SSL twoelorders.gi   Sprache: unbekannt

#############################################################################
##
##  This file is part of recog, a package for the GAP computer algebra system
##  which provides a collection of methods for the constructive recognition
##  of groups.
##
##  This files's authors include Max Neunhöffer, Ákos Seress.
##
##  Copyright of recog belongs to its developers whose names are too numerous
##  to list here. Please refer to the COPYRIGHT file for details.
##
##  SPDX-License-Identifier: GPL-3.0-or-later
##
##
##  Code to recognise (simple) groups by their two largest element orders.
##  At least recognise the "natural" characteristic.
##
#############################################################################

# If you change the following, rerun RECOG.AddInformationAboutDegree below
# to recreate RECOG.TableOfTwoLargestGroupElementOrdersWithDegreeBound!

RECOG.TableOfTwoLargestGroupElementOrders :=
[ [3,2,["l",2,5]],[4,3,["l",2,7]],[5,3,["l",2,4]],
  [5,3,["l",2,5]],[5,3,["s",4,2]],[5,4,["l",2,9]],
  [5,4,["s",4,2]],[5,4,["s",4,3]],[6,5,["l",2,11]],
  [6,5,["s",4,2]],[6,5,["s",4,3]],[7,4,["l",2,7]],
  [7,4,["l",3,2]],[7,5,["l",3,4]],[7,6,["l",2,13]],
  [8,7,["u",3,3]],[8,7,["u",3,5]],[8,7,["u",4,3]],
  [9,5,["s",4,3]],[9,5,["u",4,2]],[9,6,["s",4,3]],
  [9,6,["u",4,2]],[9,7,["l",2,8]],[9,8,["l",2,17]],
  [9,8,["u",4,3]],[10,8,["u",3,5]],
  [10,9,["l",2,19]],[11,6,["l",2,11]],
  [11,8,["M11"]],
  [11,8,["M22"]],
  [11,10,["M12"]],
  [12,5,["s",4,3]],[12,6,["s",4,3]],
  [12,8,["u",3,3]],[12,8,["u",4,3]],
  [12,9,["s",4,3]],[12,9,["u",4,2]],
  [12,9,["u",4,3]],[12,11,["l",2,23]],
  [13,5,["2F4",2]],[13,6,["2F4",2]],[13,7,["2B2",8]],
  [13,7,["l",2,13]],[13,8,["2F4",2]],[13,8,["G2",3]],
  [13,8,["l",3,3]],[13,9,["G2",3]],[13,10,["2F4",2]],
  [13,12,["2F4",2]],[13,12,["G2",3]],
  [13,12,["l",2,25]],[13,12,["s",4,5]],
  [14,13,["l",2,27]],[15,7,["l",4,2]],
  [15,9,["o+",8,2]],[15,9,["s",6,2]],
  [15,10,["o+",8,2]],[15,10,["s",6,2]],
  [15,11,["u",5,2]],[15,11,["u",6,2]],
  [15,12,["o+",8,2]],[15,12,["s",6,2]],
  [15,12,["u",5,2]],[15,12,["u",6,2]],
  [15,12,["J2"]],
  [15,13,["s",4,5]],[15,13,["u",3,4]],
  [15,14,["l",2,29]],[16,13,["2F4",2]],
  [16,15,["l",2,31]],[17,9,["l",2,17]],
  [17,15,["l",2,16]],[17,15,["s",4,4]],
  [18,15,["u",5,2]],[18,15,["u",6,2]],
  [19,10,["l",2,19]],
  [19,15,["J1"]],
  [19,16,["l",3,7]],
  [19,17,["J3"]],
  [19,18,["l",2,37]],[20,13,["l",4,3]],
  [20,13,["s",4,5]],[20,14,["o",7,3]],
  [20,14,["o+",8,3]],[20,14,["s",6,3]],
  [20,15,["o",7,3]],[20,15,["o+",8,3]],
  [20,15,["s",4,5]],[20,15,["s",6,3]],
  [20,15,["HS"]],
  [20,18,["o",7,3]],[20,18,["o+",8,3]],
  [20,18,["s",6,3]],[21,13,["3D4",2]],
  [21,14,["3D4",2]],[21,15,["G2",4]],[21,17,["F4",2]],
  [21,17,["o-",8,2]],[21,17,["s",8,2]],
  [21,18,["3D4",2]],[21,18,["F4",2]],
  [21,18,["s",8,2]],[21,19,["u",3,8]],
  [21,20,["F4",2]],[21,20,["l",2,41]],
  [21,20,["s",8,2]],[22,21,["l",2,43]],
  [23,12,["l",2,23]],
  [23,15,["M23"]],
  [23,21,["M24"]],
  [24,20,["s",6,3]],
  [24,21,["F4",2]],[24,21,["s",8,2]],
  [24,21,["Suz"]],
  [24,23,["l",2,47]],[25,24,["l",2,49]],
  [25,24,["s",4,7]],[27,26,["l",2,53]],
  [28,21,["3D4",2]],[28,21,["F4",2]],
  [28,21,["He"]],
  [28,24,["F4",2]],
  [28,25,["s",4,7]],[29,15,["l",2,29]],
  [29,26,["Ru"]],
  [30,13,["s",4,5]],[30,15,["s",4,5]],
  [30,15,["McL"]],
  [30,20,["s",4,5]],[30,20,["s",6,3]],
  [30,21,["F4",2]],[30,21,["o-",8,2]],
  [30,21,["s",8,2]],[30,24,["F4",2]],
  [30,24,["s",6,3]],[30,24,["s",8,2]],
  [30,24,["Co3"]],
  [30,24,["Fi22"]],
  [30,28,["F4",2]],
  [30,28,["Co2"]],
  [30,29,["l",2,59]],
  [31,16,["l",2,31]],[31,21,["l",5,2]],
  [31,24,["G2",5]],[31,24,["l",3,5]],
  [31,25,["G2",5]],
  [31,28,["O'N"]],
  [31,30,["G2",5]],
  [31,30,["l",2,61]],[33,31,["l",2,32]],
  [34,33,["l",2,67]],[35,33,["2E6",2]],
  [35,33,["o-",10,2]],[36,20,["s",6,3]],
  [36,24,["s",6,3]],[36,30,["s",6,3]],
  [36,35,["l",2,71]],[37,19,["l",2,37]],
  [37,26,["2G2",27]],[37,36,["l",2,73]],
  [39,31,["l",4,5]],
  [39,36,["Th"]],
  [40,35,["HN"]],
  [40,37,["u",3,11]],
  [40,39,["l",2,79]],[41,21,["l",2,41]],
  [41,31,["2B2",32]],[41,40,["l",2,81]],
  [41,40,["s",4,9]],[42,25,["s",4,7]],
  [42,28,["s",4,7]],[42,41,["l",2,83]],
  [43,22,["l",2,43]],[44,40,["u",3,11]],
  [45,44,["l",2,89]],[47,24,["l",2,47]],
  [48,43,["u",3,7]],[49,48,["l",2,97]],
  [51,45,["o+",10,2]],[51,45,["s",10,2]],
  [51,50,["l",2,101]],[52,41,["o",9,3]],
  [52,41,["o-",8,3]],[52,41,["s",8,3]],
  [52,42,["o",9,3]],[52,42,["s",8,3]],
  [52,45,["o",9,3]],[52,45,["s",8,3]],
  [52,51,["l",2,103]],[53,27,["l",2,53]],
  [54,53,["l",2,107]],[55,54,["l",2,109]],
  [56,25,["s",4,7]],[56,28,["s",4,7]],
  [56,42,["s",4,7]],[56,48,["u",3,7]],
  [57,48,["G2",7]],[57,49,["G2",7]],[57,56,["G2",7]],
  [57,56,["l",2,113]],[59,30,["l",2,59]],
  [60,42,["Co1"]],
  [60,42,["Fi23"]],
  [60,45,["Fi24'"]],
  [60,51,["o+",10,2]],[60,51,["s",10,2]],
  [60,52,["o",9,3]],[60,52,["o-",8,3]],
  [60,52,["s",8,3]],[61,31,["l",2,61]],
  [61,56,["l",3,13]],[61,60,["l",2,121]],
  [61,60,["s",4,11]],[63,31,["l",6,2]],
  [63,45,["u",7,2]],[63,52,["u",4,5]],
  [63,60,["u",4,5]],[63,60,["u",7,2]],
  [63,62,["l",2,125]],[64,63,["l",2,127]],
  [65,51,["u",4,4]],[65,51,["u",5,4]],
  [65,63,["l",2,64]],[65,63,["s",4,8]],
  [66,44,["J4"]],
  [66,61,["s",4,11]],[66,63,["u",7,2]],
  [66,65,["l",2,131]],[67,34,["l",2,67]],
  [67,42,["Ly"]],
  [69,68,["l",2,137]],
  [70,66,["B"]],
  [70,69,["l",2,139]],
  [71,36,["l",2,71]],[72,52,["s",8,3]],
  [72,60,["s",8,3]],[73,37,["l",2,73]],
  [73,63,["G2",8]],[73,63,["l",3,8]],
  [75,74,["l",2,149]],[76,75,["l",2,151]],
  [78,52,["s",8,3]],[78,60,["s",8,3]],
  [78,63,["o",7,5]],[78,63,["s",6,5]],
  [78,65,["o",7,5]],[78,65,["s",6,5]],
  [78,72,["s",8,3]],[79,40,["l",2,79]],
  [79,78,["l",2,157]],[80,61,["u",5,3]],
  [80,65,["o-",10,3]],[80,73,["u",3,9]],
  [82,81,["l",2,163]],[83,42,["l",2,83]],
  [84,52,["s",8,3]],[84,60,["s",8,3]],
  [84,72,["s",8,3]],[84,78,["s",8,3]],
  [84,80,["o-",10,3]],[84,80,["u",5,3]],
  [84,83,["l",2,167]],[85,63,["l",4,4]],
  [85,65,["s",6,4]],[85,84,["l",2,169]],
  [85,84,["s",4,13]],[86,75,["u",4,7]],
  [86,84,["u",4,7]],[87,86,["l",2,173]],
  [89,45,["l",2,89]],[90,52,["s",8,3]],
  [90,60,["s",8,3]],[90,72,["s",8,3]],
  [90,78,["s",8,3]],[90,84,["s",8,3]],
  [90,89,["l",2,179]],[91,80,["l",3,9]],
  [91,85,["l",3,16]],[91,85,["s",4,13]],
  [91,90,["l",2,181]],[93,65,["o-",12,2]],
  [93,84,["o-",12,2]],[93,91,["E6",2]],
  [96,91,["u",3,17]],[96,95,["l",2,191]],
  [97,49,["l",2,97]],[97,96,["l",2,193]],
  [99,98,["l",2,197]],[100,99,["l",2,199]],
  [101,51,["l",2,101]],[102,93,["o-",12,2]],
  [102,96,["u",3,17]],[103,52,["l",2,103]],
  [104,73,["3D4",3]],[104,78,["3D4",3]],
  [104,84,["3D4",3]],[105,85,["o+",12,2]],
  [105,93,["s",12,2]],[105,102,["s",12,2]],
  [106,105,["l",2,211]],[107,54,["l",2,107]],
  [109,55,["l",2,109]],[110,61,["s",4,11]],
  [110,66,["s",4,11]],[112,111,["l",2,223]],
  [113,57,["l",2,113]],[114,113,["l",2,227]],
  [115,114,["l",2,229]],[117,116,["l",2,233]],
  [119,110,["M"]],
  [120,78,["s",6,5]],[120,105,["s",12,2]],
  [120,119,["l",2,239]],[121,104,["l",5,3]],
  [121,120,["l",2,241]],[122,91,["u",6,3]],
  [122,120,["u",6,3]],[122,121,["l",2,243]],
  [126,93,["E6",2]],[126,125,["l",2,251]],
  [127,64,["l",2,127]],[127,105,["l",7,2]],
  [127,120,["l",3,19]],[129,99,["u",8,2]],
  [129,99,["u",9,2]],[129,126,["u",8,2]],
  [129,126,["u",9,2]],[129,127,["l",2,128]],
  [129,128,["l",2,257]],[130,78,["s",6,5]],
