sml240.z

#############################################################################
##
#W  sml240.z               GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 240 ] :=
[ 60122034543317761, 179368228103966979, 43049622260639887367,
249468880523712, 42809633060503474435, 10288562852668107681799,
297625900598452231, 297625900598448135, 71430216267960709127,
71430200806078570503, 71430200806078566407, 17143248193583157768199,
17313531758335662374919, 17143251889037444014087, 17313535453789948104711,
4155247622000617783189511, 4155247622000617783185415, 17143251888973019504647
, 4114380453353584494800903, 17313539164641691848711,
4155249399498667460816903, 997259429280148326776729607,
4114380453369046377066503, 4155248508894248962256903, 297625900598439943,
297625900598566919, 297625900598562823, 71430231729843089415,
71430216203536314375, 71430216267960823815, 71430200806078558215,
6883129021734187747072, 747367261315139, 179363031193657411,
43048359325506117699, 43048359346980954179, 10331606243296236187715,
747367261311043, 179363031193653315, 747367261286467, 179368163679547459,
179363031193628739, 747367261413443, 71427721643573280835,
17142653194476391665731, 17142653194476391669827, 4114236766674352803065923,
747367261409347, 250508264644801, 60118916397179073, 14429279038523220161,
14429279051408122049, 3463026972350166511809, 250508264640705,
60118916397174977, 250508264616129, 60121995888701633, 60118916397150401,
250508264743105, 42809134083828515009, 10274192180129057902785,
10274192180129057906881, 2465806123230984109994177, 250508264739009,
179373425015414791, 43049606669908729863, 10331909296296016896007,
10331909296360441405447, 2479658231126569510137863, 179373425015410695,
43049606669908725767, 179373425015402503, 43049622067366473735,
43049606669908717575, 179373425015529479, 51341864127584426934279,
12322047390620325036576775, 12322047390620325036580871,
2957291373748878071349800967, 179373425015525383, 1039382098032,
2065879404656, 496846111912048, 1039382155376, 248429498536048,
59623083913445488, 14309540139214508144, 3434289633411468570736,
[ ( 1,47, 7,48, 3,35,19,36)( 2,33,13,30, 4,41,21,42)( 5,34,20,29,15,44,10,
     39)( 6,27,17,43,18,25, 9,31)( 8,40,14,46,16,32,22,38)(11,37,12,28,23,
     45,24,26), ( 1,29, 3,39)( 2,34, 4,44)( 5,26,15,28)( 6,31,18,43)
    ( 7,36,19,48)( 8,41,16,33)( 9,46,17,38)(10,27,20,25)(11,32,23,40)
    (12,37,24,45)(13,42,21,30)(14,47,22,35) ],
[ ( 1,30,35,33,22,21,11, 6)( 2,12,13,19,18,25,14, 7)( 3,29,38,34,23,26,15,
      8)( 4,36,37,31,24,27,16, 9)( 5,40,39,32,20,28,17,10), 
  ( 1,35,22,11)( 2,33,18, 6)( 3,25,23,12)( 4,14,24,13)( 5,32,20,10)
    ( 7,34,19, 8)( 9,39,31,17)(15,26,38,29)(16,21,37,30)(27,40,36,28) ],
[ (1,3,2,4,5), (1,4)(6,8,7,9) ],
[ (1,4)(3,5)(6,9,7,8), (1,5,4,2,3)(6,9,7,8) ],
[ ( 1,20,17, 5,12)( 2, 3, 9,19,10)( 4,14,22,11, 6)( 7, 8,15,13,16), 
  ( 2,18)( 5,11)( 6,21)( 7,24)( 9,17)(10,16)(12,23)(13,20)(14,19)(15,22) ],
[ ( 1, 5,15,22,10)( 2, 9,12,24,13)( 3,17,20, 7, 8)( 4, 6,14,23,11)(25,26), 
  ( 1, 3,19,12,23, 4, 9,18,17,22)( 2, 5,16,14,20, 8, 6,21,15,24)( 7,13)
    (10,11)(25,26) ],
43046143208565256199, 43046143208565379079, 10331074354653958385671,
43046143208565264391, 10331074354653958270983, 10331074354653958393863,
