# Group 1728.47319 downloaded from the LMFDB on 10 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 
GPC := PcGroupCode(2140574014706471589534882536529368598341594753065,1728); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.5; e := GPC.7;
GPerm := Group( (4,5)(6,7)(8,9)(10,11)(12,14)(13,15), (6,7)(8,9)(10,11)(12,15)(13,14), (2,3)(4,5)(6,8)(7,9), (4,5)(6,7)(8,9), (6,9,7,8), (6,7)(8,9), (10,12,13)(11,14,15), (10,13,12)(11,14,15), (1,2,3) );
GLZN := Group([[[ZmodnZObj(14,66), ZmodnZObj(27,66)], [ZmodnZObj(27,66), ZmodnZObj(8,66)]],[[ZmodnZObj(23,66), ZmodnZObj(0,66)], [ZmodnZObj(0,66), ZmodnZObj(23,66)]],[[ZmodnZObj(34,66), ZmodnZObj(33,66)], [ZmodnZObj(33,66), ZmodnZObj(1,66)]],[[ZmodnZObj(1,66), ZmodnZObj(54,66)], [ZmodnZObj(24,66), ZmodnZObj(43,66)]],[[ZmodnZObj(1,66), ZmodnZObj(33,66)], [ZmodnZObj(0,66), ZmodnZObj(1,66)]],[[ZmodnZObj(23,66), ZmodnZObj(0,66)], [ZmodnZObj(0,66), ZmodnZObj(1,66)]],[[ZmodnZObj(52,66), ZmodnZObj(63,66)], [ZmodnZObj(39,66), ZmodnZObj(13,66)]],[[ZmodnZObj(1,66), ZmodnZObj(22,66)], [ZmodnZObj(0,66), ZmodnZObj(1,66)]],[[ZmodnZObj(43,66), ZmodnZObj(0,66)], [ZmodnZObj(0,66), ZmodnZObj(43,66)]]]);

 
# Booleans 
booleans_1728_47319 := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true); 

 
# Character Table 
chartbl_1728_47319:=rec(); 
chartbl_1728_47319.IsFinite:= true; 
chartbl_1728_47319.UnderlyingCharacteristic:= 0; 
chartbl_1728_47319.UnderlyingGroup:= GLZN;
chartbl_1728_47319.Size:= 1728;
chartbl_1728_47319.InfoText:= "Character table for group 1728.47319 downloaded from the LMFDB."; 
chartbl_1728_47319.Identifier:= " C12:D6^2 "; 
chartbl_1728_47319.NrConjugacyClasses:= 162; 
chartbl_1728_47319.ConjugacyClasses:= [[1, 0, 0, 1], [23, 0, 0, 23], [65, 0, 0, 65], [43, 0, 0, 43], [1, 33, 0, 1], [43, 33, 0, 43], [23, 0, 0, 1], [65, 0, 0, 43], [1, 0, 0, 23], [23, 0, 33, 23], [65, 0, 33, 65], [43, 0, 0, 65], [43, 12, 0, 1], [19, 30, 54, 25], [65, 12, 0, 23], [41, 30, 54, 47], [23, 33, 0, 1], [65, 33, 0, 43], [1, 0, 33, 23], [43, 0, 33, 65], [43, 45, 0, 1], [19, 63, 54, 25], [65, 12, 33, 23], [65, 34, 0, 1], [43, 56, 0, 23], [41, 30, 21, 47], [41, 52, 54, 25], [19, 8, 54, 47], [13, 14, 21, 53], [19, 39, 6, 47], [41, 19, 54, 25], [47, 5, 60, 19], [1, 33, 33, 34], [13, 36, 60, 19], [1, 44, 0, 1], [13, 3, 27, 52], [1, 11, 33, 34], [13, 14, 60, 19], [13, 47, 27, 52], [43, 12, 42, 1], [65, 12, 42, 23], [43, 45, 42, 1], [65, 12, 42, 1], [65, 12, 9, 23], [43, 12, 42, 23], [65, 45, 42, 1], [43, 12, 9, 23], [56, 33, 33, 23], [32, 33, 33, 65], [41, 30, 6, 35], [53, 30, 6, 47], [23, 44, 0, 23], [65, 44, 0, 65], [31, 30, 6, 25], [43, 44, 0, 43], [10, 33, 33, 43], [8, 63, 39, 35], [20, 63, 39, 47], [56, 11, 33, 