  [130,120,["s",6,5]],[131,66,["l",2,131]],
  [132,61,["s",4,11]],[132,66,["s",4,11]],
  [132,110,["s",4,11]],[132,129,["u",8,2]],
  [132,129,["u",9,2]],[132,131,["l",2,263]],
  [133,120,["G2",11]],[133,120,["l",3,11]],
  [133,121,["G2",11]],[133,132,["G2",11]],
  [135,134,["l",2,269]],[136,135,["l",2,271]],
  [137,69,["l",2,137]],[139,70,["l",2,139]],
  [139,138,["l",2,277]],[141,140,["l",2,281]],
  [142,141,["l",2,283]],[145,127,["2B2",128]],
  [145,144,["l",2,289]],[145,144,["s",4,17]],
  [147,146,["l",2,293]],[149,75,["l",2,149]],
  [151,76,["l",2,151]],[153,145,["s",4,17]],
  [154,153,["l",2,307]],[156,78,["o+",8,5]],
  [156,85,["s",4,13]],[156,91,["s",4,13]],
  [156,155,["l",2,311]],[157,79,["l",2,157]],
  [157,156,["l",2,313]],[159,158,["l",2,317]],
  [163,82,["l",2,163]],[164,140,["o+",10,3]],
  [164,140,["s",10,3]],[164,156,["o+",10,3]],
  [164,156,["s",10,3]],[166,165,["l",2,331]],
  [167,84,["l",2,167]],[168,157,["u",3,13]],
  [169,168,["l",2,337]],[172,171,["l",2,343]],
  [173,87,["l",2,173]],[174,173,["l",2,347]],
  [175,174,["l",2,349]],[176,169,["u",3,23]],
  [177,176,["l",2,353]],[179,90,["l",2,179]],
  [180,164,["s",10,3]],[180,179,["l",2,359]],
  [181,91,["l",2,181]],[181,180,["l",2,361]],
  [181,180,["s",4,19]],[182,85,["s",4,13]],
  [182,91,["s",4,13]],[182,121,["l",6,3]],
  [182,156,["s",4,13]],[182,168,["u",3,13]],
  [183,168,["G2",13]],[183,169,["G2",13]],
  [183,182,["G2",13]],[184,176,["u",3,23]],
  [184,183,["l",2,367]],[187,186,["l",2,373]],
  [190,181,["s",4,19]],[190,189,["l",2,379]],
  [191,96,["l",2,191]],[192,191,["l",2,383]],
  [193,97,["l",2,193]],[195,165,["o+",14,2]],
  [195,186,["o+",14,2]],[195,194,["l",2,389]],
  [197,99,["l",2,197]],[199,100,["l",2,199]],
  [199,198,["l",2,397]],[200,171,["l",4,7]],
  [200,172,["o",7,7]],[200,172,["s",6,7]],
  [200,175,["o",7,7]],[200,175,["s",6,7]],
  [201,200,["l",2,401]],[204,195,["o+",14,2]],
  [205,182,["l",4,9]],[205,204,["l",2,409]],
  [210,209,["l",2,419]],[211,106,["l",2,211]],
  [211,210,["l",2,421]],[216,215,["l",2,431]],
  [217,208,["l",3,25]],[217,216,["l",2,433]],
  [220,219,["l",2,439]],[222,221,["l",2,443]],
  [223,112,["l",2,223]],[225,224,["l",2,449]],
  [227,114,["l",2,227]],[229,115,["l",2,229]],
  [229,228,["l",2,457]],[231,230,["l",2,461]],
  [232,231,["l",2,463]],[233,117,["l",2,233]],
  [234,164,["s",10,3]],[234,180,["s",10,3]],
  [234,233,["l",2,467]],[239,120,["l",2,239]],
  [240,164,["s",10,3]],[240,180,["s",10,3]],
  [240,234,["s",10,3]],[240,239,["l",2,479]],
  [241,121,["l",2,241]],[244,243,["l",2,487]],
  [246,164,["s",10,3]],[246,180,["s",10,3]],
  [246,234,["s",10,3]],[246,240,["s",10,3]],
  [246,245,["l",2,491]],[250,249,["l",2,499]],
  [251,126,["l",2,251]],[252,164,["s",10,3]],
  [252,180,["s",10,3]],[252,234,["s",10,3]],
  [252,240,["s",10,3]],[252,246,["s",10,3]],
  [252,251,["l",2,503]],[255,85,["o+",8,4]],
  [255,155,["o-",14,2]],[255,195,["s",14,2]],
  [255,204,["s",14,2]],[255,210,["o-",14,2]],
  [255,210,["s",14,2]],[255,217,["l",8,2]],
  [255,241,["u",3,16]],[255,254,["l",2,509]],
  [257,129,["l",2,257]],[257,255,["l",2,256]],
  [257,255,["s",4,16]],[261,260,["l",2,521]],
  [262,261,["l",2,523]],[263,132,["l",2,263]],
  [265,264,["l",2,529]],[265,264,["s",4,23]],
  [269,135,["l",2,269]],[271,136,["l",2,271]],
  [271,270,["l",2,541]],[272,145,["s",4,17]],
  [272,153,["s",4,17]],[273,255,["G2",16]],
  [274,273,["l",2,547]],[276,265,["s",4,23]],
  [277,139,["l",2,277]],[279,278,["l",2,557]],
  [280,271,["u",3,29]],[281,141,["l",2,281]],
  [282,281,["l",2,563]],[283,142,["l",2,283]],
  [285,284,["l",2,569]],[286,285,["l",2,571]],
  [289,288,["l",2,577]],[290,280,["u",3,29]],
  [293,147,["l",2,293]],[294,293,["l",2,587]],
  [297,296,["l",2,593]],[300,299,["l",2,599]],
  [301,300,["l",2,601]],[304,303,["l",2,607]],
  [306,145,["s",4,17]],[306,153,["s",4,17]],
  [306,272,["s",4,17]],[307,154,["l",2,307]],
  [307,288,["G2",17]],[307,288,["l",3,17]],
  [307,289,["G2",17]],[307,306,["G2",17]],
  [307,306,["l",2,613]],[309,308,["l",2,617]],
  [310,309,["l",2,619]],[311,156,["l",2,311]],
  [313,157,["l",2,313]],[313,312,["l",2,625]],
  [313,312,["s",4,25]],[315,241,["3D4",4]],
  [315,257,["o-",8,4]],[316,315,["l",2,631]],
  [317,159,["l",2,317]],[321,320,["l",2,641]],
  [322,321,["l",2,643]],[324,323,["l",2,647]],
  [327,326,["l",2,653]],[330,329,["l",2,659]],
  [331,166,["l",2,331]],[331,320,["l",3,31]],
  [331,330,["l",2,661]],[333,305,["u",4,11]],
  [333,330,["u",4,11]],[336,200,["s",6,7]],
  [337,169,["l",2,337]],[337,336,["l",2,673]],
  [339,338,["l",2,677]],[341,315,["l",5,4]],
  [341,331,["u",3,32]],[342,181,["s",4,19]],
  [342,190,["s",4,19]],[342,341,["l",2,683]],
  [346,345,["l",2,691]],[347,174,["l",2,347]],
  [349,175,["l",2,349]],[350,200,["s",6,7]],
  [350,336,["s",6,7]],[351,350,["l",2,701]],
  [353,177,["l",2,353]],[355,354,["l",2,709]],
  [359,180,["l",2,359]],[360,343,["u",3,19]],
  [360,359,["l",2,719]],[364,363,["l",2,727]],
  [365,328,["u",4,9]],[365,364,["l",2,729]],
  [365,364,["s",4,27]],[367,184,["l",2,367]],
  [367,366,["l",2,733]],[370,369,["l",2,739]],
  [372,313,["o-",8,5]],[372,313,["s",8,5]],
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  [9203,4602,["l",2,9203]],[9209,4605,["l",2,9209]],
  [9221,4611,["l",2,9221]],[9227,4614,["l",2,9227]],
  [9239,4620,["l",2,9239]],[9241,4621,["l",2,9241]],
  [9257,4629,["l",2,9257]],[9277,4639,["l",2,9277]],
  [9281,4641,["l",2,9281]],[9283,4642,["l",2,9283]],
  [9293,4647,["l",2,9293]],[9311,4656,["l",2,9311]],
  [9319,4660,["l",2,9319]],[9323,4662,["l",2,9323]],
  [9337,4669,["l",2,9337]],[9341,4671,["l",2,9341]],
  [9343,4672,["l",2,9343]],[9349,4675,["l",2,9349]],
  [9371,4686,["l",2,9371]],[9377,4689,["l",2,9377]],
  [9391,4696,["l",2,9391]],[9397,4699,["l",2,9397]],
  [9403,4702,["l",2,9403]],[9413,4707,["l",2,9413]],
  [9419,4710,["l",2,9419]],[9421,4711,["l",2,9421]],
  [9431,4716,["l",2,9431]],[9433,4717,["l",2,9433]],
  [9437,4719,["l",2,9437]],[9439,4720,["l",2,9439]],
  [9461,4731,["l",2,9461]],[9463,4732,["l",2,9463]],
  [9467,4734,["l",2,9467]],[9473,4737,["l",2,9473]],
  [9479,4740,["l",2,9479]],[9491,4746,["l",2,9491]],
  [9497,4749,["l",2,9497]],[9511,4756,["l",2,9511]],
  [9521,4761,["l",2,9521]],[9533,4767,["l",2,9533]],
  [9539,4770,["l",2,9539]],[9547,4774,["l",2,9547]],
  [9551,4776,["l",2,9551]],[9587,4794,["l",2,9587]],
  [9601,4801,["l",2,9601]],[9613,4807,["l",2,9613]],
  [9619,4810,["l",2,9619]],[9623,4812,["l",2,9623]],
  [9629,4815,["l",2,9629]],[9631,4816,["l",2,9631]],
  [9643,4822,["l",2,9643]],[9649,4825,["l",2,9649]],
  [9661,4831,["l",2,9661]],[9677,4839,["l",2,9677]],
  [9679,4840,["l",2,9679]],[9689,4845,["l",2,9689]],
  [9697,4849,["l",2,9697]],[9719,4860,["l",2,9719]],
  [9721,4861,["l",2,9721]],[9733,4867,["l",2,9733]],
  [9739,4870,["l",2,9739]],[9743,4872,["l",2,9743]],
  [9749,4875,["l",2,9749]],[9767,4884,["l",2,9767]],
  [9769,4885,["l",2,9769]],[9781,4891,["l",2,9781]],
  [9787,4894,["l",2,9787]],[9791,4896,["l",2,9791]],
  [9803,4902,["l",2,9803]],[9811,4906,["l",2,9811]],
  [9817,4909,["l",2,9817]],[9829,4915,["l",2,9829]],
  [9833,4917,["l",2,9833]],[9839,4920,["l",2,9839]],
  [9851,4926,["l",2,9851]],[9857,4929,["l",2,9857]],
  [9859,4930,["l",2,9859]],[9871,4936,["l",2,9871]],
  [9883,4942,["l",2,9883]],[9887,4944,["l",2,9887]],
  [9901,4951,["l",2,9901]],[9907,4954,["l",2,9907]],
  [9923,4962,["l",2,9923]],[9929,4965,["l",2,9929]],
  [9931,4966,["l",2,9931]],[9941,4971,["l",2,9941]],
  [9949,4975,["l",2,9949]],[9967,4984,["l",2,9967]],
  [9973,4987,["l",2,9973]] ];