2479457845101548278018055, 48266869992731710449979855680,
201111958303048794260734784, 6882769813387242640144,
11584048798485920810446119473600, 48266869993691336710736019904,
1651864757200176176435312, 923521514296459461185804, 3848006309568643645708,
891844547382874371, 42809627864398344259, 10274310682087455371331,
178373471802241091, 42809627864398442563, 178373471802265667,
42809627864398467139, 178373471802363971, 10288562837077611278343,
2469255080883228758929415, 42869011885314813959, 10288562837077611393031,
42869011885314822151, 10288562837077611401223, 42869011885314936839,
72139715595061977095, 71430200741654192135, 17313531742873779986439,
71430200741654188039, 17313531742873779982343, 17143248178056851124231,
4155247618289766039318535, 297625836174065671, 72139715595062099975,
17313531742873779855367, 1240107401101319, 300582148067311623,
297625836174196743, 72139715595062231047, 1240107401093127,
297625836174188551, 72139715595062222855, 1240107401089031,
300582148067299335, 297625836173930503, 1240107401216007, 297625836174057479,
297625836174053383, 71430200741654048775, 1252425371484167, 1240107401347079,
300582148067557383, 497889839157696, 14548271601939481024,
3491585184335420035520, 179363009718931475, 3113853403155, 747345786716179,
747345786707987, 5166851948563, 297615485290422291, 297615485290176531,
71427716489607929875, 3113853390867, 3113853648915, 60118903512387633,
1043679166513, 250495379980337, 250495379972145, 3096677711921,
178371379083878449, 178371379083632689, 42809130991447466033, 1043679154225,
1043679412273, 43049606605484347399, 747388737175559, 179373360591159303,
179373360591151111, 3713965602373639, 213924433800249745415,
213924433800249499655, 51341864112122544545799, 747388737163271,
747388737421319, 4294971420, 4295098396, 248425203511324, 1035087265820,
[ (1,2,3,4), (1,5,2,4,3)(6,7) ],
[ (1,2,3,4,5)(6,9)(7,8), (2,3)(4,5)(6,7)(8,9) ],
2171000129190068835512485632, 396478320479373188929425520,
43640854573997887747, 6882769829878760472688, 179358930590240775,
28678207557172986064, 6882769821666731884656, 3716018792824899,
834955081357985536, 743224765321235, 178620883394367495, 5166864531463,
2074871857264, 119497724029306624, 12886999047, 4297064461, 3113854435335, 7
]; 

PROPERTIES_SMALL_GROUPS[ 240 ] := rec(
isNilpotent := [ 4, 81, -88, 185, -188, 208 ], 
isSupersolvable := [ 1, -31, 33, -88, 95, -101, 111, -151, 155, -188, 195,
200, -202, 205, -208 ], 
isSolvable := [ 1, -88, 95, -188, 191, -208 ], 
isAbelian := [ 4, 81, 84, 185, 208 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6, false ], pos := [ [ 191, 199, 202,
204, -208 ], [ 25, -32, 40, -43, 48, 56, -59, 64, 72, -75, 80, -83, 95, -97,
113, -114, 117, 120, -121, 124, -151, 155, -188, 194, -198, 200, -201, 203 ],
[ 7, -24, 33, -39, 44, -47, 49, -55, 60, -63, 65, -71, 76, -79, 84, -88, 98,
-112, 115, -116, 118, -119, 122, -123, 152, -154, 192, -193 ], [ 1, -6 ], [
89, -94, 189, -190 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 26, 30, 34, 38, 42, 46, 50, 54
, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179, 183, 187, 191 ],
pos := [ 1, 2, 3, 4, 5, 6, 31, 32, 48, 64, 80, 88, 91, 94, 101, 104, 107, 110
, 117, 124, 151, 154, 164, 174, 184, 188 ] ) );