23], [32, 11, 33, 65], [41, 8, 6, 35], [53, 8, 6, 47], [31, 8, 6, 25], [64, 63, 39, 25], [10, 11, 33, 43], [19, 63, 6, 13], [31, 63, 6, 25], [1, 55, 0, 1], [41, 30, 6, 13], [53, 30, 6, 25], [23, 33, 33, 34], [34, 33, 33, 23], [41, 30, 39, 35], [53, 30, 39, 47], [23, 44, 33, 23], [43, 55, 0, 43], [65, 33, 33, 10], [10, 33, 33, 65], [19, 30, 6, 35], [31, 30, 6, 47], [65, 44, 33, 65], [8, 41, 39, 35], [20, 41, 39, 47], [64, 41, 39, 25], [43, 56, 0, 1], [19, 8, 54, 25], [43, 45, 33, 34], [32, 45, 33, 23], [65, 34, 0, 23], [19, 19, 6, 13], [31, 19, 6, 25], [41, 63, 39, 46], [53, 63, 39, 58], [52, 63, 39, 35], [64, 63, 39, 47], [19, 63, 21, 58], [8, 63, 21, 47], [41, 52, 54, 47], [41, 8, 39, 35], [53, 8, 39, 47], [41, 63, 6, 13], [53, 63, 6, 25], [19, 30, 39, 35], [31, 30, 39, 47], [43, 23, 33, 34], [32, 1, 33, 23], [19, 41, 21, 58], [8, 19, 21, 47], [43, 23, 0, 1], [19, 41, 54, 25], [65, 34, 33, 23], [65, 1, 33, 34], [10, 23, 33, 23], [41, 52, 21, 47], [41, 19, 21, 58], [52, 41, 21, 47], [13, 6, 54, 25], [19, 6, 54, 31], [35, 6, 54, 47], [41, 6, 54, 53], [43, 34, 42, 1], [43, 45, 9, 34], [32, 45, 9, 23], [65, 56, 42, 23], [13, 28, 54, 25], [19, 28, 54, 31], [13, 39, 21, 58], [19, 39, 21, 64], [2, 39, 21, 47], [8, 39, 21, 53], [35, 50, 54, 47], [41, 50, 54, 53], [13, 39, 54, 25], [19, 39, 54, 31], [35, 6, 54, 25], [41, 6, 54, 31], [35, 6, 21, 47], [41, 6, 21, 53], [13, 6, 54, 47], [19, 6, 54, 53], [43, 1, 9, 34], [32, 23, 9, 23], [13, 61, 21, 58], [19, 61, 21, 64], [2, 17, 21, 47], [8, 17, 21, 53], [43, 1, 42, 1], [65, 45, 9, 34], [10, 45, 9, 23], [65, 56, 9, 23], [13, 61, 54, 25], [19, 61, 54, 31], [35, 39, 21, 58], [41, 39, 21, 64], [46, 39, 21, 47], [52, 39, 21, 53], [35, 50, 21, 47], [41, 50, 21, 53], [35, 39, 54, 25], [41, 39, 54, 31], [13, 6, 21, 47], [19, 6, 21, 53]];
chartbl_1728_47319.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];
chartbl_1728_47319.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 33, 34, 35, 36, 37, 38, 39, 4, 4, 4, 4, 4, 4, 4, 4, 33, 33, 34, 34, 35, 35, 34, 35, 33, 36, 36, 37, 37, 38, 38, 38, 36, 37, 34, 34, 35, 34, 34, 33, 33, 34, 34, 35, 35, 33, 33, 34, 34, 35, 39, 39, 39, 35, 35, 33, 33, 35, 38, 38, 36, 36, 36, 36, 33, 33, 35, 38, 38, 34, 34, 34, 34, 37, 37, 37, 37, 35, 35, 35, 33, 33, 35, 33, 33, 54, 54, 54, 54, 55, 56, 56, 55, 63, 63, 64, 64, 64, 64, 63, 63, 54, 54, 54, 54, 54, 54, 54, 54, 65, 65, 84, 84, 84, 84, 55, 56, 56, 55, 63, 63, 64, 64, 64, 64, 63, 63, 54, 54, 54, 54], [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, 1, 1, 1, 1, 1, 1, 1, 40, 41, 42, 43, 44, 45, 46, 47, 2, 3, 2, 3, 2, 3, 4, 4, 4, 2, 3, 2, 3, 2, 3, 4, 4, 4, 5, 6, 5, 7, 8, 7, 9, 10, 11, 10, 6, 8, 12, 9, 12, 11, 2, 3, 4, 13, 14, 13, 15, 15, 5, 6, 7, 8, 9, 12, 14, 16, 16, 10, 11, 17, 18, 19, 20, 13, 15, 14, 16, 21, 22, 23, 24, 25, 26, 27, 28, 40, 40, 41, 41, 40, 40, 41, 41, 40, 40, 40, 40, 41, 41, 41, 41, 42, 42, 43, 43, 44, 44, 45, 45, 40, 41, 40, 40, 41, 41, 42, 43, 45, 44, 42, 42, 43, 43, 45, 45, 44, 44, 46, 46, 47, 47]];
