# Group 691200.g downloaded from the LMFDB on 12 November 2025. ## Various presentations of this group are stored in this file: # GPC is polycyclic presentation GPerm is permutation group # GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups # Many characteristics of the group are stored as booleans in a record: # Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, # metacyclic, monomial, nilpotent, perfect, quasisimple, rational, # solvable, supersolvable # The character table is stored as a record chartbl_n_i where n is the order # of the group and i is which group of that order it is. The record is # converted to a character table using ConvertToLibraryCharacterTableNC # Constructions GPerm := Group( (1,3,7,6,4,2,5,8)(9,10)(11,13,12), (2,6,8)(5,9,7)(11,14,12,13), (1,2,4,6,7,8,9,10,5,3)(11,12,13) ); # Booleans booleans_691200_g := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, monomial := false, nilpotent := false, perfect := false, quasisimple := false, rational := true, solvable := false, supersolvable := false); # Character Table chartbl_691200_g:=rec(); chartbl_691200_g.IsFinite:= true; chartbl_691200_g.UnderlyingCharacteristic:= 0; chartbl_691200_g.UnderlyingGroup:= GPerm; chartbl_691200_g.Size:= 691200; chartbl_691200_g.InfoText:= "Character table for group 691200.g downloaded from the LMFDB."; chartbl_691200_g.Identifier:= " S4*S5wrC2 "; chartbl_691200_g.NrConjugacyClasses:= 175; chartbl_691200_g.ConjugacyClasses:= [(), (11,14)(12,13), (11,12), (7,9), (1,4)(5,9), (1,9)(11,13)(12,14), (2,3)(6,10)(11,14)(12,13), (2,3)(7,9), (1,8)(2,9)(3,7)(4,10)(5,6), (4,5)(12,13), (2,3)(6,10)(13,14), (2,8)(3,10)(4,9)(5,7), (2,3)(4,5)(7,9), (3,8)(4,9)(11,14)(12,13), (1,10)(2,7)(3,9)(4,6)(5,8)(11,12)(13,14), (1,4)(2,6)(12,14), (1,7)(2,10)(3,8)(5,9)(11,14)(12,13), (1,6)(2,4)(3,9)(5,8)(7,10)(11,12), (1,5)(2,3)(6,8)(11,13)(12,14), (3,6)(4,9)(5,7)(8,10)(11,13), (1,7)(2,8)(3,6)(13,14), (11,13,14), (6,10,8), (3,10,6)(11,12,13), (5,9,7)(6,10,8), (1,5,7)(2,6,3)(12,13,14), (11,13,12,14), (4,5,9,7), (2,8)(11,12,14,13), (1,9,4,5)(11,13)(12,14), (3,6)(8,10)(11,12,13,14), (2,10,3,6)(11,13,14,12), (1,4,7,5)(12,14), (1,5,4,9)(3,8), (1,9)(6,10)(11,14,13,12), (1,6)(2,7)(3,4)(5,8)(9,10)(11,13,14,12), (2,10,8,3)(4,5,9,7), (1,7)(3,6,8,10)(4,5), (1,10,4,6)(2,9)(3,5)(7,8), (2,8)(3,10)(4,7)(5,9)(11,12,13,14), (1,5)(2,3)(6,8)(11,13,14,12), (3,10)(4,9,7,5)(11,13)(12,14), (1,6,5,3)(2,9)(4,10,7,8), (1,9,5,7)(2,10,8,6)(11,14)(12,13), (1,4)(3,8,10,6)(5,7)(11,12)(13,14), (1,2)(3,4,6,7)(5,10)(8,9)(11,14)(12,13), (2,10,8,6)(4,5)(11,13), (2,10,3,6)(7,9)(11,14,12,13), (1,7,4,9)(3,6,8,10)(11,13,12,14), (1,5)(3,6,8,10)(7,9)(11,14,12,13), (1,4,5,7)(2,3,6,8)(12,14), (1,10,9,6)(2,5,3,4)(7,8)(11,12)(13,14), (1,5,9,7)(2,10)(6,8)(12,14), (1,2)(3,4,8,9)(5,6)(7,10)(11,12,14,13), (1,3,5,6)(2,7)(4,10)(8,9)(11,12), (1,8,4,10)(2,7,3,9)(5,6)(11,14), (1,10,7,2)(3,9,8,5)(4,6)(11,12,14,13), (1,4,9,5,7), (1,9,4,5