# Group 768.1088504 downloaded from the LMFDB on 07 October 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(1482085955519320388227563783068344264788363336708,768); a := GPC.1; b := GPC.2; c := GPC.6; d := GPC.8; e := GPC.9;
GPerm := Group( (1,2)(3,5)(4,6)(7,8,10,13,11,14,17,20,9,12,15,18,16,19,21,22), (1,2)(3,4)(5,6)(7,9)(8,12)(10,15)(11,16)(13,18)(14,19)(17,21)(20,22), (8,12)(13,18)(14,19)(20,22), (7,10,11,17,9,15,16,21)(8,13,14,20,12,18,19,22), (7,11,9,16)(8,14,12,19)(10,17,15,21)(13,20,18,22), (7,9)(8,12)(10,15)(11,16)(13,18)(14,19)(17,21)(20,22), (1,3,6)(2,4,5), (1,2)(3,4), (3,4)(5,6) );
GLZN := Group([[[ZmodnZObj(25,68), ZmodnZObj(34,68)], [ZmodnZObj(34,68), ZmodnZObj(25,68)]],[[ZmodnZObj(13,68), ZmodnZObj(0,68)], [ZmodnZObj(0,68), ZmodnZObj(13,68)]],[[ZmodnZObj(9,68), ZmodnZObj(0,68)], [ZmodnZObj(0,68), ZmodnZObj(9,68)]],[[ZmodnZObj(1,68), ZmodnZObj(34,68)], [ZmodnZObj(0,68), ZmodnZObj(1,68)]],[[ZmodnZObj(35,68), ZmodnZObj(17,68)], [ZmodnZObj(51,68), ZmodnZObj(52,68)]],[[ZmodnZObj(0,68), ZmodnZObj(9,68)], [ZmodnZObj(1,68), ZmodnZObj(0,68)]],[[ZmodnZObj(33,68), ZmodnZObj(0,68)], [ZmodnZObj(0,68), ZmodnZObj(33,68)]],[[ZmodnZObj(33,68), ZmodnZObj(0,68)], [ZmodnZObj(0,68), ZmodnZObj(1,68)]],[[ZmodnZObj(59,68), ZmodnZObj(0,68)], [ZmodnZObj(34,68), ZmodnZObj(59,68)]]]);
GLZq := Group([[[ZmodnZObj(17,32), ZmodnZObj(0,32)], [ZmodnZObj(0,32), ZmodnZObj(1,32)]],[[ZmodnZObj(3,32), ZmodnZObj(0,32)], [ZmodnZObj(0,32), ZmodnZObj(3,32)]],[[ZmodnZObj(23,32), ZmodnZObj(13,32)], [ZmodnZObj(4,32), ZmodnZObj(9,32)]],[[ZmodnZObj(9,32), ZmodnZObj(0,32)], [ZmodnZObj(0,32), ZmodnZObj(9,32)]],[[ZmodnZObj(28,32), ZmodnZObj(11,32)], [ZmodnZObj(25,32), ZmodnZObj(3,32)]],[[ZmodnZObj(29,32), ZmodnZObj(16,32)], [ZmodnZObj(16,32), ZmodnZObj(13,32)]],[[ZmodnZObj(1,32), ZmodnZObj(16,32)], [ZmodnZObj(0,32), ZmodnZObj(1,32)]],[[ZmodnZObj(17,32), ZmodnZObj(0,32)], [ZmodnZObj(0,32), ZmodnZObj(17,32)]],[[ZmodnZObj(1,32), ZmodnZObj(16,32)], [ZmodnZObj(16,32), ZmodnZObj(17,32)]]]);

 
# Booleans 
booleans_768_1088504 := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false); 

 
# Character Table 
chartbl_768_1088504:=rec(); 
chartbl_768_1088504.IsFinite:= true; 
chartbl_768_1088504.UnderlyingCharacteristic:= 0; 
chartbl_768_1088504.UnderlyingGroup:= GLZq;
chartbl_768_1088504.Size:= 768;
chartbl_768_1088504.InfoText:= "Character table for group 768.1088504 downloaded from the LMFDB."; 
chartbl_768_1088504.Identifier:= " C2*A4:OD32 "; 