chartbl_1728_47319.SizesCentralizers:= [1728, 1728, 1728, 1728, 576, 576, 576, 576, 576, 576, 576, 576, 288, 288, 288, 288, 192, 192, 192, 192, 96, 96, 96, 96, 96, 96, 96, 96, 32, 32, 32, 32, 864, 864, 864, 432, 432, 432, 216, 864, 864, 288, 288, 288, 288, 96, 96, 864, 864, 864, 864, 864, 864, 864, 864, 864, 432, 432, 432, 432, 432, 432, 432, 432, 432, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 216, 216, 216, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 96, 96, 96, 96, 72, 72, 72, 72, 48, 48, 48, 48, 48, 48, 48, 48, 864, 864, 864, 864, 432, 432, 432, 432, 432, 432, 432, 432, 432, 432, 432, 432, 288, 288, 288, 288, 288, 288, 288, 288, 216, 216, 216, 216, 216, 216, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 96, 96, 96, 96];
chartbl_1728_47319.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "2N", "2O", "2P", "2Q", "2R", "2S", "2T", "2U", "2V", "2W", "2X", "2Y", "2Z", "2AA", "2AB", "2AC", "2AD", "2AE", "3A", "3B", "3C", "3D", "3E", "3F", "3G", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "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", "6BO", "6BP", "6BQ", "12A1", "12A5", "12B1", "12B5", "12C", "12D", "12E", "12F", "12G1", "12G5", "12H1", "12H5", "12I1", "12I5", "12J1", "12J5", "12K1", "12K5", "12L1", "12L5", "12M1", "12M5", "12N1", "12N5", "12O", "12P", "12Q1", "12Q5", "12R1", "12R5", "12S", "12T", "12U", "12V", "12W1", "12W5", "12X1", "12X5", "12Y1", "12Y5", "12Z1", "12Z5", "12AA1", "12AA5", "12AB1", "12AB5"];
chartbl_1728_47319.OrderClassRepresentatives:= [1, 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, 3, 3, 3, 3, 3, 3, 3, 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, 6, 6, 6, 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, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12];
chartbl_1728_47319.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, 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0, -1, 2, 2, 2, -1, -1, -1, 2, 2, -2, 0, -2, 0, 0, 0, -1, 2, -1, 2, -1, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, 0, 0, -2, 0, 0, 1, 0, -2, 1, -2, 1, 0, 0, 0, 1, -2, -1, -1, -1, 2, 2, 1, 0, -1, 0, 0, 2, 1, 1, 1, -1, -1, -1, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, -1, 2, 2, -1, -1, -1, 2, -1, 2, -1, 2, -2, -2, 0, 0, -2, -2, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, -1, 2, 2, 2, -1, -1, -1, 2, 2, 2, 0, 2, 0, 0, 0, -1, 2, -1, 