,7)(2,10,6,3,8), (1,5)(4,7,9), (5,7,9)(11,14)(12,13), (1,9)(4,5,7)(11,13)(12,14), (4,7)(11,14,12), (3,8)(6,10)(11,12,14), (1,7,9)(4,5)(12,13), (1,4,9)(12,14), (2,3)(6,10,8)(11,13,12), (6,8,10)(7,9), (2,3)(6,8,10)(7,9), (1,9,5)(2,8,10)(3,6)(4,7), (2,3)(4,5)(6,8,10)(7,9), (1,4)(2,10,6)(5,9), (2,3)(5,7,9)(6,8,10), (1,5)(2,8)(11,14,12), (1,8)(2,9)(3,7)(4,10)(5,6)(11,14,12), (1,7,5)(2,10,6)(3,8)(4,9)(11,14)(12,13), (1,5,4)(3,10,8)(11,12)(13,14), (3,8,10)(5,7)(11,12)(13,14), (1,4,9)(5,7)(8,10)(11,12)(13,14), (2,8)(3,10)(4,9)(5,7)(11,14,13), (1,5)(2,3)(4,9,7)(6,8)(11,13)(12,14), (1,4,5)(2,3)(6,10)(11,12)(13,14), (2,8,6)(5,9,7)(11,12), (1,9)(2,6)(8,10)(11,13,14), (2,3,8)(7,9)(13,14), (1,4)(2,6)(3,10,8)(5,7,9)(12,14), (1,3)(2,9)(4,10,7,6,5,8), (2,10)(3,8,6)(4,7,5)(11,12)(13,14), (2,8,6)(3,10)(4,9)(12,13), (1,4)(2,3,8)(5,7,9)(6,10)(11,14,12), (1,5)(2,8,3)(6,10)(12,13,14), (1,4)(3,8,6)(11,14,12), (1,7)(2,8)(3,6)(4,9,5)(13,14), (1,4)(2,6,8)(5,7)(13,14), (3,6,10)(4,9)(5,7)(11,13,12), (1,9)(2,3)(4,5,7)(6,10)(12,14,13), (1,7,5)(2,3)(6,8,10)(11,12), (1,7,5)(2,3,6)(4,9)(12,14,13), (1,10,9,8,4,2)(3,7)(5,6)(11,14)(12,13), (1,2,5,6,4,8)(3,9)(7,10)(11,12), (1,3,4,2,7,6)(5,10)(8,9)(11,14,13), (1,6)(2,4,10,5,8,9,3,7), (1,2,9,8,5,3,4,6)(7,10)(11,13)(12,14), (1,8,9,2,4,3,5,6)(7,10)(11,14), (1,8,9,6,5,2,7,10)(3,4)(11,12,14,13), (1,9,4,5,7)(11,14)(12,13), (2,3,6,8,10)(12,14), (1,5,4,7,9)(2,3), (2,10,6,8,3)(4,9)(5,7), (1,9)(2,3,8,10,6)(11,13)(12,14), (1,4,9,5,7)(2,6,3,10,8)(11,14)(12,13), (1,4,7,9,5)(2,3)(6,10)(11,14)(12,13), (1,6,9,3,4,8,5,2,7,10), (2,6,8,3,10)(4,5)(12,13), (1,5,9,4,7)(2,6,10,3,8)(11,14), (1,9,4,5,7)(2,3)(6,10)(13,14), (1,2,9,6,5,10,7,3,4,8)(11,12)(13,14), (1,8,9,10,4,2,7,3,5,6)(13,14), (2,6,3)(8,10)(11,13,14,12), (1,4,5)(11,13,12,14), (4,7,9,5)(12,13,14), (1,5)(2,8,10,3)(4,9,7), (1,9,7)(3,6,8,10), (2,8)(5,9,7)(11,13,14,12), (2,6,8)(4,5,7)(11,14,12,13), (1,9)(4,5,7)(6,10)(11,12,13,14), (1,9,5)(2,3,8)(4,7)(6,10)(11,14,13,12), (1,6,5,2,7,3)(4,10,9,8), (1,5)(2,3)(4,7,9)(6,8)(11,12,14,13), (1,5,4,9)(2,6,10)(11,13)(12,14), (2,6,8)(3,10)(4,5,7,9)(11,13)(12,14), (3,6)(4,5,9)(8,10)(11,14,13,12), (1,4,5)(2,6)(3,8,10)(11,14,12,13), (1,4,5,7)(6,10)(11,12,13), (2,3,8,10)(4,7,9,5)(11,13,14), (1,7)(3,10,8,6)(4,5)(11,14,12), (1,10,9,2,5,8)(3,7,6,4)(11,14)(12,13), (1,9,7)(2,6,8,10)(4,5)(11,13), (1,7,4)(2,10,8,3)(13,14), (1,5,4)(2,6,3,10)(7,9)(11,13,12,14), (1,9,5,7)(3,6,8)(11,13,14,12), (1,2,5,8)(3,4)(6,9)(7,10)(11,12,14), (3,10,6)(4,7,9,5)(11,12,13), (1,9,4,5)(2,6,10)(3,8)(11,12,14), (1,6,7,2,5,10)(3,9,8,4)(11,13,14,12), (1,6,5,3)(2,4,8,7,10,9)(11,12), (1,10,5,8,9,6)(2,7)(3,4)(11,12,14,13), (1,3,5,6)(2,9)(4,8,7,10)(11,12,13), (1,6,4,10)(2,7,3,9,8,5)(11,12,14), (2,3,8,6,10)(12,14,13), (1,7,5,4,9)(2,3,6), (1,4,7,9,5)(2,6,8,10,3)(11,14,12), (1,9,7,4,5)(6,10,8)(11,13,12), (2,6,10,8,3)(11,14,12,13), (2,8,10,3,6)(4,5,9,7), (1,5,9,7,4)(8,10)(11,12,14,13), (1,5,7,4,9)(2,6,3,10,8)(11,13,14,12), (1,