# Group 279936.mf downloaded from the LMFDB on 03 February 2026. ## 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 GPC := PcGroupCode(29818780681381465093698648767333813009330980932151475002636213193471251067095917123552168982840977949438705372678728328731698882772116673132088742171503364912710998289105831049063985627125524870365876972973469092915031209349553350885946803837637043561110049579648922840402288771588902813210832713140493764500259863393800172705492981282680508148466356092949405083496110692185444539561396982566719703135,279936); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.5; e := GPC.7; f := GPC.9; g := GPC.11; h := GPC.12; i := GPC.13; j := GPC.14; GPerm := Group( (1,2,4,7,13,11,16,12,17,8,15,9,6,3,5,10,14,18), (1,3,4,8,13,11,6,12,17,10,15,9,16,2,5,7,14,18)(19,20), (1,2,6,3)(4,9,17,18,5,11)(7,14,10,15)(8,13)(12,16)(19,20) ); # Booleans booleans_279936_mf := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := false); # Character Table chartbl_279936_mf:=rec(); chartbl_279936_mf.IsFinite:= true; chartbl_279936_mf.UnderlyingCharacteristic:= 0; chartbl_279936_mf.UnderlyingGroup:= GPerm; chartbl_279936_mf.Size:= 279936; chartbl_279936_mf.InfoText:= "Character table for group 279936.mf downloaded from the LMFDB."; chartbl_279936_mf.Identifier:= " C3^6.C2^4:S4 "; chartbl_279936_mf.NrConjugacyClasses:= 144; chartbl_279936_mf.ConjugacyClasses:= [(), (19,20), (8,10)(11,18), (8,10)(11,18)(19,20), (1,10)(2,14)(3,15)(4,11)(5,18)(6,8)(7,16)(9,17)(12,13), (1,10)(2,14)(3,13)(4,9)(5,11)(6,7)(8,16)(12,15)(17,18)(19,20), (1,6)(2,3)(7,10)(14,15), (1,16)(2,3)(7,8)(13,14)(19,20), (1,18)(2,14)(3,13)(4,8)(5,10)(6,11)(7,17)(9,16)(12,15), (1,18)(2,15)(3,14)(4,7)(5,10)(6,9)(8,17)(11,16)(12,13)(19,20), (2,3)(4,5)(7,8)(13,15), (3,12)(4,5)(7,8)(14,15)(19,20), (1,4)(2,3)(5,6)(7,9)(8,11)(10,18)(13,14)(16,17)(19,20), (1,6)(2,18)(3,11)(4,13)(5,15)(7,8)(9,12)(14,17), (13,15,14), (4,17,5)(9,18,11), (2,12,3)(7,10,8)(9,18,11), (9,18,11)(13,15,14), (7,10,8)(9,18,11), (1,6,16)(2,3,12)(4,17,5)(7,8,10)(9,18,11)(13,15,14), (1,6,16)(2,3,12)(4,5,17)(7,8,10)(9,11,18)(13,14,15), (7,10,8)(9,18,11)(13,15,14), (2,12,3)(4,17,5)(9,18,11)(13,15,14), (4,17,5)(9,18,11)(13,15,14), (4,17,5)(7,10,8)(9,18,11)(13,15,14), (2,12,3)(7,10,8)(9,18,11)(13,15,14), (2,12,3)(4,17,5)(7,10,8)(9,18,11)(13,15,14), (1,17,13)(2,7,18)(3,8,11)(4,15,6)(5,14,16)(9,12,10), (1,4,16,5)(6,17)(7,11,10,18)(8,9), (1,5)(4,6,17,16)(7,9,8,18)(10,11)(19,20), (1,15)(2,7,12,10)(3,8)(4,5)(6,14)(13,16), (2,9)(3,11)(4,14,17,13)(5,15)(7,10)(12,18)(19,20), (1,3,6,2)(4,11)(