478219847,
5704651154543083591, 4107348863845479252039, 4107348863845479235655,
2957291182001319496958023, 5723624327258046535, 5704651154544132167,
4121009548152757289031, 2136365808957068943456043031,
2136331384032614774411984919, 1538183382449089737592936693783,
2136331384032614774411968535, 1538183382449089737592936677399,
1538158596503482735927956193303, 1107492035363344611165217495302167,
2967126922267383919869975, 2136365808957068943457058839,
1538183382449089737592935645207, 4121009614123654250519,
2967174734662459220623383, 2967126922267383920918551,
2136365808957068943458107415, 4121009614123654217751,
2967126922267383920885783, 2136365808957068943458074647,
4121009614123654201367, 2967174734662459220574231, 2967126922267383918805015,
4121009614123655233559, 2967126922267383919837207, 2967126922267383919820823,
2136331384032614774410887191, 4121076020227992453143, 4121009614123656282135,
2967174734662459222654999, 1780275212842582132490437,
1773718084375121309565125, 1281798153246678468146593989,
922894670337608516396791218373, 2463497339382973661381,
1281798153246678468145545413, 3421524055558258885, 2472604462254512996549,
1780275212842582134554821, 3421524055558226117, 2463497339382974677189,
1780275212842582134522053, 2463497339382972596421, 3421524055559241925,
2463497339382973628613, 1773718084375121308467397, 3434172837391237317,
2472604462254515028165, 6408989079072381934248230935,
6384170347823042965480243223, 4614472136932115091337259352087,
6384170347823042965480226839, 4614472136932115091337259335703,
4596602650432591033871049539607, 3322419938591122865861503756648471,
8866903260865200332537879, 6408989079072381934249246743,
4614472136932115091337258303511, 12315143417731213230103,
8901373720933726744018967, 8866903260865200333586455,
6408989079072381934250295319, 12315143417731213197335,
8866903260865200333553687, 6408989079072381934250262551,
12315143417731213180951, 8901373720933726743969815, 8866903260865200331472919
, 12315143417731214213143, 8866903260865200332505111,
8866903260865200332488727, 6384170347823042965479145495,
12363019056715344642071, 12315143417731215261719, 8901373720933726746050583,
1538183382414890527922598281239, 1538158571880051773279777685527,
1107492035338721180202569316794391, 1538158571880051773279777669143,
2136331349833405104074588183, 1538183382414890527922599297047,
2967126874768481607286807, 2136365808909570041144475671,
2136331349833405104075636759, 2967126874768481607254039,
2136331349833405104075603991, 1538183382414890527922600312855,
2967126874768481607237655, 2967126874768481608269847,
2136331349833405104074555415, 1538158571880051773279776587799,
2967174734596488531279895, 2967126874768481609318423, 3421513061482120640,
594253448633270775055808, 427862483015758940266579392, 2468050892022081470547
, 4760885381890131, 3427848445906452563, 3427848445906419795,
7923080890417235, 4107333008887338008659, 4107333008887335977043,
2957279766409804574195795, 4760885381840979, 4760885383921747,
824205709542644858993, 1589893847384177, 1144730143015633009,
1144730143015600241, 4752089355911281, 2463487826407901397105,
2463487826407899365489, 1773711235020212167344241, 1589893847335025,
1589893849415793, 1777008057858382553497671, 3427870436153688135,