# This is the same as above, however the fourth position now holds
# the minimum degree this group occurs:

RECOG.TableOfTwoLargestGroupElementOrdersWithDegreeBound :=
[ [3,2,["l",2,5],2],[4,3,["l",2,7],3],
  [5,3,["l",2,4],2],[5,3,["l",2,5],2],
  [5,3,["s",4,2],4],[5,4,["l",2,9],4],
  [5,4,["s",4,2],4],[5,4,["s",4,3],9],
  [6,5,["l",2,11],5],[6,5,["s",4,2],4],
  [6,5,["s",4,3],9],[7,4,["l",2,7],3],
  [7,4,["l",3,2],8],[7,5,["l",3,4],19],
  [7,6,["l",2,13],6],[8,7,["u",3,3],9],
  [8,7,["u",3,5],25],[8,7,["u",4,3],20],
  [9,5,["s",4,3],9],[9,5,["u",4,2],16],
  [9,6,["s",4,3],9],[9,6,["u",4,2],16],
  [9,7,["l",2,8],4],[9,8,["l",2,17],8],
  [9,8,["u",4,3],20],[10,8,["u",3,5],25],
  [10,9,["l",2,19],9],[11,6,["l",2,11],5],
  [11,8,["M11"],5],[11,8,["M22"],6],[11,10,["M12"],6],
  [12,5,["s",4,3],9],[12,6,["s",4,3],9],
  [12,8,["u",3,3],9],[12,8,["u",4,3],20],
  [12,9,["s",4,3],9],[12,9,["u",4,2],16],
  [12,9,["u",4,3],20],[12,11,["l",2,23],11],
  [13,5,["2F4",2],16],[13,6,["2F4",2],16],
  [13,7,["2B2",8],14],[13,7,["l",2,13],6],
  [13,8,["2F4",2],16],[13,8,["G2",3],90],
  [13,8,["l",3,3],11],[13,9,["G2",3],90],
  [13,10,["2F4",2],16],[13,12,["2F4",2],16],
  [13,12,["G2",3],90],[13,12,["l",2,25],12],
  [13,12,["s",4,5],25],[14,13,["l",2,27],13],
  [15,7,["l",4,2],16],[15,9,["o+",8,2],35],
  [15,9,["s",6,2],8],[15,10,["o+",8,2],35],
  [15,10,["s",6,2],8],[15,11,["u",5,2],32],
  [15,11,["u",6,2],64],[15,12,["o+",8,2],35],
  [15,12,["s",6,2],8],[15,12,["u",5,2],32],
  [15,12,["u",6,2],64],[15,12,["J2"],6],
  [15,13,["s",4,5],25],[15,13,["u",3,4],16],
  [15,14,["l",2,29],14],[16,13,["2F4",2],16],
  [16,15,["l",2,31],15],[17,9,["l",2,17],8],
  [17,15,["l",2,16],8],[17,15,["s",4,4],18],
  [18,15,["u",5,2],32],[18,15,["u",6,2],64],
  [19,10,["l",2,19],9],[19,15,["J1"],7],
  [19,16,["l",3,7],55],[19,17,["J3"],9],
  [19,18,["l",2,37],18],[20,13,["l",4,3],38],
  [20,13,["s",4,5],25],[20,14,["o",7,3],78],
  [20,14,["o+",8,3],260],[20,14,["s",6,3],13],
  [20,15,["o",7,3],78],[20,15,["o+",8,3],260],
  [20,15,["s",4,5],25],[20,15,["s",6,3],13],
  [20,15,["HS"],20],[20,18,["o",7,3],78],
  [20,18,["o+",8,3],260],[20,18,["s",6,3],13],
  [21,13,["3D4",2],25],[21,14,["3D4",2],25],
  [21,15,["G2",4],63],[21,17,["F4",2],448],
  [21,17,["o-",8,2],33],[21,17,["s",8,2],35],
  [21,18,["3D4",2],25],[21,18,["F4",2],448],
  [21,18,["s",8,2],35],[21,19,["u",3,8],64],
  [21,20,["F4",2],448],[21,20,["l",2,41],20],
  [21,20,["s",8,2],35],[22,21,["l",2,43],21],
  [23,12,["l",2,23],11],[23,15,["M23"],11],
  [23,21,["M24"],11],[24,20,["s",6,3],13],
  [24,21,["F4",2],448],[24,21,["s",8,2],35],
  [24,21,["Suz"],12],[24,23,["l",2,47],23],
  [25,24,["l",2,49],24],[25,24,["s",4,7],49],
  [27,26,["l",2,53],26],[28,21,["3D4",2],25],
  [28,21,["F4",2],448],[28,21,["He"],50],
  [28,24,["F4",2],448],[28,25,["s",4,7],49],
  [29,15,["l",2,29],14],[29,26,["Ru"],28],
  [30,13,["s",4,5],25],[30,15,["s",4,5],25],
  [30,15,["McL"],21],[30,20,["s",4,5],25],
  [30,20,["s",6,3],13],[30,21,["F4",2],448],
  [30,21,["o-",8,2],33],[30,21,["s",8,2],35],
  [30,24,["F4",2],448],[30,24,["s",6,3],13],
  [30,24,["s",8,2],35],[30,24,["Co3"],22],
  [30,24,["Fi22"],27],[30,28,["F4",2],448],
  [30,28,["Co2"],22],[30,29,["l",2,59],29],
  [31,16,["l",2,31],15],[31,21,["l",5,2],32],
  [31,24,["G2",5],124],[31,24,["l",3,5],29],
  [31,25,["G2",5],124],[31,28,["O'N"],45],
  [31,30,["G2",5],124],[31,30,["l",2,61],30],
  [33,31,["l",2,32],16],[34,33,["l",2,67],33],
  [35,33,["2E6",2],1536],[35,33,["o-",10,2],153],
  [36,20,["s",6,3],13],[36,24,["s",6,3],13],
  [36,30,["s",6,3],13],[36,35,["l",2,71],35],
  [37,19,["l",2,37],18],[37,26,["2G2",27],702],
  [37,36,["l",2,73],36],[39,31,["l",4,5],154],
  [39,36,["Th"],248],[40,35,["HN"],132],
  [40,37,["u",3,11],121],[40,39,["l",2,79],39],
  [41,21,["l",2,41],20],[41,31,["2B2",32],124],
  [41,40,["l",2,81],40],[41,40,["s",4,9],81],
  [42,25,["s",4,7],49],[42,28,["s",4,7],49],
  [42,41,["l",2,83],41],[43,22,["l",2,43],21],
  [44,40,["u",3,11],121],[45,44,["l",2,89],44],
  [47,24,["l",2,47],23],[48,43,["u",3,7],49],
  [49,48,["l",2,97],48],[51,45,["o+",10,2],155],
  [51,45,["s",10,2],155],[51,50,["l",2,101],50],
  [52,41,["o",9,3],780],[52,41,["o-",8,3],245],
  [52,41,["s",8,3],40],[52,42,["o",9,3],780],
  [52,42,["s",8,3],40],[52,45,["o",9,3],780],
  [52,45,["s",8,3],40],[52,51,["l",2,103],51],
  [53,27,["l",2,53],26],[54,53,["l",2,107],53],
  [55,54,["l",2,109],54],[56,25,["s",4,7],49],
  [56,28,["s",4,7],49],[56,42,["s",4,7],49],
  [56,48,["u",3,7],49],[57,48,["G2",7],342],
  [57,49,["G2",7],342],[57,56,["G2",7],342],
  [57,56,["l",2,113],56],[59,30,["l",2,59],29],
  [60,42,["Co1"],24],[60,42,["Fi23"],253],
  [60,45,["Fi24'"],781],[60,51,["o+",10,2],155],
  [60,51,["s",10,2],155],[60,52,["o",9,3],780],
  [60,52,["o-",8,3],245],[60,52,["s",8,3],40],
  [61,31,["l",2,61],30],[61,56,["l",3,13],181],
  [61,60,["l",2,121],60],[61,60,["s",4,11],121],
  [63,31,["l",6,2],64],[63,45,["u",7,2],128],
  [63,52,["u",4,5],104],[63,60,["u",4,5],104],
  [63,60,["u",7,2],128],[63,62,["l",2,125],62],
  [64,63,["l",2,127],63],[65,51,["u",4,4],51],
  [65,51,["u",5,4],205],[65,63,["l",2,64],32],
  [65,63,["s",4,8],196],[66,44,["J4"],112],
  [66,61,["s",4,11],121],[66,63,["u",7,2],128],
  [66,65,["l",2,131],65],[67,34,["l",2,67],33],
  [67,42,["Ly"],111],[69,68,["l",2,137],68],
  [70,66,["B"],4370],[70,69,["l",2,139],69],
  [71,36,["l",2,71],35],[72,52,["s",8,3],40],
  [72,60,["s",8,3],40],[73,37,["l",2,73],36],
  [73,63,["G2",8],511],[73,63,["l",3,8],71],
  [75,74,["l",2,149],74],[76,75,["l",2,151],75],
  [78,52,["s",8,3],40],[78,60,["s",8,3],40],
  [78,63,["o",7,5],649],[78,63,["s",6,5],62],
  [78,65,["o",7,5],649],[78,65,["s",6,5],62],
  [78,72,["s",8,3],40],[79,40,["l",2,79],39],
  [79,78,["l",2,157],78],[80,61,["u",5,3],61],
  [80,65,["o-",10,3],2378],[80,73,["u",3,9],81],
  [82,81,["l",2,163],81],[83,42,["l",2,83],41],
  [84,52,["s",8,3],40],[84,60,["s",8,3],40],
  [84,72,["s",8,3],40],[84,78,["s",8,3],40],
  [84,80,["o-",10,3],2378],[84,80,["u",5,3],61],
  [84,83,["l",2,167],83],[85,63,["l",4,4],83],
  [85,65,["s",6,4],378],[85,84,["l",2,169],84],
  [85,84,["s",4,13],169],[86,75,["u",4,7],300],
  [86,84,["u",4,7],300],[87,86,["l",2,173],86],
  [89,45,["l",2,89],44],[90,52,["s",8,3],40],
  [90,60,["s",8,3],40],[90,72,["s",8,3],40],
  [90,78,["s",8,3],40],[90,84,["s",8,3],40],
  [90,89,["l",2,179],89],[91,80,["l",3,9],89],