5,9)(7,14,10,15)(8,13)(12,16)(17,18)(19,20), (1,10,16,7)(2,15,12,14)(3,13)(4,9)(5,18)(6,8)(11,17), (1,8)(2,14,12,13)(3,15)(4,9)(5,18)(6,7,16,10)(11,17)(19,20), (1,9)(2,14)(3,13)(4,8)(5,10,17,7)(6,18,16,11)(12,15), (1,11)(2,15,3,13)(4,8,5,7)(6,18)(9,16)(10,17)(12,14), (1,7)(2,17)(3,5)(4,12)(6,8,16,10)(9,13,11,14)(15,18)(19,20), (13,14,15)(19,20), (4,5,17)(9,11,18)(19,20), (2,3,12)(7,8,10)(9,11,18)(19,20), (9,11,18)(13,14,15)(19,20), (7,8,10)(9,11,18)(19,20), (1,16,6)(2,12,3)(4,17,5)(7,10,8)(9,18,11)(13,15,14)(19,20), (1,6,16)(2,12,3)(4,5,17)(7,8,10)(9,18,11)(13,15,14)(19,20), (7,8,10)(9,11,18)(13,14,15)(19,20), (2,3,12)(4,5,17)(9,11,18)(13,14,15)(19,20), (4,5,17)(9,11,18)(13,14,15)(19,20), (4,5,17)(7,8,10)(9,11,18)(13,14,15)(19,20), (2,3,12)(7,8,10)(9,11,18)(13,14,15)(19,20), (8,10)(11,18)(13,14,15), (8,10)(11,18)(13,14,15)(19,20), (5,17)(6,16)(13,14,15)(19,20), (2,3)(8,10)(9,11,18), (2,3,12)(4,5,17)(7,8,10)(9,11,18)(13,14,15)(19,20), (6,16)(7,8,10)(14,15), (6,16)(7,8,10)(14,15)(19,20), (5,17)(6,16)(7,8,10)(9,11,18)(19,20), (4,5,17)(6,16)(9,11,18)(14,15), (4,5,17)(6,16)(9,11,18)(14,15)(19,20), (2,12,3)(6,16)(7,10,8)(13,15), (6,16)(7,8,10)(9,11,18)(14,15), (6,16)(7,8,10)(9,11,18)(14,15)(19,20), (5,17)(6,16)(9,11,18)(13,14,15), (5,17)(6,16)(9,11,18)(13,14,15)(19,20), (5,17)(6,16)(7,8,10)(9,11,18)(13,14,15)(19,20), (2,3,12)(6,16)(7,8,10)(9,11,18)(14,15), (2,3,12)(6,16)(7,8,10)(9,11,18)(14,15)(19,20), (1,6,16)(2,12)(7,10)(9,18,11)(13,15,14), (1,3)(2,6)(4,18,17,9,5,11)(7,14)(8,15)(10,13)(12,16)(19,20), (1,18)(2,15,3,14,12,13)(4,7)(5,10)(6,9)(8,17)(11,16), (1,10)(2,13,12,15,3,14)(4,11)(5,18)(6,8)(7,16)(9,17)(19,20), (1,7)(2,15)(3,13)(4,11,5,18,17,9)(6,10)(8,16)(12,14), (1,8,6,10,16,7)(2,15,3,14,12,13)(4,11,17,9,5,18)(19,20), (1,8,16,7,6,10)(2,13,3,15,12,14)(4,11,17,9,5,18), (1,16,6)(2,12,3)(4,5,17)(7,8)(11,18)(13,14,15), (1,16)(2,12,3)(4,17)(7,8,10)(13,14,15), (1,6,16)(2,12,3)(4,17,5)(8,10)(11,18)(13,14,15)(19,20), (1,16,6)(3,12)(4,17,5)(7,8,10)(9,11)(19,20), (1,6)(2,3)(4,17,5)(7,10)(9,11,18)(14,15), (4,5)(6,16)(8,10)(9,18)(13,15,14), (1,16)(2,3)(4,5,17)(7,8)(9,18,11)(13,14)(19,20), (1,16)(4,17)(7,10)(9,18)(13,14,15)(19,20), (1,11,16,18,6,9)(2,14)(3,13)(4,10,17,8,5,7)(12,15), (1,11,6,18,16,9)(2,15)(3,14)(4,10,17,7,5,8)(12,13)(19,20), (1,7)(2,5)(3,4)(6,8)(9,13,18,14,11,15)(10,16)(12,17), (1,18,6,9,16,11)(2,15)(3,14)(4,8)(5,7)(10,17)(12,13)(19,20), (1,7,6,8,16,10)(2,15)(3,13)(4,9,5,18,17,11)(12,14), (1,8,6,7,16,10)(2,14)(3,13)(4,11,5,9,17,18)(12,15)(19,20), (1,6,16)(2,3)(4,5)(7,8)(9,11,18)(13,15), (1,16,6)(3,12)(4,5