2468066746979770761287, 2468066746979770728519, 17104365720638062663,
8866903213300327114637383, 8866903213300327112605767,
6384170313576268421916622919, 3427870436153638983, 3427870436155719751,
593434960232184365007045, 1144743337169846469, 824215222517265137861,
824215222517265105093, 10261352795034616005, 5319485303154525698293957,
5319485303154525696262341, 3830029418271278208009732293, 1144743337169797317,
1144743337171878085, 1279445835904842929482579991, 2468066812950474719255,
1777008105423255579459607, 1777008105423255579426839, 36938574314408509440023
, 19148956924660653373534535703, 19148956924660653373532504087,
13787248985755670527808909705239, 2468066812950474670103,
2468066812950476750871, 2199023272028, 2199024304220, 1141559151446507612,
1585495768367196,
[ (1,2), (1,2,3,4,5,6) ],
[ ( 1, 9)( 2, 6)( 3,10)( 4, 5)( 7, 8), ( 1, 8, 6, 2,10, 3, 5, 9, 4, 7) ],
[ ( 2, 5, 6)( 3,10, 7)( 4, 9, 8), ( 1, 8, 9, 7, 2, 6, 3, 5)( 4,10) ],
[ (2,4)(5,6), (1,3,4,6,5)(7,8) ],
[ (2,3)(4,6,7)(5,8), (1,2,3)(4,8,5,7) ],
[ (1,3,4)(5,9)(6,8), (2,3,4)(6,9,7) ],
[ ( 1, 2)( 3, 4, 5)( 7, 8,10), ( 3, 5, 4)( 6, 9, 8,10) ],
[ ( 1, 2)( 3, 4)( 6, 9,10, 8), ( 4, 5)( 6, 9, 8)( 7,10) ],
[ (1,2)(3,4)(6,7,8), ( 3, 5)( 7,10, 9) ],
[ ( 1, 3, 2)( 4, 5)( 6, 7)( 8, 9,11,12,10), 
  ( 1, 3, 2)( 4, 6)( 5, 7)( 8,12,10,11, 9) ],
1107474171733067592315804862955543, 797381403637191031565411535008317463,
413362521862906650285653103108266386309143,
413362521862906644363717956690333488168983,
214287130187093928542816802256205484111723347991,
797388154092481120567136794991230999,
59524934486884725848267613533038281017672453,
214288118708869643054364306431105960853332115479,
214288944291867084507129927802763699332175724567,
214289354226693982499795337784927723938800304151, 1785204446342667034443799,
1538171585329116230924653035543, 574121667519582235813313086245826560023,
2427866672489748309583476010522368, 442075197603430091684096071713904,
476667360349067934200687537845977456, 1785204446287687426524419,
1303084280546819127887545351, 852761126893141770951983472,
852761126880457804813960016, 919501950594329826217754100080,
919491904299475476171727044976, 343198514278979259281143396383758221680,
919491904253952510596256629104, 36952253971895255302407,
9853937031771695617792, 221497556910135948369753154929413,
574114616749264871915135777077997944855, 797385082023790373486291397512347671
, 2468044581375628558407, 1777008035758337060519959,
1785201032754882429337623, 1279445786838476971227234327,
477550582322331185592240161255604247, 2136341204839160081561976855,
427269885953617877556789445, 1538165653555981324919879237655,
797388154082434797213434347539955735, 159478549459409765991886472394883269,
574119470939347132058526237559901700119, 17107527920827498519,
1184390453983855840854480, 852761126880492987495743856,
852761126867809021357720400, 919491904244769495032432427376,
17107527928880562499, 10264515003277115841, 36952250809699293724935,
11508054656752086423296, 3421516358439944275, 2464630993595049984071,
1774534315091669096087575, 593432669202620432269509,
921200965725666444553404563479, 2136331349793822787764240407,
7923081360179223, 5723624327459373079, 4752089825673269, 17104365720839389207
, 4121009548152964907031, 3173216327565680, 1644994677905874228992,