  [91,85,["l",3,16],271],[91,85,["s",4,13],169],
  [91,90,["l",2,181],90],[93,65,["o-",12,2],649],
  [93,84,["o-",12,2],649],[93,91,["E6",2],1536],
  [96,91,["u",3,17],289],[96,95,["l",2,191],95],
  [97,49,["l",2,97],48],[97,96,["l",2,193],96],
  [99,98,["l",2,197],98],[100,99,["l",2,199],99],
  [101,51,["l",2,101],50],[102,93,["o-",12,2],649],
  [102,96,["u",3,17],289],[103,52,["l",2,103],51],
  [104,73,["3D4",3],218],[104,78,["3D4",3],218],
  [104,84,["3D4",3],218],[105,85,["o+",12,2],651],
  [105,93,["s",12,2],651],[105,102,["s",12,2],651],
  [106,105,["l",2,211],105],[107,54,["l",2,107],53],
  [109,55,["l",2,109],54],[110,61,["s",4,11],121],
  [110,66,["s",4,11],121],[112,111,["l",2,223],111],
  [113,57,["l",2,113],56],[114,113,["l",2,227],113],
  [115,114,["l",2,229],114],[117,116,["l",2,233],116],
  [119,110,["M"]],[120,78,["s",6,5],62],
  [120,105,["s",12,2],651],[120,119,["l",2,239],119],
  [121,104,["l",5,3],119],[121,120,["l",2,241],120],
  [122,91,["u",6,3],182],[122,120,["u",6,3],182],
  [122,121,["l",2,243],121],[126,93,["E6",2],1536],
  [126,125,["l",2,251],125],[127,64,["l",2,127],63],
  [127,105,["l",7,2],128],[127,120,["l",3,19],379],
  [129,99,["u",8,2],256],[129,99,["u",9,2],512],
  [129,126,["u",8,2],256],[129,126,["u",9,2],512],
  [129,127,["l",2,128],64],[129,128,["l",2,257],128],
  [130,78,["s",6,5],62],[130,120,["s",6,5],62],
  [131,66,["l",2,131],65],[132,61,["s",4,11],121],
  [132,66,["s",4,11],121],[132,110,["s",4,11],121],
  [132,129,["u",8,2],256],[132,129,["u",9,2],512],
  [132,131,["l",2,263],131],[133,120,["G2",11],1330],
  [133,120,["l",3,11],131],[133,121,["G2",11],1330],
  [133,132,["G2",11],1330],[135,134,["l",2,269],134],
  [136,135,["l",2,271],135],[137,69,["l",2,137],68],
  [139,70,["l",2,139],69],[139,138,["l",2,277],138],
  [141,140,["l",2,281],140],[142,141,["l",2,283],141],
  [145,127,["2B2",128],1016],[145,144,["l",2,289],144],
  [145,144,["s",4,17],289],[147,146,["l",2,293],146],
  [149,75,["l",2,149],74],[151,76,["l",2,151],75],
  [153,145,["s",4,17],289],[154,153,["l",2,307],153],
  [156,78,["o+",8,5],3380],[156,85,["s",4,13],169],
  [156,91,["s",4,13],169],[156,155,["l",2,311],155],
  [157,79,["l",2,157],78],[157,156,["l",2,313],156],
  [159,158,["l",2,317],158],[163,82,["l",2,163],81],
  [164,140,["o+",10,3],2420],[164,140,["s",10,3],121],
  [164,156,["o+",10,3],2420],[164,156,["s",10,3],121],
  [166,165,["l",2,331],165],[167,84,["l",2,167],83],
  [168,157,["u",3,13],169],[169,168,["l",2,337],168],
  [172,171,["l",2,343],171],[173,87,["l",2,173],86],
  [174,173,["l",2,347],173],[175,174,["l",2,349],174],
  [176,169,["u",3,23],529],[177,176,["l",2,353],176],
  [179,90,["l",2,179],89],[180,164,["s",10,3],121],
  [180,179,["l",2,359],179],[181,91,["l",2,181],90],
  [181,180,["l",2,361],180],[181,180,["s",4,19],361],
  [182,85,["s",4,13],169],[182,91,["s",4,13],169],
  [182,121,["l",6,3],362],[182,156,["s",4,13],169],
  [182,168,["u",3,13],169],[183,168,["G2",13],2196],
  [183,169,["G2",13],2196],[183,182,["G2",13],2196],
  [184,176,["u",3,23],529],[184,183,["l",2,367],183],
  [187,186,["l",2,373],186],[190,181,["s",4,19],361],
  [190,189,["l",2,379],189],[191,96,["l",2,191],95],
  [192,191,["l",2,383],191],[193,97,["l",2,193],96],
  [195,165,["o+",14,2],2667],[195,186,["o+",14,2],2667],
  [195,194,["l",2,389],194],[197,99,["l",2,197],98],
  [199,100,["l",2,199],99],[199,198,["l",2,397],198],
  [200,171,["l",4,7],398],[200,172,["o",7,7],2449],
  [200,172,["s",6,7],171],[200,175,["o",7,7],2449],
  [200,175,["s",6,7],171],[201,200,["l",2,401],200],
  [204,195,["o+",14,2],2667],[205,182,["l",4,9],818],
  [205,204,["l",2,409],204],[210,209,["l",2,419],209],
  [211,106,["l",2,211],105],[211,210,["l",2,421],210],
  [216,215,["l",2,431],215],[217,208,["l",3,25],649],
  [217,216,["l",2,433],216],[220,219,["l",2,439],219],
  [222,221,["l",2,443],221],[223,112,["l",2,223],111],
  [225,224,["l",2,449],224],[227,114,["l",2,227],113],
  [229,115,["l",2,229],114],[229,228,["l",2,457],228],
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  [1867,1866,["l",2,3733],1866],
  [1870,1869,["l",2,3739],1869],
  [1871,936,["l",2,1871],935],[1873,937,["l",2,1873],936],
  [1877,939,["l",2,1877],938],[1878,1638,["s",10,5],1562],
  [1878,1860,["s",10,5],1562],[1879,940,["l",2,1879],939],
  [1881,1880,["l",2,3761],1880],
  [1884,1883,["l",2,3767],1883],
  [1885,1884,["l",2,3769],1884],
  [1889,945,["l",2,1889],944],
  [1890,1889,["l",2,3779],1889],
  [1891,1861,["s",4,61],3721],[1892,925,["s",4,43],1849],
  [1892,946,["s",4,43],1849],[1892,1806,["s",4,43],1849],
  [1892,1848,["u",3,43],1849],
  [1897,1896,["l",2,3793],1896],
  [1899,1898,["l",2,3797],1898],
  [1901,951,["l",2,1901],950],
  [1902,1901,["l",2,3803],1901],
  [1907,954,["l",2,1907],953],
  [1911,1910,["l",2,3821],1910],
  [1912,1911,["l",2,3823],1911],
  [1913,957,["l",2,1913],956],
  [1917,1916,["l",2,3833],1916],
  [1924,1923,["l",2,3847],1923],
  [1926,1925,["l",2,3851],1925],
  [1927,1926,["l",2,3853],1926],
  [1931,966,["l",2,1931],965],
  [1932,1931,["l",2,3863],1931],
  [1933,967,["l",2,1933],966],
  [1939,1938,["l",2,3877],1938],
  [1941,1940,["l",2,3881],1940],
  [1945,1944,["l",2,3889],1944],
  [1949,975,["l",2,1949],974],[1951,976,["l",2,1951],975],
  [1953,1562,["l",6,5],3904],[1954,1953,["l",2,3907],1953]
    ,[1956,1955,["l",2,3911],1955],
  [1959,1958,["l",2,3917],1958],
  [1960,1959,["l",2,3919],1959],
  [1962,1961,["l",2,3923],1961],
  [1965,1964,["l",2,3929],1964],
  [1966,1965,["l",2,3931],1965],
  [1972,1971,["l",2,3943],1971],
  [1973,987,["l",2,1973],986],
  [1974,1973,["l",2,3947],1973],
  [1979,990,["l",2,1979],989],
  [1984,1983,["l",2,3967],1983],
  [1987,994,["l",2,1987],993],[1993,997,["l",2,1993],996],
  [1995,1994,["l",2,3989],1994],
  [1997,999,["l",2,1997],998],[1999,1000,["l",2,1999],999]
    ,[2001,2000,["l",2,4001],2000],
  [2002,2001,["l",2,4003],2001],
  [2003,1002,["l",2,2003],1001],
  [2004,2003,["l",2,4007],2003],
  [2007,2006,["l",2,4013],2006],
  [2010,2009,["l",2,4019],2009],
  [2011,1006,["l",2,2011],1005],
  [2011,2010,["l",2,4021],2010],
  [2014,2013,["l",2,4027],2013],
  [2017,1009,["l",2,2017],1008],
  [2025,2024,["l",2,4049],2024],
  [2026,2025,["l",2,4051],2025],
  [2027,1014,["l",2,2027],1013],
  [2029,1015,["l",2,2029],1014],
  [2029,2028,["l",2,4057],2028],
  [2037,2036,["l",2,4073],2036],
  [2039,1020,["l",2,2039],1019],
  [2040,2039,["l",2,4079],2039],
