sml1056.z

#############################################################################
##
#W  sml1056.z              GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1056 ] :=
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2323238137034898717466801076500837191540019000,
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58177585393580793145664060000019, 52170843191802705960000019,
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3342813984274461509120001900, 3727703860418774281013180160910000,
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4743091647730073600190000, 12079616000000019, 1342197760000091,
12770816849920000019, 19 ]; 

PROPERTIES_SMALL_GROUPS[ 1056 ] := rec(
isNilpotent := [ 4, 196, -214, 830, -853, 1009, -1014, 1028 ], 
isSupersolvable := [ 1, -71, 73, -214, 230, -564, 572, -853, 902, -954, 964,
-1014, 1022, 1025, -1028 ], 
isAbelian := [ 4, 197, 210, 830, 845, 1009, 1028 ], 
lgLength := rec( lgLength := [ 3, 4, 5, 6, 7 ], pos := [ [ 1022, 1025, -1028
], [ 68, 72, 107, 148, 189, 196, 229, 268, -318, 361, -463, 512, -564, 567,
572, -602, 626, -639, 643, -646, 650, -651, 656, -688, 712, -725, 729, -732,
736, -737, 742, -774, 798, -811, 815, -818, 822, -823, 828, -844, 902, -954,
962, -1021, 1023, -1024 ], [ 23, -67, 69, -71, 78, -86, 89, -101, 106, 108,
-113, 119, -127, 130, -142, 147, 149, -154, 160, -168, 171, -183, 188, 190,
-195, 197, -209, 215, 219, 223, -225, 230, -267, 319, -360, 464, -511, 565,
568, -569, 603, -625, 640, -642, 647, -649, 652, -655, 689, -711, 726, -728,
733, -735, 738, -741, 775, -797, 812, -814, 819, -821, 824, -827, 845, -901,
955, -961 ], [ 5, -22, 73, -77, 87, -88, 102, -105, 114, -118, 128, -129, 143
, -146, 155, -159, 169, -170, 184, -187, 210, -214, 216, -218, 220, -222, 226
, -228, 566, 570, -571 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 6, 11, 16, 21, 27, 32, 37, 42, 47, 52, 158,
163, 168, 173, 178, 183, 188, 193, 198, 804, 809, 814, 819, 824, 829, 834,
839, 844, 849, 854 ], pos := [ 1, 2, 3, 4, 71, 72, 113, 154, 195, 214, 218,
222, 229, 564, 571, 657, 743, 829, 853, 868, 879, 890, 901, 954, 961, 963,
978, 993, 1008, 1014 ] ) );