9,7,4)(2,8,6,10,3)(11,13)(12,14), (1,5,9,4,7)(3,8)(6,10)(11,13,12,14), (1,9,4,5,7)(2,10,3,6)(11,13,14,12), (1,4,7,5)(2,6,3,8,10)(12,14), (1,8,4,2,9,6,5,3,7,10)(11,13,14,12), (1,6)(2,5,3,4,8,7,10,9)(11,14,13), (1,5)(2,6,8,3,10)(4,9,7), (1,4,7,9,5)(2,6,3)(11,14)(12,13), (1,9)(2,8,6,3,10)(4,7,5)(11,13)(12,14), (2,10,3,8,6)(4,7)(11,12,14), (2,6,3,10,8)(4,9)(5,7)(12,13,14), (1,9,7)(2,8,10,6,3)(4,5)(12,13), (1,9,4)(2,6,10,3,8)(12,14), (1,4,9,5,7)(2,3)(6,8,10)(11,12,13), (1,2,4,6,7,8,9,10,5,3)(11,12,14), (1,9,4,5,7)(2,3,6)(8,10)(11,13,14,12), (1,5,4)(2,10,3,6,8)(11,13,12,14), (2,10,6,8,3)(4,7,9,5)(12,14,13)]; chartbl_691200_g.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 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, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175]; chartbl_691200_g.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 22, 23, 24, 25, 26, 2, 5, 2, 5, 2, 7, 5, 5, 2, 2, 12, 5, 8, 2, 2, 5, 12, 12, 5, 8, 5, 7, 17, 7, 12, 12, 5, 14, 8, 12, 17, 58, 59, 23, 23, 23, 22, 22, 23, 23, 24, 23, 23, 25, 23, 23, 25, 22, 22, 25, 25, 23, 23, 22, 23, 23, 25, 22, 23, 25, 25, 25, 23, 26, 24, 24, 23, 23, 24, 24, 25, 26, 25, 25, 26, 37, 37, 37, 44, 58, 58, 58, 58, 58, 59, 58, 59, 58, 59, 58, 59, 59, 61, 61, 64, 72, 72, 61, 77, 61, 77, 70, 61, 72, 72, 61, 77, 64, 80, 64, 70, 72, 72, 82, 82, 74, 95, 95, 76, 70, 77, 80, 90, 150, 151, 152, 153, 106, 109, 106, 111, 109, 106, 112, 109, 111, 135, 151, 151, 151, 150, 150, 151, 151, 153, 152, 165, 165, 168], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 1, 1, 1, 1, 1, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 4, 2, 6, 4, 5, 10, 3, 4, 4, 8, 8, 13, 5, 4, 8, 9, 14, 2, 6, 14, 12, 19, 7, 3, 13, 10, 16, 9, 6, 16, 8, 8, 4, 21, 11, 5, 13, 10, 4, 15, 18, 9, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 29, 27, 28, 34, 28, 29, 27, 35, 35, 39, 41, 30, 42, 31, 29, 34, 37, 38, 46, 47, 33, 48, 32, 39, 28, 34, 54, 55, 36, 43, 39, 58, 58, 59, 58, 154, 155, 156, 157, 158, 159, 160, 161, 162, 102, 108, 106, 110, 108, 109, 114, 107, 108, 113, 156, 154, 155], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 1, 1, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 2, 3, 4, 5, 6, 2, 7, 9, 10, 3, 11, 15, 18, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 22, 23, 22, 24, 27, 28, 29, 27, 30, 31, 32, 33, 36, 163, 60, 61, 62, 63, 64, 65, 66, 67, 75, 119, 120, 121]]; chartbl_691200_g.SizesCentralizers:= [691200, 230400, 115200, 34560, 23040, 11520, 7680, 6912, 5760, 5760, 3840, 3072, 2304, 2304, 1920, 1152, 1024, 960, 768, 512, 384, 86400, 17280, 2160, 1728, 216, 115200, 11520, 5760, 3840, 3840, 1920, 1920, 1152, 1152, 960, 768, 768, 576, 512, 384, 384, 384, 256, 256, 192, 192, 192, 128, 128, 128, 128, 128, 96, 96, 64, 64, 14400, 1200, 17280, 5760, 5760, 4320, 2880, 2880, 2880, 2160, 1728, 1728, 1728, 1152, 1152, 864, 864, 720, 576, 576, 576, 576, 384, 384, 384, 288, 288, 288, 288, 288, 288, 288, 216, 216, 216, 192, 192, 144, 144, 144, 108, 96, 48, 36, 192, 64, 32, 32, 4800, 2400, 1440, 960, 480, 400, 320, 240, 240, 200, 160, 80, 40, 2880, 2880, 1440, 576, 576, 288, 288, 288, 288, 288, 192, 192, 192, 192, 144, 144, 96, 96, 96, 96, 96, 96, 96, 72, 72, 72, 48, 48, 48, 48, 36, 1800, 720, 150, 90, 2400, 480, 240, 200, 160, 160, 80, 80, 40, 24, 720, 240, 240, 180, 120, 120, 120, 90, 30, 120, 120, 60]; chartbl_691200_g.