  [2046,2045,["l",2,4091],2045],
  [2047,1953,["l",11,2],2048],
  [2047,2046,["l",2,4093],2046],
  [2049,2047,["l",2,2048],1024],
  [2050,2049,["l",2,4099],2049],
  [2053,1027,["l",2,2053],1026],
  [2056,2055,["l",2,4111],2055],
  [2063,1032,["l",2,2063],1031],
  [2064,2063,["l",2,4127],2063],
  [2065,2064,["l",2,4129],2064],
  [2067,2066,["l",2,4133],2066],
  [2069,1035,["l",2,2069],1034],
  [2070,2069,["l",2,4139],2069],
  [2077,2076,["l",2,4153],2076],
  [2079,2078,["l",2,4157],2078],
  [2080,2079,["l",2,4159],2079],
  [2081,1041,["l",2,2081],1040],
  [2083,1042,["l",2,2083],1041],
  [2087,1044,["l",2,2087],1043],
  [2089,1045,["l",2,2089],1044],
  [2089,2088,["l",2,4177],2088],
  [2099,1050,["l",2,2099],1049],
  [2101,2100,["l",2,4201],2100],
  [2106,2105,["l",2,4211],2105],
  [2109,2108,["l",2,4217],2108],
  [2110,2109,["l",2,4219],2109],
  [2111,1056,["l",2,2111],1055],
  [2113,1057,["l",2,2113],1056],
  [2115,2114,["l",2,4229],2114],
  [2116,2115,["l",2,4231],2115],
  [2121,2120,["l",2,4241],2120],
  [2122,2121,["l",2,4243],2121],
  [2127,2126,["l",2,4253],2126],
  [2129,1065,["l",2,2129],1064],
  [2130,2129,["l",2,4259],2129],
  [2131,1066,["l",2,2131],1065],
  [2131,2130,["l",2,4261],2130],
  [2136,2135,["l",2,4271],2135],
  [2137,1069,["l",2,2137],1068],
  [2137,2136,["l",2,4273],2136],
  [2141,1071,["l",2,2141],1070],
  [2142,2141,["l",2,4283],2141],
  [2143,1072,["l",2,2143],1071],
  [2145,2144,["l",2,4289],2144],
  [2149,2148,["l",2,4297],2148],
  [2153,1077,["l",2,2153],1076],
  [2161,1081,["l",2,2161],1080],
  [2162,1105,["s",4,47],2209],[2162,1128,["s",4,47],2209],
  [2164,2163,["l",2,4327],2163],
  [2169,2168,["l",2,4337],2168],
  [2170,2169,["l",2,4339],2169],
  [2175,2174,["l",2,4349],2174],
  [2178,1460,["s",14,3],1093],[2178,1476,["s",14,3],1093],
  [2179,1090,["l",2,2179],1089],
  [2179,2178,["l",2,4357],2178],
  [2182,2181,["l",2,4363],2181],
  [2184,1190,["s",6,13],1098],[2184,1460,["s",14,3],1093],
  [2184,1476,["s",14,3],1093],[2184,2178,["s",14,3],1093],
  [2187,2186,["l",2,4373],2186],
  [2190,1460,["s",14,3],1093],[2190,1476,["s",14,3],1093],
  [2190,2178,["s",14,3],1093],[2190,2184,["s",14,3],1093],
  [2196,1460,["s",14,3],1093],[2196,1476,["s",14,3],1093],
  [2196,2178,["s",14,3],1093],[2196,2184,["s",14,3],1093],
  [2196,2190,["s",14,3],1093],
  [2196,2195,["l",2,4391],2195],
  [2199,2198,["l",2,4397],2198],
  [2203,1102,["l",2,2203],1101],
  [2205,2204,["l",2,4409],2204],
  [2207,1104,["l",2,2207],1103],
  [2210,1190,["s",6,13],1098],[2210,2184,["s",6,13],1098],
  [2211,2210,["l",2,4421],2210],
  [2212,2211,["l",2,4423],2211],
  [2213,1107,["l",2,2213],1106],
  [2221,1111,["l",2,2221],1110],
  [2221,2220,["l",2,4441],2220],
  [2224,2223,["l",2,4447],2223],
  [2226,2225,["l",2,4451],2225],
  [2229,2228,["l",2,4457],2228],
  [2232,2231,["l",2,4463],2231],
  [2237,1119,["l",2,2237],1118],
  [2239,1120,["l",2,2239],1119],
  [2241,2240,["l",2,4481],2240],
  [2242,2241,["l",2,4483],2241],
  [2243,1122,["l",2,2243],1121],
  [2245,2244,["l",2,4489],2244],
  [2245,2244,["s",4,67],4489],
  [2247,2246,["l",2,4493],2246],
  [2251,1126,["l",2,2251],1125],
  [2254,2253,["l",2,4507],2253],
  [2256,1105,["s",4,47],2209],[2256,1128,["s",4,47],2209],
  [2256,2162,["s",4,47],2209],[2257,2208,["l",3,47],2255],
  [2257,2256,["l",2,4513],2256],
  [2259,2258,["l",2,4517],2258],
  [2260,2259,["l",2,4519],2259],
  [2262,2261,["l",2,4523],2261],
  [2267,1134,["l",2,2267],1133],
  [2269,1135,["l",2,2269],1134],
  [2273,1137,["l",2,2273],1136],
  [2274,2273,["l",2,4547],2273],
  [2275,2274,["l",2,4549],2274],
  [2278,2245,["s",4,67],4489],
  [2281,1141,["l",2,2281],1140],
  [2281,2280,["l",2,4561],2280],
  [2284,2283,["l",2,4567],2283],
  [2287,1144,["l",2,2287],1143],
  [2292,2291,["l",2,4583],2291],
  [2293,1147,["l",2,2293],1146],
  [2296,2295,["l",2,4591],2295],
  [2297,1149,["l",2,2297],1148],
  [2299,2298,["l",2,4597],2298],
  [2302,2301,["l",2,4603],2301],
  [2309,1155,["l",2,2309],1154],
  [2311,1156,["l",2,2311],1155],
  [2311,2310,["l",2,4621],2310],
  [2319,2318,["l",2,4637],2318],
  [2320,2319,["l",2,4639],2319],
  [2322,2321,["l",2,4643],2321],
  [2325,2324,["l",2,4649],2324],
  [2326,2325,["l",2,4651],2325],
  [2329,2328,["l",2,4657],2328],
  [2332,2331,["l",2,4663],2331],
  [2333,1167,["l",2,2333],1166],
  [2337,2336,["l",2,4673],2336],
  [2339,1170,["l",2,2339],1169],
  [2340,2339,["l",2,4679],2339],
  [2341,1171,["l",2,2341],1170],
  [2346,2345,["l",2,4691],2345],
  [2347,1174,["l",2,2347],1173],
  [2351,1176,["l",2,2351],1175],
  [2352,2351,["l",2,4703],2351],
  [2357,1179,["l",2,2357],1178],
  [2361,2360,["l",2,4721],2360],
  [2362,2361,["l",2,4723],2361],
  [2365,2364,["l",2,4729],2364],
  [2367,2366,["l",2,4733],2366],
  [2371,1186,["l",2,2371],1185],
  [2376,2375,["l",2,4751],2375],
  [2377,1189,["l",2,2377],1188],
  [2380,2379,["l",2,4759],2379],
  [2381,1191,["l",2,2381],1190],
  [2383,1192,["l",2,2383],1191],
  [2389,1195,["l",2,2389],1194],
  [2392,2391,["l",2,4783],2391],
  [2393,1197,["l",2,2393],1196],[2394,1368,["s",8,7],1200]
    ,[2394,1400,["s",8,7],1200],
  [2394,2393,["l",2,4787],2393],
  [2395,2394,["l",2,4789],2394],
  [2397,2396,["l",2,4793],2396],
  [2399,1200,["l",2,2399],1199],[2400,2101,["u",5,7],2101]
    ,[2400,2353,["u",3,49],2401],
  [2400,2399,["l",2,4799],2399],
  [2401,2400,["l",2,4801],2400],
  [2407,2406,["l",2,4813],2406],[2408,1368,["s",8,7],1200]
    ,[2408,1400,["s",8,7],1200],
  [2408,2394,["s",8,7],1200],[2408,2400,["u",5,7],2101],
  [2409,2408,["l",2,4817],2408],
  [2411,1206,["l",2,2411],1205],
  [2416,2415,["l",2,4831],2415],
  [2417,1209,["l",2,2417],1208],
  [2423,1212,["l",2,2423],1211],
  [2431,2430,["l",2,4861],2430],
  [2436,2435,["l",2,4871],2435],
  [2437,1219,["l",2,2437],1218],
  [2439,2438,["l",2,4877],2438],
  [2441,1221,["l",2,2441],1220],
  [2445,2444,["l",2,4889],2444],
  [2447,1224,["l",2,2447],1223],
  [2452,2451,["l",2,4903],2451],
  [2455,2454,["l",2,4909],2454],
  [2457,2320,["u",4,17],4640],[2457,2448,["u",4,17],4640],
  [2457,2456,["l",2,4913],2456],
  [2459,1230,["l",2,2459],1229],
  [2460,2459,["l",2,4919],2459],
  [2466,2465,["l",2,4931],2465],
  [2467,1234,["l",2,2467],1233],
  [2467,2466,["l",2,4933],2466],
  [2469,2468,["l",2,4937],2468],
  [2472,2471,["l",2,4943],2471],
  [2473,1237,["l",2,2473],1236],
  [2476,2475,["l",2,4951],2475],
  [2477,1239,["l",2,2477],1238],
  [2479,2478,["l",2,4957],2478],