)(7,8)(14,15)(19,20), (1,6,16)(2,12)(5,17)(8,10)(9,11,18)(13,14)(19,20), (1,6)(3,12)(4,17)(7,10,8)(11,18), (1,18,16,11,6,9)(2,13,12,14,3,15)(4,7)(5,10)(8,17), (1,9,16,11,6,18)(2,13,12,14,3,15)(4,8,5,10,17,7), (1,10,16,7,6,8)(2,4,3,5,12,17)(9,14,11,13,18,15)(19,20), (1,4,14)(2,10,9)(3,8,11)(5,13,6)(7,18,12)(15,16,17)(19,20), (1,12)(2,6)(3,16)(4,18,5,9,17,11)(7,13,8,14,10,15)(19,20), (1,5,16,4,6,17)(2,3)(7,9)(8,11)(10,18)(13,14)(19,20), (1,6)(2,9,3,18,12,11)(4,15,17,13,5,14)(7,8), (1,13)(2,7,3,8,12,10)(5,17)(6,15)(9,11)(14,16), (1,13,16,15,6,14)(2,7,12,10,3,8)(4,5)(11,18)(19,20), (1,12,17,10,13,9)(2,5,7,14,18,16)(3,4,8,15,11,6), (1,11,15,10,17,2)(3,16,18,13,7,4)(5,12,6,9,14,8)(19,20), (1,4,14,6,17,13,16,5,15)(2,7,18,3,8,11,12,10,9), (1,4,13,16,17,15,6,5,14)(2,8,11,3,7,9,12,10,18), (1,13,5,6,14,17,16,15,4)(2,11,10,3,18,7,12,9,8), (1,14,5)(2,18,8,12,11,7,3,9,10)(4,16,13)(6,15,17), (1,5,13,6,4,15,16,17,14)(2,7,18)(3,8,9)(10,11,12), (1,5)(2,3,12)(4,16,17,6)(7,18,8,9)(10,11)(13,14,15)(19,20), (1,5)(2,12,3)(4,16,17,6)(7,18,8,9)(10,11)(13,15,14)(19,20), (1,16,6)(2,9)(3,11,12,18)(4,13)(5,15,17,14)(7,8,10), (1,6,16)(2,9)(3,11,12,18)(4,13)(5,15,17,14)(7,10,8), (1,5,16,4)(2,3,12)(6,17)(7,18,10,11)(8,9)(13,14,15), (1,13)(2,7,12,8)(3,10)(4,17,5)(6,15,16,14)(9,11,18)(19,20), (1,17)(4,6,5,16)(7,11)(8,18,10,9)(13,14,15), (1,17)(4,6,5,16)(7,11)(8,18,10,9)(13,15,14), (1,4,16,17)(5,6)(7,9,8,11)(10,18)(13,14,15)(19,20), (1,4,16,17)(5,6)(7,9,8,11)(10,18)(13,15,14)(19,20), (1,14)(2,10,3,8)(4,5)(6,13)(7,12)(9,18,11)(15,16)(19,20), (1,14)(2,10,3,8)(4,5)(6,13)(7,12)(9,11,18)(15,16)(19,20), (1,16)(2,18,3,11)(4,14)(5,13)(7,10,8)(9,12)(15,17), (1,16)(2,18,3,11)(4,14)(5,13)(7,8,10)(9,12)(15,17), (1,14)(2,7,12,10,3,8)(6,13,16,15)(9,11), (2,18,3,9,12,11)(4,13,17,14)(5,15)(7,10)(19,20), (1,13,6,15,16,14)(2,10,12,7)(3,8)(4,5)(9,11,18), (1,14,16,15,6,13)(2,10,12,7)(3,8)(4,5)(9,18,11), (1,5,16,17)(2,12)(4,6)(7,18,10,9,8,11)(13,14,15)(19,20), (1,5,16,17)(2,12)(4,6)(7,11,8,9,10,18)(13,15,14)(19,20), (1,2,6,3)(4,9,17,11,5,18)(7,15,10,14)(8,13)(12,16)(19,20), (1,7,16,10)(2,14,12,15)(3,13)(4,18,17,9,5,11)(6,8), (1,8)(2,13,12,14)(3,15)(4,18,17,9,5,11)(6,10,16,7)(19,20), (1,9)(2,15,3,14,12,13)(4,8)(5,7,17,10)(6,11,16,18), (1,9,6,11,16,18)(2,13,3,15)(4,7,5,8)(10,17)(12,14), (1,7)(2,5,12,17,3,4)(6,10,16,8)(9,14,11,13)(15,18)(19,20), (1,5,14,6,17,13,16,4,15)(2,10,11,12,7,9,3,8,18)(19,20), (1,14,17,6,13,4,16,15,5)(2,11,7,12,9,8,3,18,10)(19,20), (1,17,13,16,5,15,6,4,14)(2,7,11,12,10,9,3,8,18)(19,20), (1,5,14)(2,7,18,3,8,9,12,10,11)(4,13,16)(6,17,15)(19,20), (1,15,5,16,13,17,6,14,4)(2,18,7)(3,9,8)(10,12,11)(19,20), (1,3,4,8,14,11,6,12,17,10,13,9,16,2,5,7,15,18)(19,20), (1,2,4,8,13,11,16,3,17,7,15,9,6,12,5,10,14,18), (1,11,14,7,17,2,16,18,13,10,4,3,6,9,15,8,5,12)(19,20), (1,9,13,8,5,3,6,18,14,10,4,2,16,11,15,7,17,12)]; chartbl_279936_mf.