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "2N", "2O", "2P", "2Q", "2R", "2S", "2T", "3A", "3B", "3C", "3D", "3E", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "4J", "4K", "4L", "4M", "4N", "4O", "4P", "4Q", "4R", "4S", "4T", "4U", "4V", "4W", "4X", "4Y", "4Z", "4AA", "4AB", "4AC", "4AD", "4AE", "5A", "5B", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "6H", "6I", "6J", "6K", "6L", "6M", "6N", "6O", "6P", "6Q", "6R", "6S", "6T", "6U", "6V", "6W", "6X", "6Y", "6Z", "6AA", "6AB", "6AC", "6AD", "6AE", "6AF", "6AG", "6AH", "6AI", "6AJ", "6AK", "6AL", "6AM", "6AN", "6AO", "6AP", "8A", "8B", "8C", "8D", "10A", "10B", "10C", "10D", "10E", "10F", "10G", "10H", "10I", "10J", "10K", "10L", "10M", "12A", "12B", "12C", "12D", "12E", "12F", "12G", "12H", "12I", "12J", "12K", "12L", "12M", "12N", "12O", "12P", "12Q", "12R", "12S", "12T", "12U", "12V", "12W", "12X", "12Y", "12Z", "12AA", "12AB", "12AC", "12AD", "12AE", "15A", "15B", "15C", "15D", "20A", "20B", "20C", "20D", "20E", "20F", "20G", "20H", "20I", "24A", "30A", "30B", "30C", "30D", "30E", "30F", "30G", "30H", "30I", "60A", "60B", "60C"]; chartbl_691200_g.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 15, 15, 15, 15, 20, 20, 20, 20, 20, 20, 20, 20, 20, 24, 30, 30, 30, 30, 30, 30, 30, 30, 30, 60, 60, 60]; chartbl_691200_g.Irr:= [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1], [1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 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-1], [10, 10, 10, 4, 6, 4, 6, -2, 0, 4, 6, 2, 0, -2, 0, -2, 2, 0, 0, 2, 0, 10, 4, 4, -2, -2, 10, 6, 4, 6, 6, 6, 6, 0, -2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 5, 0, 4, 4, 4, 4, 4, 4, 6, 4, -2, -2, -2, 0, 0, -2, -2, 0, -2, -2, -2, -2, 2, 0, 0, -2, 0, 0, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 5, 5, -1, 1, -1, 0, 1, 0, -1, 0, 1, 0, 0, 4, 4, 6, 0, 0, -2, 0, -2, -2, -2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -1, 0, -1, 5, 1, -1, 0, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, 1, -1, -1, -1, 0, -1, -1, 1], [10, 10, 10, 6, 6, 6, 6, 2, 0, 6, 6, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 10, 4, 4, -2, -2, 10, 4, 6, 4, 6, 4, 4, 0, 2, 0, -2, 0, 0, 2, 2, 0, 0, -2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 5, 0, 6, 4, 6, 6, 6, 4, 6, 6, 0, 2, 2, 2, 0, 0, 2, 0, 0, -2, 2, 2, 2, 2, 0, -2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 6, 4, 4, 0, -2, 2, 0, -2, 0, 2, 0, 0, -2, 2, 0, 0, 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