  [2484,2483,["l",2,4967],2483],
  [2485,2484,["l",2,4969],2484],
  [2487,2486,["l",2,4973],2486],
  [2494,2493,["l",2,4987],2493],
  [2497,2496,["l",2,4993],2496],
  [2500,2499,["l",2,4999],2499],
  [2502,2501,["l",2,5003],2501],
  [2503,1252,["l",2,2503],1251],
  [2505,2504,["l",2,5009],2504],
  [2506,2505,["l",2,5011],2505],
  [2511,2510,["l",2,5021],2510],
  [2512,2511,["l",2,5023],2511],
  [2520,2519,["l",2,5039],2519],
  [2521,1261,["l",2,2521],1260],
  [2521,2520,["l",2,5041],2520],
  [2526,2525,["l",2,5051],2525],
  [2530,2529,["l",2,5059],2529],
  [2531,1266,["l",2,2531],1265],
  [2539,1270,["l",2,2539],1269],
  [2539,2538,["l",2,5077],2538],
  [2541,2540,["l",2,5081],2540],
  [2543,1272,["l",2,2543],1271],
  [2544,2543,["l",2,5087],2543],
  [2549,1275,["l",2,2549],1274],
  [2550,2549,["l",2,5099],2549],
  [2551,1276,["l",2,2551],1275],
  [2551,2550,["l",2,5101],2550],
  [2554,2553,["l",2,5107],2553],
  [2557,1279,["l",2,2557],1278],
  [2557,2556,["l",2,5113],2556],
  [2560,2559,["l",2,5119],2559],
  [2574,2573,["l",2,5147],2573],
  [2577,2576,["l",2,5153],2576],
  [2579,1290,["l",2,2579],1289],
  [2584,2583,["l",2,5167],2583],
  [2586,2585,["l",2,5171],2585],
  [2590,2589,["l",2,5179],2589],
  [2591,1296,["l",2,2591],1295],
  [2593,1297,["l",2,2593],1296],
  [2595,2594,["l",2,5189],2594],
  [2599,2598,["l",2,5197],2598],
  [2605,2604,["l",2,5209],2604],
  [2609,1305,["l",2,2609],1304],
  [2610,2457,["s",6,17],2456],[2610,2465,["s",6,17],2456],
  [2614,2613,["l",2,5227],2613],
  [2616,2615,["l",2,5231],2615],
  [2617,1309,["l",2,2617],1308],
  [2617,2616,["l",2,5233],2616],
  [2619,2618,["l",2,5237],2618],
  [2621,1311,["l",2,2621],1310],
  [2631,2630,["l",2,5261],2630],
  [2633,1317,["l",2,2633],1316],
  [2637,2636,["l",2,5273],2636],
  [2640,2639,["l",2,5279],2639],
  [2641,2640,["l",2,5281],2640],
  [2647,1324,["l",2,2647],1323],
  [2649,2648,["l",2,5297],2648],
  [2652,2651,["l",2,5303],2651],
  [2655,2654,["l",2,5309],2654],
  [2657,1329,["l",2,2657],1328],
  [2659,1330,["l",2,2659],1329],
  [2662,2661,["l",2,5323],2661],
  [2663,1332,["l",2,2663],1331],
  [2665,2664,["l",2,5329],2664],
  [2667,2666,["l",2,5333],2666],
  [2671,1336,["l",2,2671],1335],
  [2674,2673,["l",2,5347],2673],
  [2676,2675,["l",2,5351],2675],
  [2677,1339,["l",2,2677],1338],
  [2683,1342,["l",2,2683],1341],
  [2687,1344,["l",2,2687],1343],
  [2689,1345,["l",2,2689],1344],
  [2691,2690,["l",2,5381],2690],
  [2693,1347,["l",2,2693],1346],
  [2694,2693,["l",2,5387],2693],
  [2697,2696,["l",2,5393],2696],
  [2699,1350,["l",2,2699],1349],
  [2700,2699,["l",2,5399],2699],
  [2704,2703,["l",2,5407],2703],
  [2707,1354,["l",2,2707],1353],
  [2707,2706,["l",2,5413],2706],
  [2709,2708,["l",2,5417],2708],
  [2710,2709,["l",2,5419],2709],
  [2711,1356,["l",2,2711],1355],
  [2713,1357,["l",2,2713],1356],
  [2716,2715,["l",2,5431],2715],
  [2719,1360,["l",2,2719],1359],
  [2719,2718,["l",2,5437],2718],
  [2721,2720,["l",2,5441],2720],
  [2722,2721,["l",2,5443],2721],
  [2725,2724,["l",2,5449],2724],
  [2729,1365,["l",2,2729],1364],
  [2731,1366,["l",2,2731],1365],
  [2736,2735,["l",2,5471],2735],
  [2739,2738,["l",2,5477],2738],
  [2740,2739,["l",2,5479],2739],
  [2741,1371,["l",2,2741],1370],
  [2742,2741,["l",2,5483],2741],
  [2749,1375,["l",2,2749],1374],
  [2751,2750,["l",2,5501],2750],
  [2752,2751,["l",2,5503],2751],
  [2753,1377,["l",2,2753],1376],
  [2754,2753,["l",2,5507],2753],
  [2756,1405,["s",4,53],2809],[2756,1431,["s",4,53],2809],
  [2760,2759,["l",2,5519],2759],
  [2761,2760,["l",2,5521],2760],
  [2764,2763,["l",2,5527],2763],
  [2766,2765,["l",2,5531],2765],
  [2767,1384,["l",2,2767],1383],
  [2777,1389,["l",2,2777],1388],
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  [7541,3771,["l",2,7541],3770],
  [7547,3774,["l",2,7547],3773],
  [7549,3775,["l",2,7549],3774],
  [7559,3780,["l",2,7559],3779],
  [7561,3781,["l",2,7561],3780],
  [7573,3787,["l",2,7573],3786],
  [7577,3789,["l",2,7577],3788],
  [7583,3792,["l",2,7583],3791],
  [7589,3795,["l",2,7589],3794],
  [7591,3796,["l",2,7591],3795],
  [7603,3802,["l",2,7603],3801],
  [7607,3804,["l",2,7607],3803],
  [7621,3811,["l",2,7621],3810],
  [7639,3820,["l",2,7639],3819],
  [7643,3822,["l",2,7643],3821],
  [7649,3825,["l",2,7649],3824],
  [7669,3835,["l",2,7669],3834],
  [7673,3837,["l",2,7673],3836],
  [7681,3841,["l",2,7681],3840],
  [7687,3844,["l",2,7687],3843],
  [7691,3846,["l",2,7691],3845],
  [7699,3850,["l",2,7699],3849],
  [7703,3852,["l",2,7703],3851],
  [7717,3859,["l",2,7717],3858],
  [7723,3862,["l",2,7723],3861],
  [7727,3864,["l",2,7727],3863],
  [7741,3871,["l",2,7741],3870],
  [7753,3877,["l",2,7753],3876],
  [7757,3879,["l",2,7757],3878],
  [7759,3880,["l",2,7759],3879],
  [7789,3895,["l",2,7789],3894],
  [7793,3897,["l",2,7793],3896],
  [7817,3909,["l",2,7817],3908],
  [7823,3912,["l",2,7823],3911],
  [7829,3915,["l",2,7829],3914],
  [7841,3921,["l",2,7841],3920],
  [7853,3927,["l",2,7853],3926],
  [7867,3934,["l",2,7867],3933],
  [7873,3937,["l",2,7873],3936],
  [7877,3939,["l",2,7877],3938],
  [7879,3940,["l",2,7879],3939],
  [7883,3942,["l",2,7883],3941],
  [7901,3951,["l",2,7901],3950],
  [7907,3954,["l",2,7907],3953],
  [7919,3960,["l",2,7919],3959],
  [7927,3964,["l",2,7927],3963],
  [7933,3967,["l",2,7933],3966],
  [7937,3969,["l",2,7937],3968],
  [7949,3975,["l",2,7949],3974],
  [7951,3976,["l",2,7951],3975],
  [7963,3982,["l",2,7963],3981],
  [7993,3997,["l",2,7993],3996],
  [8009,4005,["l",2,8009],4004],
  [8011,4006,["l",2,8011],4005],
  [8017,4009,["l",2,8017],4008],
  [8039,4020,["l",2,8039],4019],
  [8053,4027,["l",2,8053],4026],
  [8059,4030,["l",2,8059],4029],
  [8069,4035,["l",2,8069],4034],
  [8081,4041,["l",2,8081],4040],
  [8087,4044,["l",2,8087],4043],
  [8089,4045,["l",2,8089],4044],
  [8093,4047,["l",2,8093],4046],
  [8101,4051,["l",2,8101],4050],
  [8111,4056,["l",2,8111],4055],
  [8117,4059,["l",2,8117],4058],
  [8123,4062,["l",2,8123],4061],
  [8147,4074,["l",2,8147],4073],
  [8161,4081,["l",2,8161],4080],
  [8167,4084,["l",2,8167],4083],
  [8171,4086,["l",2,8171],4085],
  [8179,4090,["l",2,8179],4089],
  [8191,4096,["l",2,8191],4095],
  [8193,8191,["l",2,8192],4096],
  [8209,4105,["l",2,8209],4104],
  [8219,4110,["l",2,8219],4109],
  [8221,4111,["l",2,8221],4110],
  [8231,4116,["l",2,8231],4115],
  [8233,4117,["l",2,8233],4116],
  [8237,4119,["l",2,8237],4118],
  [8243,4122,["l",2,8243],4121],