2, -1, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, 0, 0, 2, 0, 0, -1, 0, 2, -1, 2, -1, 0, 0, 0, -1, 2, -1, -1, -1, -2, -2, -1, 0, 1, 0, 0, -2, -1, -1, -1, 1, 1, 1, -2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, -1, 2, 2, -1, -1, -1, 2, -1, 2, -1, 2, 2, 2, 0, 0, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0], [2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, -2, 2, -2, 2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, -1, 2, 2, 2, -1, -1, -1, -2, -2, -2, 0, -2, 0, 0, 0, -1, 2, -1, 2, -1, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, 0, 0, 2, 0, 0, -1, 0, 2, -1, 2, -1, 0, 0, 0, -1, 2, -1, -1, -1, -2, 2, -1, 0, 1, 0, 0, -2, -1, -1, -1, -1, -1, 1, 2, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, 0, 0, 1, -1, -1, 0, 0, -2, -2, -2, -2, -2, 1, -2, -2, 1, 1, 1, -2, 1, -2, 1, -2, -2, -2, 0, 0, -2, -2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, -1, 2, 2, 2, -1, -1, -1, -2, -2, -2, 0, -2, 0, 0, 0, -1, 2, -1, 2, -1, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, 0, 0, 2, 0, 0, -1, 0, 2, -1, 2, -1, 0, 0, 0, -1, 2, -1, -1, -1, 2, -2, -1, 0, -1, 0, 0, 2, -1, -1, -1, 1, 1, -1, -2, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, 0, 0, -1, 1, 1, 0, 0, -2, -2, -2, -2, -2, 1, -2, -2, 1, 1, 1, -2, 1, -2, 1, -2, -2, -2, 0, 0, -2, -2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 2, -1, -1, 2, -1, -2, -2, 2, -2, 2, -2, 2, 2, 2, 2, 2, -1, 2, 2, -1, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, 1, -1, 2, -2, -1, 1, -2, 1, -2, -1, 2, 2, -2, 1, -1, -1, -1, 0, 0, 1, -1, 0, -1, -1, 0, 1, 1, 1, 0, 0, 0, 0, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, -2, 1, -2, -2, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -2, 1, 1, -2, 1, 2, 2, -2, -1, 1, 1, 1, 1, -2, -1, -1, -1, -1, -1, -1, -1], [2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 2, -1, -1, 2, -1, 2, 2, -2, 2, -2, 2, -2, -2, 2, 2, 2, -1, 2, 2, -1, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, 1, -1, 2, -2, -1, 1, -2, 1, -2, -1, 2, 2, -2, 1, -1, -1, -1, 0, 0, 1, -1, 0, -1, -1, 0, 1, 1, 1, 0, 0, 0, 0, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 2, -1, -1, 2, -1, -2, -2, 2, 1, -1, -1, -1, -1, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, -2, -2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 2, -1, -1, 2, 2, 0, 2, 0, 2, 0, 0, 2, -1, 2, 2, 2, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, 2, 0, 2, -1, 0, 2, 0, 0, 0, 0, 2, -1, -1, 0, 0, -1, -1, -1, 1, 1, 0, -1, -2, -1, -1, 1, 0, 0, 0, -2, -2, -2, 1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 2, 2, 2, 2, -1, 2, -1, -1, 2, 2, 2, -1, 2, -1, 2, -1, 0, 0, 2, 2, 0, 0, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, -1, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 