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]; chartbl_279936_mf.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 7, 7, 3, 3, 7, 7, 7, 7, 11, 11, 15, 16, 17, 18, 19, 21, 20, 22, 23, 24, 25, 26, 15, 15, 15, 15, 27, 15, 15, 19, 16, 16, 19, 19, 19, 18, 18, 22, 17, 17, 22, 16, 16, 16, 16, 20, 20, 26, 24, 26, 24, 16, 15, 16, 15, 23, 23, 18, 18, 23, 23, 18, 15, 18, 15, 25, 21, 21, 28, 25, 19, 23, 19, 23, 28, 28, 105, 106, 107, 108, 109, 80, 80, 80, 80, 80, 80, 81, 81, 81, 81, 54, 54, 54, 54, 61, 61, 69, 69, 69, 69, 80, 80, 80, 80, 90, 90, 106, 105, 107, 108, 109, 105, 106, 106, 105], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 3, 2, 3, 4, 4, 3, 4, 3, 3, 4, 3, 4, 4, 3, 4, 3, 10, 9, 6, 5, 6, 5, 3, 3, 4, 4, 7, 7, 8, 8, 9, 10, 9, 10, 5, 6, 11, 12, 12, 11, 9, 9, 10, 2, 10, 13, 14, 14, 13, 5, 6, 20, 20, 21, 17, 17, 30, 30, 29, 29, 29, 30, 29, 29, 30, 30, 32, 32, 31, 31, 31, 32, 31, 31, 32, 32, 33, 34, 35, 36, 37, 38, 45, 45, 44, 41, 41, 74, 75, 74, 75]]; chartbl_279936_mf.SizesCentralizers:= [279936, 279936, 5184, 5184, 2592, 2592, 1152, 1152, 864, 864, 576, 576, 288, 288, 23328, 23328, 17496, 11664, 11664, 8748, 8748, 5832, 5832, 2916, 2916, 2916, 1458, 108, 288, 288, 144, 144, 96, 96, 96, 96, 48, 48, 23328, 23328, 17496, 11664, 11664, 8748, 8748, 5832, 5832, 2916, 2916, 2916, 2592, 2592, 2592, 2592, 1458, 1296, 1296, 1296, 1296, 1296, 1296, 648, 648, 648, 648, 648, 648, 648, 648, 432, 432, 432, 432, 324, 324, 324, 324, 324, 324, 288, 288, 288, 288, 216, 216, 216, 216, 216, 216, 144, 144, 144, 144, 108, 108, 108, 108, 108, 72, 72, 72, 72, 36, 36, 108, 108, 54, 54, 54, 288, 288, 288, 288, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 72, 72, 72, 72, 72, 72, 48, 48, 48, 48, 24, 24, 108, 108, 54, 54, 54, 36, 36, 36, 36]; chartbl_279936_mf.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "3A", "3B", "3C", "3D", "3E", "3F", "3G", "3H", "3I", "3J", "3K", "3L", "3M", "3N", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "4J", "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", "6AQ", "6AR", "6AS", "6AT", "6AU", "6AV", "6AW", "6AX", "6AY", "6AZ", "6BA", "6BB", "6BC", "6BD", "6BE", "6BF", "6BG", "6BH", "6BI", "6BJ", "6BK", "6BL", "6BM", "6BN", "9A", "9B", "9C", "9D", "9E", "12A1", "12A5", "12B1", "12B5", "12C", "12D", "12E1", "12E5", "12F1", "12F5", "12G1", "12G5", "12H1", "12H5", "12I", "12J", "12K1", "12K5", "12L1", "12L5", "12M", "12N", "12O", "12P", "12Q", "12R", "18A", "18B", "18C", "18D", "18E", "18F", "18G", "18H", "18I"]; chartbl_279936_mf.