  [8263,4132,["l",2,8263],4131],
  [8269,4135,["l",2,8269],4134],
  [8273,4137,["l",2,8273],4136],
  [8287,4144,["l",2,8287],4143],
  [8291,4146,["l",2,8291],4145],
  [8293,4147,["l",2,8293],4146],
  [8297,4149,["l",2,8297],4148],
  [8311,4156,["l",2,8311],4155],
  [8317,4159,["l",2,8317],4158],
  [8329,4165,["l",2,8329],4164],
  [8353,4177,["l",2,8353],4176],
  [8363,4182,["l",2,8363],4181],
  [8369,4185,["l",2,8369],4184],
  [8377,4189,["l",2,8377],4188],
  [8387,4194,["l",2,8387],4193],
  [8389,4195,["l",2,8389],4194],
  [8419,4210,["l",2,8419],4209],
  [8423,4212,["l",2,8423],4211],
  [8429,4215,["l",2,8429],4214],
  [8431,4216,["l",2,8431],4215],
  [8443,4222,["l",2,8443],4221],
  [8447,4224,["l",2,8447],4223],
  [8461,4231,["l",2,8461],4230],
  [8467,4234,["l",2,8467],4233],
  [8501,4251,["l",2,8501],4250],
  [8513,4257,["l",2,8513],4256],
  [8521,4261,["l",2,8521],4260],
  [8527,4264,["l",2,8527],4263],
  [8537,4269,["l",2,8537],4268],
  [8539,4270,["l",2,8539],4269],
  [8543,4272,["l",2,8543],4271],
  [8563,4282,["l",2,8563],4281],
  [8573,4287,["l",2,8573],4286],
  [8581,4291,["l",2,8581],4290],
  [8597,4299,["l",2,8597],4298],
  [8599,4300,["l",2,8599],4299],
  [8609,4305,["l",2,8609],4304],
  [8623,4312,["l",2,8623],4311],
  [8627,4314,["l",2,8627],4313],
  [8629,4315,["l",2,8629],4314],
  [8641,4321,["l",2,8641],4320],
  [8647,4324,["l",2,8647],4323],
  [8663,4332,["l",2,8663],4331],
  [8669,4335,["l",2,8669],4334],
  [8677,4339,["l",2,8677],4338],
  [8681,4341,["l",2,8681],4340],
  [8689,4345,["l",2,8689],4344],
  [8693,4347,["l",2,8693],4346],
  [8699,4350,["l",2,8699],4349],
  [8707,4354,["l",2,8707],4353],
  [8713,4357,["l",2,8713],4356],
  [8719,4360,["l",2,8719],4359],
  [8731,4366,["l",2,8731],4365],
  [8737,4369,["l",2,8737],4368],
  [8741,4371,["l",2,8741],4370],
  [8747,4374,["l",2,8747],4373],
  [8753,4377,["l",2,8753],4376],
  [8761,4381,["l",2,8761],4380],
  [8779,4390,["l",2,8779],4389],
  [8783,4392,["l",2,8783],4391],
  [8803,4402,["l",2,8803],4401],
  [8807,4404,["l",2,8807],4403],
  [8819,4410,["l",2,8819],4409],
  [8821,4411,["l",2,8821],4410],
  [8831,4416,["l",2,8831],4415],
  [8837,4419,["l",2,8837],4418],
  [8839,4420,["l",2,8839],4419],
  [8849,4425,["l",2,8849],4424],
  [8861,4431,["l",2,8861],4430],
  [8863,4432,["l",2,8863],4431],
  [8867,4434,["l",2,8867],4433],
  [8887,4444,["l",2,8887],4443],
  [8893,4447,["l",2,8893],4446],
  [8923,4462,["l",2,8923],4461],
  [8929,4465,["l",2,8929],4464],
  [8933,4467,["l",2,8933],4466],
  [8941,4471,["l",2,8941],4470],
  [8951,4476,["l",2,8951],4475],
  [8963,4482,["l",2,8963],4481],
  [8969,4485,["l",2,8969],4484],
  [8971,4486,["l",2,8971],4485],
  [8999,4500,["l",2,8999],4499],
  [9001,4501,["l",2,9001],4500],
  [9007,4504,["l",2,9007],4503],
  [9011,4506,["l",2,9011],4505],
  [9013,4507,["l",2,9013],4506],
  [9029,4515,["l",2,9029],4514],
  [9041,4521,["l",2,9041],4520],
  [9043,4522,["l",2,9043],4521],
  [9049,4525,["l",2,9049],4524],
  [9059,4530,["l",2,9059],4529],
  [9067,4534,["l",2,9067],4533],
  [9091,4546,["l",2,9091],4545],
  [9103,4552,["l",2,9103],4551],
  [9109,4555,["l",2,9109],4554],
  [9127,4564,["l",2,9127],4563],
  [9133,4567,["l",2,9133],4566],
  [9137,4569,["l",2,9137],4568],
  [9151,4576,["l",2,9151],4575],
  [9157,4579,["l",2,9157],4578],
  [9161,4581,["l",2,9161],4580],
  [9173,4587,["l",2,9173],4586],
  [9181,4591,["l",2,9181],4590],
  [9187,4594,["l",2,9187],4593],
  [9199,4600,["l",2,9199],4599],
  [9203,4602,["l",2,9203],4601],
  [9209,4605,["l",2,9209],4604],
  [9221,4611,["l",2,9221],4610],
  [9227,4614,["l",2,9227],4613],
  [9239,4620,["l",2,9239],4619],
  [9241,4621,["l",2,9241],4620],
  [9257,4629,["l",2,9257],4628],
  [9277,4639,["l",2,9277],4638],
  [9281,4641,["l",2,9281],4640],
  [9283,4642,["l",2,9283],4641],
  [9293,4647,["l",2,9293],4646],
  [9311,4656,["l",2,9311],4655],
  [9319,4660,["l",2,9319],4659],
  [9323,4662,["l",2,9323],4661],
  [9337,4669,["l",2,9337],4668],
  [9341,4671,["l",2,9341],4670],
  [9343,4672,["l",2,9343],4671],
  [9349,4675,["l",2,9349],4674],
  [9371,4686,["l",2,9371],4685],
  [9377,4689,["l",2,9377],4688],
  [9391,4696,["l",2,9391],4695],
  [9397,4699,["l",2,9397],4698],
  [9403,4702,["l",2,9403],4701],
  [9413,4707,["l",2,9413],4706],
  [9419,4710,["l",2,9419],4709],
  [9421,4711,["l",2,9421],4710],
  [9431,4716,["l",2,9431],4715],
  [9433,4717,["l",2,9433],4716],
  [9437,4719,["l",2,9437],4718],
  [9439,4720,["l",2,9439],4719],
  [9461,4731,["l",2,9461],4730],
  [9463,4732,["l",2,9463],4731],
  [9467,4734,["l",2,9467],4733],
  [9473,4737,["l",2,9473],4736],
  [9479,4740,["l",2,9479],4739],
  [9491,4746,["l",2,9491],4745],
  [9497,4749,["l",2,9497],4748],
  [9511,4756,["l",2,9511],4755],
  [9521,4761,["l",2,9521],4760],
  [9533,4767,["l",2,9533],4766],
  [9539,4770,["l",2,9539],4769],
  [9547,4774,["l",2,9547],4773],
  [9551,4776,["l",2,9551],4775],
  [9587,4794,["l",2,9587],4793],
  [9601,4801,["l",2,9601],4800],
  [9613,4807,["l",2,9613],4806],
  [9619,4810,["l",2,9619],4809],
  [9623,4812,["l",2,9623],4811],
  [9629,4815,["l",2,9629],4814],
  [9631,4816,["l",2,9631],4815],
  [9643,4822,["l",2,9643],4821],
  [9649,4825,["l",2,9649],4824],
  [9661,4831,["l",2,9661],4830],
  [9677,4839,["l",2,9677],4838],
  [9679,4840,["l",2,9679],4839],
  [9689,4845,["l",2,9689],4844],
  [9697,4849,["l",2,9697],4848],
  [9719,4860,["l",2,9719],4859],
  [9721,4861,["l",2,9721],4860],
  [9733,4867,["l",2,9733],4866],
  [9739,4870,["l",2,9739],4869],
  [9743,4872,["l",2,9743],4871],
  [9749,4875,["l",2,9749],4874],
  [9767,4884,["l",2,9767],4883],
  [9769,4885,["l",2,9769],4884],
  [9781,4891,["l",2,9781],4890],
  [9787,4894,["l",2,9787],4893],
  [9791,4896,["l",2,9791],4895],
  [9803,4902,["l",2,9803],4901],
  [9811,4906,["l",2,9811],4905],
  [9817,4909,["l",2,9817],4908],
  [9829,4915,["l",2,9829],4914],
  [9833,4917,["l",2,9833],4916],
  [9839,4920,["l",2,9839],4919],
  [9851,4926,["l",2,9851],4925],
  [9857,4929,["l",2,9857],4928],
  [9859,4930,["l",2,9859],4929],
  [9871,4936,["l",2,9871],4935],
  [9883,4942,["l",2,9883],4941],
  [9887,4944,["l",2,9887],4943],
  [9901,4951,["l",2,9901],4950],
  [9907,4954,["l",2,9907],4953],
  [9923,4962,["l",2,9923],4961],
  [9929,4965,["l",2,9929],4964],
  [9931,4966,["l",2,9931],4965],
  [9941,4971,["l",2,9941],4970],
  [9949,4975,["l",2,9949],4974],
  [9967,4984,["l",2,9967],4983],
  [9973,4987,["l",2,9973],4986] ];