6597103321111, 2199056810013, 4760885398601751, 1589893864095797,
3427870436162011159, 23 ]; 

PROPERTIES_SMALL_GROUPS[ 720 ] := rec(
isNilpotent := [ 4, 81, -88, 94, 185, -188, 383, -390, 408, 759, -762, 840 ],

isSupersolvable := [ 1, -31, 33, -101, 111, -151, 155, -191, 195, -301, 303,
-390, 395, 400, -402, 405, -408, 425, -452, 487, -525, 547, -567, 589, -705,
709, -762, 783, 802, -805, 813, 822, -824, 828, -832, 835, -840 ], 
isSolvable := [ 1, -408, 422, -762, 773, -840 ], 
isAbelian := [ 4, 81, 84, 94, 185, 383, 386, 408, 759, 840 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6, 7, false ], pos := [ [ 786, 798,
813, 821, 829, -832, 834, -835, 838, -840 ], [ 238, -244, 256, -260, 279,
-285, 297, -302, 310, -313, 318, 358, -361, 366, 374, -377, 382, -385, 391,
399, 402, 404, -408, 432, -434, 439, -441, 446, -448, 453, -455, 460, -462,
467, -468, 472, -474, 479, -480, 484, -525, 549, -550, 553, 563, -564, 567,
570, -571, 574, 577, -578, 581, 584, -585, 588, 616, -705, 709, -718, 739,
-762, 773, -776, 783, -785, 792, -796, 803, -812, 816, -818, 822, 824, -828,
833, 836, -837 ], [ 25, -32, 40, -43, 48, 56, -59, 64, 72, -75, 80, -83, 99,
-101, 113, -114, 117, 120, -121, 124, -151, 155, -188, 213, -237, 245, -255,
261, -278, 286, -296, 303, -309, 314, -317, 326, -329, 334, 342, -345, 350,
-357, 362, -365, 367, -373, 378, -381, 386, -390, 394, -398, 400, -401, 403,
425, -427, 435, -438, 442, -445, 449, -452, 456, -459, 463, -466, 469, -471,
475, -478, 481, -483, 532, -540, 547, -548, 551, -552, 556, -557, 560, -562,
565, -566, 568, -569, 572, -573, 575, -576, 579, -580, 582, -583, 586, -587,
589, -615, 706, -708, 719, -738, 777, -782, 788, -789, 791, 797, 799, -802,
814, -815, 819, -820, 823 ], [ 7, -24, 33, -39, 44, -47, 49, -55, 60, -63, 65
, -71, 76, -79, 84, -89, 92, -98, 102, -112, 115, -116, 118, -119, 122, -123,
152, -154, 189, 191, -212, 319, -325, 330, -333, 335, -341, 346, -349, 392,
-393, 422, -424, 428, -431, 526, -531, 541, -546, 554, -555, 558, -559, 787,
790 ], [ 1, -6, 90, -91, 190 ], [ 409, -421, 763, -772 ] ] ),
frattFacs := rec( frattFacs := [ 9, 17, 25, 33, 50, 58, 66, 74, 82, 90, 98,
106, 43, 51, 59, 67, 75, 83, 292, 300, 308, 316, 324, 332, 340, 348, 356, 364
, 372, 380, 165, 173, 181, 189, 197, 205, 213, 221, 229, 237, 245, 253, 261,
269, 277, 285, 293, 301, 1534, 1542, 1550, 1558, 1566, 1574, 1582, 1590, 1598
, 1606, 1614, 1622, 1630, 1638, 1646, 1654, 1662, 1670, 951, 959, 967, 975,
983, 991, 999, 1007, 1015, 1023, 1031, 1039, 1047, 1055, 1063, 1071, 1079,
1087, 1095, 1103, 1111, 1119, 1127, 1135, 1143, 1151, 1159, 1167, 1175, 1183,
1191, 1199, 1207, 1215, 1223, 1231, 1239, 1247, 1255, 1263, 1271, 1279, 1287,
1295, 1303 ], pos := [ 1, 2, 3, 4, 5, 6, 31, 32, 48, 64, 80, 88, 89, 90, 91,
92, 93, 94, 101, 104, 107, 110, 117, 124, 151, 154, 164, 174, 184, 188, 189,
190, 191, 192, 193, 194, 219, 244, 260, 285, 301, 302, 318, 334, 350, 366,
382, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403,
404, 405, 406, 407, 408, 409, 412, 415, 418, 421, 422, 423, 424, 431, 438,
445, 452, 459, 466, 471, 478, 483, 484, 486, 525, 528, 531, 534, 537, 540,
543, 546, 553, 560, 567, 574, 581, 588, 615, 642, 660, 687, 705, 708, 718,
728, 738, 748, 758, 762 ] ) );