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 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, 18, 18, 18, 18, 18, 18, 18, 18, 18]; chartbl_279936_mf.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, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1], [1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1], [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1], [1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1], [2, -2, 2, -2, -2, 2, 2, -2, 0, 0, 2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, 2, -2, -2, 2, -2, 2, -2, 2, 0, 0, -2, 2, -2, 2, 2, -2, 2, 2, -2, -2, 0, -2, 0, 0, 2, 0, 2, -2, -2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 1, 1, 1, 1, 1, 1, 1, -1, -1], [2, -2, 2, -2, 2, -2, 2, -2, 0, 0, 2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, 2, -2, -2, 2, -2, 2, 2, -2, 0, 0, -2, -2, -2, 2, 2, 2, 2, 2, -2, -2, 0, 2, 0, 0, -2, 0, 2, -2, -2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 1, 1, 1, 1, 1, -1, -1, 1, 1], [2, 2, 2, 2, -2, -2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 0, 0, 2, -2, 2, 2, 2, -2, 2, 2, 2, 2, 0, -2, 0, 0, -2, 0, 2, 2, 2, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, -1, -1, -1, -1, -1, 1, 1, 1, 1], [3, 3, -1, -1, 3, 3, 3, 3, 1, 1, -1, -1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, 1, 1, -1, 3, -1, -1, -1, 3, 3, 3, 3, 3, 1, 3, 1, 1, 3, 1, -1, -1, -1, -1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, -1, -1, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, -1, -1, -1, 3, -1, -1, -1, 3, 3, 3, 3, 3, -1, 3, -1, -1, 3, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -3, -1, 1, -3, 3, 3, -3, -1, 1, -1, 1, -1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -1, -1, 1, 1, -3, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -3, 3, -1, 1, 1, 3, 1, -1, -1, -3, 3, 3, -3, -3, 1, -3, -1, -1, 3, 1, -1, 1, 1, -1, 1, 0, 1, -1, -1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -3, -1, 1, -3, 3, 3, -3, 1, -1, -1, 1, 1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -1, -1, 1, 1, -3, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -3, 3, 1, -1, 1, 3, 1, -1, -1, -3, 3, 3, -3, -3, -1, -3, 1, 1, 3, -1, -1, 1, 1, -1, -1, 0, -1, 1, 1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 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