2, -2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 2, -1, -1, -2, -2, 0, -2, 0, -2, 0, 0, 2, -1, 2, 2, 2, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, 2, 0, 2, -1, 0, 2, 0, 0, 0, 0, 2, -1, -1, 0, 0, -1, -1, -1, 1, -1, 0, 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-2*E(12)-2*E(12)^-1, -2*E(12)-2*E(12)^-1, -2*E(12)-2*E(12)^-1, -1*E(12)-E(12)^-1, 0, 2*E(12)+2*E(12)^-1, E(12)+E(12)^-1, -1*E(12)-E(12)^-1, 0, 2*E(12)+2*E(12)^-1, 0, 0, E(12)+E(12)^-1, -2*E(12)-2*E(12)^-1, -2*E(12)-2*E(12)^-1, 2*E(12)+2*E(12)^-1, 0, 0, -2*E(12)-2*E(12)^-1, 2*E(12)+2*E(12)^-1, 0, 0, -1*E(12)-E(12)^-1, 0, E(12)+E(12)^-1, E(12)+E(12)^-1, 0, -1*E(12)-E(12)^-1, 0, 0, 0, -1*E(12)-E(12)^-1, 0, 0, 0, 0, 0, E(12)+E(12)^-1, E(12)+E(12)^-1, -1*E(12)-E(12)^-1, 0, 0, 0, 0], [4, 4, -4, -4, 4, -4, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 1, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 4, -2, -4, 2, 2, 2, -2, 2, -2, -2, -1, 2, 2, -1, 2, 1, -2, -2, 0, -2, -2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, -1, 1, -1, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(12)-2*E(12)^-1, -2*E(12)-2*E(12)^-1, 2*E(12)+2*E(12)^-1, 2*E(12)+2*E(12)^-1, -1*E(12)-E(12)^-1, -2*E(12)-2*E(12)^-1, 0, E(12)+E(12)^-1, 2*E(12)+2*E(12)^-1, -2*E(12)-2*E(12)^-1, 0, E(12)+E(12)^-1, 0, 0, 2*E(12)+2*E(12)^-1, -1*E(12)-E(12)^-1, 0, 0, 2*E(12)+2*E(12)^-1, 2*E(12)+2*E(12)^-1, 0, 0, -2*E(12)-2*E(12)^-1, -2*E(12)-2*E(12)^-1, E(12)+E(12)^-1, 0, -1*E(12)-E(12)^-1, -1*E(12)-E(12)^-1, 0, E(12)+E(12)^-1, 0, 0, 0, 0, -1*E(12)-E(12)^-1, -1*E(12)-E(12)^-1, E(12)+E(12)^-1, E(12)+E(12)^-1, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, -4, -4, 4, -4, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 1, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 4, -2, -4, 2, 2, 2, -2, 2, -2, -2, -1, 2, 2, -1, 2, 1, -2, -2, 0, -2, -2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, -1, 1, -1, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*E(12)+2*E(12)^-1, 2*E(12)+2*E(12)^-1, -2*E(12)-2*E(12)^-1, -2*E(12)-2*E(12)^-1, E(12)+E(12)^-1, 2*E(12)+2*E(12)^-1, 0, -1*E(12)-E(12)^-1, -2*E(12)-2*E(12)^-1, 2*E(12)+2*E(12)^-1, 0, -1*E(12)-E(12)^-1, 0, 0, -2*E(12)-2*E(12)^-1, E(12)+E(12)^-1, 0, 0, -2*E(12)-2*E(12)^-1, -2*E(12)-2*E(12)^-1, 0, 0, 2*E(12)+2*E(12)^-1, 2*E(12)+2*E(12)^-1, -1*E(12)-E(12)^-1, 0, E(12)+E(12)^-1, E(12)+E(12)^-1, 0, -1*E(12)-E(12)^-1, 0, 0, 0, 0, E(12)+E(12)^-1, E(12)+E(12)^-1, -1*E(12)-E(12)^-1, -1*E(12)-E(12)^-1, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 8, 8, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 2, -4, 2, 2, 2, -4, 2, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 