RECOG.ListOfGroupsCrossCharRepsByBound :=
function(dimbound)
    local list, q, n;

    list:=[];
    for q in [4..2*dimbound+1] do
      if IsPrimePowerInt(q) then
        Add(list, ["l",2,q]);
      fi;
    od;

    for n in [3..LogInt(dimbound,2)] do
      for q in [2..RootInt(dimbound,2)] do
        if IsPrimePowerInt(q) and (q^n-q)/(q-1)-1 <= dimbound then
          Add(list, ["l",n,q]);
        fi;
      od;
    od;

    for n in [2..LogInt(dimbound,2)] do
      for q in [2..RootInt(dimbound,2)] do
        if IsPrimePowerInt(q) and (q mod 2 = 1) and (q^n-1)/2 <= dimbound then
          Add(list, ["s",2*n,q]);
        fi;
        if IsPrimePowerInt(q) and (q mod 2 = 0) and
            (q^n-1)*(q^n-q)/(2*(q+1)) <= dimbound then
          Add(list, ["s",2*n,q]);
        fi;
      od;
    od;

    for n in [3..LogInt(dimbound,2)] do
      for q in [2..RootInt(dimbound,2)] do
        if IsPrimePowerInt(q) and  (q^n-1)/(q+1) <= dimbound and
             [n,q]<>[3,2] then
          Add(list, ["u",n,q]);
        fi;
      od;
    od;

    for n in [4..LogInt(dimbound,2)] do
      if (2^n-1)*(2^(n-1)-1)/3 <= dimbound then
        Add(list, ["o+",2*n,2]);
      fi;
      if (3^n-1)*(3^(n-1)-1)/8 <= dimbound then
        Add(list, ["o+",2*n,3]);
      fi;
      for q in [4..RootInt(dimbound,2)] do
        if IsPrimePowerInt(q) and (q^n-1)*(q^(n-1)+q)/(q^2-1) <= dimbound then
          Add(list, ["o+",2*n,q]);
        fi;
      od;
    od;

    for n in [4..LogInt(dimbound,2)] do
      for q in [2..RootInt(dimbound,2)] do
        if IsPrimePowerInt(q) and (q^n+1)*(q^(n-1)-q)/(q^2-1)-1 <= dimbound then
          Add(list, ["o-",2*n,q]);
        fi;
      od;
    od;

    for n in [3..LogInt(dimbound,2)] do
      if (3^n-1)*(3^n-3)/8 <= dimbound then
        Add(list, ["o",2*n+1,3]);
      fi;
      for q in [5..RootInt(dimbound,2)] do
        if IsPrimePowerInt(q) and (q mod 2 = 1) and
            (q^(2*n)-1)/(q^2-1)-2 <= dimbound then
          Add(list, ["o",2*n+1,q]);
        fi;
      od;
    od;

    for n in [2..LogInt(dimbound,2)] do
      if (n mod 2 = 1) and (2^n-1)*RootInt(2^n/2) <= dimbound then
        Add(list, ["2B2",2^n]);
      fi;
    od;

    for n in [2..LogInt(dimbound,2)] do
      if (n mod 2 = 1) and (3^n-1)*3^n <= dimbound then
        Add(list, ["2G2",3^n]);
      fi;
    od;

    for q in [3..RootInt(dimbound,2)] do
      if IsPrimePowerInt(q) and (q mod 3 <> 0) and q^3-1 <= dimbound then
        Add(list, ["G2",q]);
      fi;
      if IsPrimePowerInt(q) and (q mod 3 = 0) and q^4+q^2 <= dimbound then
        Add(list, ["G2",q]);
      fi;
    od;

    for q in [2..RootInt(dimbound,2)] do
      if IsPrimePowerInt(q) and q^5-q^3+q-1 <= dimbound then
        Add(list, ["3D4",q]);
      fi;
    od;

    for n in [1..LogInt(dimbound,2)] do
      if (n mod 2 = 1) and (2^(5*n)-2^(4*n))*RootInt(2^n/2) <= dimbound then
        Add(list, ["2F4",2^n]);
      fi;
    od;

    for q in [2..RootInt(dimbound,2)] do
      if IsPrimePowerInt(q) and (q mod 2 = 1) and q^8+q^4-2 <= dimbound then
        Add(list, ["F4",q]);
      fi;
      if IsPrimePowerInt(q) and (q mod 2 = 0) and
         (q^3-1)*(q^8-q^7)/2 <= dimbound then
        Add(list, ["F4",q]);
      fi;
    od;

    for q in [2..RootInt(dimbound,2)] do
      if IsPrimePowerInt(q) and q^11-q^9 <= dimbound then
        Add(list, ["2E6",q]);
        Add(list, ["E6",q]);
      fi;
      if IsPrimePowerInt(q) and q^17-q^15 <= dimbound then
        Add(list, ["E7",q]);
      fi;
      if IsPrimePowerInt(q) and q^29-q^27 <= dimbound then
        Add(list, ["E8",q]);
      fi;
    od;

    # Note that the following are lower bounds for faithful *projective*
    # representations, because we recognise simple groups in their
    # projective representations!
    if dimbound >= 5 then Add(list,["M11"]); fi;
    if dimbound >= 6 then Add(list,["M12"]); fi;
    if dimbound >= 6 then Add(list,["M22"]); fi;
    if dimbound >= 11 then Add(list,["M23"]); fi;
    if dimbound >= 11 then Add(list,["M24"]); fi;
    if dimbound >= 20 then Add(list,["HS"]); fi;
    if dimbound >= 21 then Add(list,["McL"]); fi;
    if dimbound >= 22 then Add(list,["Co3"]); fi;
    if dimbound >= 22 then Add(list,["Co2"]); fi;
    if dimbound >= 24 then Add(list,["Co1"]); fi;
    if dimbound >= 6 then Add(list,["J2"]); fi;
    if dimbound >= 12 then Add(list,["Suz"]); fi;
    if dimbound >= 27 then Add(list,["Fi22"]); fi;
    if dimbound >= 253 then Add(list,["Fi23"]); fi;
    if dimbound >= 781 then Add(list,["Fi24'"]); fi;
    if dimbound >= 50 then Add(list,["He"]); fi;
    if dimbound >= 132 then Add(list,["HN"]); fi;
    if dimbound >= 248 then Add(list,["Th"]); fi;
    if dimbound >= 7 then Add(list,["J1"]); fi;
    if dimbound >= 9 then Add(list,["J3"]); fi;
    if dimbound >= 28 then Add(list,["Ru"]); fi;
    if dimbound >= 45 then Add(list,["O'N"]); fi;
    if dimbound >= 111 then Add(list,["Ly"]); fi;
    if dimbound >= 112 then Add(list,["J4"]); fi;
    if dimbound >= 4370 then Add(list,["B"]); fi;
    if dimbound >= 196882 then Add(list,["M"]); fi;

    return list;

end;

# The following function was used to convert
#  RECOG.TableOfTwoLargestGroupElementOrders
# into
#  RECOG.TableOfTwoLargestGroupElementOrdersWithDegreeBound:
# Then the following is used:
#   PrintTo("tmp.g",
#           "RECOG.TableOfTwoLargestGroupElementOrdersWithDegreeBound := \n",
#           RECOG.TableOfTwoLargestGroupElementOrders,";\n");
# Then copy the output "tmp.g" to this file.

RECOG.AddInformationAboutDegree := function()
  local i,j,l,ll,new,t;
  l := [];
  t := RECOG.TableOfTwoLargestGroupElementOrders;
  for i in [1..5000] do
      Print(i," \c");
      ll := Set(RECOG.ListOfGroupsCrossCharRepsByBound(i));
      new := Difference(ll,l);
      for j in [1..Length(t)] do
          if t[j][3] in new then
              Add(t[j],i);
          fi;
      od;
      l := ll;
  od;
  Print("\n");
end;

RECOG.MakePSL2Hint := function( name, G )
  local d,defchar,f,p,q;
  f := DefaultFieldOfMatrixGroup(G);
  q := Size(f);
  p := Characteristic(f);
  d := DimensionOfMatrixGroup(G);
  defchar := Factors(name[3])[1];
  if p = defchar then return fail; fi;
  Info(InfoRecog,2,"Making hint for group ",name,"...");
  # we are in cross characteristic.
  # to be made better...
  return rec( elordersstart := [defchar], numberrandgens := 1, tries := 10,
              triesforgens := 3*(name[3]+1),
              orblenlimit := 3*(name[3]+1) );
end;

FindHomMethodsProjective.TwoLargeElOrders := function(ri,G)
  local d,epsilon,hint,i,max,name,namecat,nr,o,p,res,tab;
  d := ri!.dimension;
  epsilon := 1/100;
  #nr := 16 * LogInt(3*d,2) * LogInt(2/epsilon,2);
  # A cheat: 16 is theoretically OK for up to degree 5000,
  # for smaller degrees, our 4 here is also OK.
  nr := 4 * LogInt(3*d,2) * LogInt(2/epsilon,2);
  Info(InfoRecog,2,"Looking at the projective orders of ",nr,
       " random elements...");
  max := [0,0];
  ri!.projelorders := [];
  for i in [1..nr] do
      o := ProjectiveOrder(PseudoRandom(G))[1];
      Add(ri!.projelorders,o);
      # FIXME: Changed
      #if o > 3*d then
      if o > 10000 then   # we would not know about such orders anyway...
          #Info(InfoRecog,2,"Saw large projective order ",o," > 3*",d,
          Info(InfoRecog,2,"Saw large projective order ",o," > 10000,",
               " giving up.");
          return false;
      fi;
      if o > max[1] then
          max[2] := max[1];
          max[1] := o;
      elif o < max[1] and o > max[2] then
          max[2] := o;
      fi;
  od;
  Info(InfoRecog,2,"Two largest projective orders found: ",max,".");
  tab := RECOG.TableOfTwoLargestGroupElementOrdersWithDegreeBound;
  p := PositionSorted(tab,max);
  if p > Length(tab) or tab[p]{[1..2]} <> max then
      Info(InfoRecog,2,"Those orders are not in table, giving up.");
      return false;
  fi;
  # Try all possibilities:
  while p <= Length(tab) and tab[p]{[1..2]} = max do
      if tab[p][4] <= d then   # ruled out by degree bound
          name := tab[p][3];
          Info(InfoRecog,2,"Trying ",name);
          if name[1] = "l" then  # Handle PSL specially
              if name[2] = 2 then
                  hint := RECOG.MakePSL2Hint(name,G);
                  if hint <> fail then
                      res := DoHintedLowIndex(ri,G,hint);
                  else   # we use Pete Brooksbank's methods
                      return SLCR.FindHom(ri,G,2,name[3]);
                  fi;
              else
                  return SLCR.FindHom(ri,G,name[2],name[3]);
              fi;
          else
              if Length(name) = 3 then
                  namecat := Concatenation(name[1],String(name[2]),
                                           "(",String(name[3]),")");
              else
                  namecat := name[1];
              fi;
              res := LookupHintForSimple(ri,G,namecat);
          fi;
          if res = true then return true; fi;
      else
          Info(InfoRecog,2,"Cannot be ",tab[p][3]," in degree ",d,".");
      fi;
      p := p + 1;
  od;
  Info(InfoRecog,2,"Did not succeed with hints, giving up...");
  return fail;
end;

#AddMethod( FindHomDbMatrix, FindHomMethodsMatrix.TwoLargeElOrds,
#           950, "TwoLargeElOrds",
#           "look at two largest element orders" );