8, -4, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, -8, 4, -4, -8, 8, 4, 2, -2, 4, -4, -2, -4, 4, 4, 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-2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, -2, 2, -4, -2, -2, -2, 4, 2, -4, 4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 8, -8, 0, 0, 0, 0, 0, 0, 4, -4, 4, 4, -4, 4, -4, 4, 4, -2, -2, -2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, 2, -2, 4, 2, 2, 2, -4, -2, 4, -4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, -8, -8, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, -2, 4, -2, -2, -2, 4, -2, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 4, 4, -4, 4, -4, 4, 2, -2, -2, 2, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4*E(12)-4*E(12)^-1, 4*E(12)+4*E(12)^-1, 4*E(12)+4*E(12)^-1, -4*E(12)-4*E(12)^-1, 2*E(12)+2*E(12)^-1, 2*E(12)+2*E(12)^-1, 0, -2*E(12)-2*E(12)^-1, 2*E(12)+2*E(12)^-1, -2*E(12)-2*E(12)^-1, 0, 2*E(12)+2*E(12)^-1, 0, 0, -2*E(12)-2*E(12)^-1, -2*E(12)-2*E(12)^-1, 0, 0, 0, 0, 0, 0, 0, 0, E(12)+E(12)^-1, 0, -1*E(12)-E(12)^-1, E(12)+E(12)^-1, 0, -1*E(12)-E(12)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 4, 4, -4, 4, -4, 4, 2, -2, -2, 2, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4*E(12)+4*E(12)^-1, -4*E(12)-4*E(12)^-1, -4*E(12)-4*E(12)^-1, 4*E(12)+4*E(12)^-1, -2*E(12)-2*E(12)^-1, -2*E(12)-2*E(12)^-1, 0, 2*E(12)+2*E(12)^-1, -2*E(12)-2*E(12)^-1, 2*E(12)+2*E(12)^-1, 0, -2*E(12)-2*E(12)^-1, 0, 0, 2*E(12)+2*E(12)^-1, 2*E(12)+2*E(12)^-1, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(12)-E(12)^-1, 0, E(12)+E(12)^-1, -1*E(12)-E(12)^-1, 0, E(12)+E(12)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 4, 4, 4, 4, -4, -2, 2, 2, -2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4*E(12)-4*E(12)^-1, -4*E(12)-4*E(12)^-1, 4*E(12)+4*E(12)^-1, 4*E(12)+4*E(12)^-1, -2*E(12)-2*E(12)^-1, 2*E(12)+2*E(12)^-1, 0, 2*E(12)+2*E(12)^-1, -2*E(12)-2*E(12)^-1, 2*E(12)+2*E(12)^-1, 0, 2*E(12)+2*E(12)^-1, 0, 0, -2*E(12)-2*E(12)^-1, -2*E(12)-2*E(12)^-1, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(12)-E(12)^-1, 0, E(12)+E(12)^-1, E(12)+E(12)^-1, 0, -1*E(12)-E(12)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 4, 4, 4, 4, -4, -2, 2, 2, -2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4*E(12)+4*E(12)^-1, 4*E(12)+4*E(12)^-1, -4*E(12)-4*E(12)^-1, -4*E(12)-4*E(12)^-1, 2*E(12)+2*E(12)^-1, -2*E(12)-2*E(12)^-1, 0, -2*E(12)-2*E(12)^-1, 2*E(12)+2*E(12)^-1, -2*E(12)-2*E(12)^-1, 0, -2*E(12)-2*E(12)^-1, 0, 0, 2*E(12)+2*E(12)^-1, 2*E(12)+2*E(12)^-1, 0, 0, 0, 0, 0, 0, 0, 0, E(12)+E(12)^-1, 0, -1*E(12)-E(12)^-1, -1*E(12)-E(12)^-1, 0, E(12)+E(12)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_1728_47319);