chartbl_768_1088504.NrConjugacyClasses:= 112; 
chartbl_768_1088504.ConjugacyClasses:= [[1, 0, 0, 1], [17, 0, 0, 17], [15, 0, 0, 15], [31, 0, 0, 31], [17, 16, 16, 1], [31, 16, 16, 15], [17, 16, 0, 17], [1, 16, 0, 1], [31, 16, 0, 31], [15, 16, 0, 15], [1, 0, 16, 17], [15, 0, 16, 31], [19, 21, 23, 12], [25, 0, 0, 25], [9, 0, 0, 9], [7, 0, 0, 7], [23, 0, 0, 23], [25, 16, 16, 9], [23, 16, 16, 7], [9, 16, 0, 9], [25, 16, 0, 25], [7, 16, 0, 7], [23, 16, 0, 23], [25, 0, 16, 9], [23, 0, 16, 7], [20, 5, 7, 29], [20, 21, 23, 13], [3, 5, 7, 12], [19, 5, 7, 28], [28, 11, 9, 3], [4, 5, 7, 13], [4, 21, 23, 29], [5, 0, 0, 5], [13, 0, 0, 13], [29, 0, 0, 29], [21, 0, 0, 21], [19, 0, 0, 19], [27, 0, 0, 27], [11, 0, 0, 11], [3, 0, 0, 3], [13, 16, 16, 29], [5, 16, 16, 21], [3, 16, 16, 19], [11, 16, 16, 27], [27, 16, 0, 27], [19, 16, 0, 19], [3, 16, 0, 3], [11, 16, 0, 11], [21, 16, 0, 21], [29, 16, 0, 29], [13, 16, 0, 13], [5, 16, 0, 5], [5, 0, 16, 21], [29, 0, 16, 13], [11, 0, 16, 27], [19, 0, 16, 3], [20, 29, 15, 21], [20, 13, 31, 5], [27, 29, 15, 28], [28, 19, 1, 11], [4, 29, 15, 5], [4, 13, 31, 21], [12, 19, 1, 27], [11, 29, 15, 12], [23, 13, 4, 9], [27, 25, 20, 5], [19, 1, 20, 13], [31, 5, 4, 1], [23, 29, 20, 25], [27, 9, 4, 21], [19, 17, 4, 29], [31, 21, 20, 17], [7, 12, 15, 25], [11, 28, 19, 21], [3, 28, 11, 29], [15, 12, 23, 17], [7, 13, 20, 25], [11, 25, 4, 21], [3, 1, 4, 29], [15, 5, 20, 17], [23, 28, 31, 25], [27, 12, 3, 21], [19, 12, 27, 29], [31, 28, 7, 17], [7, 29, 4, 9], [11, 9, 20, 5], [3, 17, 20, 13], [15, 21, 4, 1], [7, 28, 31, 25], [11, 12, 3, 21], [3, 12, 27, 29], [15, 28, 7, 17], [23, 12, 15, 25], [27, 28, 19, 21], [19, 28, 11, 29], [31, 12, 23, 17], [31, 9, 19, 28], [23, 17, 11, 28], [15, 25, 3, 28], [7, 1, 27, 28], [4, 25, 3, 17], [4, 1, 27, 25], [4, 9, 19, 1], [4, 17, 11, 9], [31, 25, 3, 12], [7, 17, 11, 12], [12, 31, 5, 23], [12, 23, 13, 15], [20, 25, 3, 1], [20, 17, 11, 25], [20, 1, 27, 9], [20, 9, 19, 17]];
chartbl_768_1088504.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];
chartbl_768_1088504.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 13, 13, 13, 13, 13, 13, 13, 14, 15, 15, 14, 15, 14, 14, 15, 15, 14, 15, 14, 14, 15, 15, 14, 14, 15, 15, 14, 14, 15, 14, 15, 28, 28, 28, 28, 28, 28, 28, 28, 33, 34, 35, 36, 49, 50, 51, 52, 33, 34, 35, 36, 36, 35, 34, 33, 49, 50, 51, 52, 52, 51, 50, 49, 36, 35, 34, 33, 52, 51, 50, 49, 63, 64, 63, 64, 63, 64, 63, 64, 63, 64, 64, 63, 63, 64, 64, 63], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 15, 14, 17, 16, 18, 19, 21, 20, 23, 22, 24, 25, 3, 4, 2, 5, 5, 6, 6, 35, 36, 33, 34, 39, 40, 37, 38, 42, 41, 44, 43, 47, 48, 45, 46, 51, 52, 49, 50, 54, 53, 56, 55, 16, 17, 18, 18, 19, 19, 15, 14, 67, 68, 65, 66, 71, 72, 69, 70, 75, 76, 73, 74, 79, 80, 77, 78, 83, 84, 81, 82, 87, 88, 85, 86, 91, 92, 89, 90, 95, 96, 93, 94, 35, 36, 34, 33, 37, 38, 40, 39, 41, 42, 42, 41, 43, 44, 44, 43]];
chartbl_768_1088504.SizesCentralizers:= [768, 768, 768, 768, 384, 384, 256, 256, 256, 256, 128, 128, 96, 768, 768, 768, 768, 384, 384, 256, 256, 256, 256, 128, 128, 96, 96, 96, 96, 96, 96, 96, 768, 768, 768, 768, 768, 768, 768, 768, 384, 384, 384, 384, 256, 256, 256, 256, 256, 256, 256, 256, 128, 128, 128, 128, 96, 96, 96, 96, 96, 96, 96, 96, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96];
chartbl_768_1088504.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "3A", "4A1", "4A-1", "4B1", "4B-1", "4C", "4D", "4E1", "4E-1", "4F1", "4F-1", "4G", "4H", "6A", "6B", "6C", "6D1", "6D-1", "6E1", "6E-1", "8A1", "8A-1", "8A3", "8A-3", "8B1", "8B-1", "8B3", "8B-3", "8C1", "8C-1", "8D1", "8D-1", "8E1", "8E-1", "8E3", "8E-3", "8F1", "8F-1", "8F3", "8F-3", "8G1", "8G-1", "8H1", "8H-1", "12A1", "12A-1", "12B1", "12B5", "12C1", "12C5", "12D1", "12D-1", "16A1", "16A-1", "16A3", "16A-3", "16B1", "16B-1", "16B3", "16B-3", "16C1", "16C-1", "16C3", "16C-3", "16D1", "16D-1", "16D3", "16D-3", "16E1", "16E-1", "16E3", "16E-3", "16F1", "16F-1", "16F3", "16F-3", "16G1", "16G-1", "16G3", "16G-3", "16H1", "16H-1", "16H3", "16H-3", "24A1", "24A-1", "24A5", "24A-5", "24B1", "24B-1", "24B5", "24B-5", "24C1", "24C-1", "24C7", "24C-7", "24D1", "24D-1", "24D7", "24D-7"];
chartbl_768_1088504.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 12, 12, 12, 12, 12, 12, 12, 12, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24];
chartbl_768_1088504.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, 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0, 0, E(24)^3, -1*E(24)^3+2*E(24)^7, -1*E(24)^9, E(24)+E(24)^5, -1*E(24)-E(24)^5, -1*E(24)^3+2*E(24)^7, E(24)^3, E(24)+E(24)^5, -1*E(24)^3, -1*E(24)^3, E(24)^9, -1*E(24)-E(24)^5, E(24)^9, E(24)^3-2*E(24)^7, E(24)^3-2*E(24)^7, -1*E(24)^9], [2, -2, 2, -2, 0, 0, 2, -2, 2, -2, 0, 0, -1, -2*E(24)^6, 2*E(24)^6, 2*E(24)^6, -2*E(24)^6, 0, 0, 2*E(24)^6, 2*E(24)^6, -2*E(24)^6, -2*E(24)^6, 0, 0, 1-2*E(24)^4, -1, -1+2*E(24)^4, -1+2*E(24)^4, 1, 1-2*E(24)^4, 1, -2*E(24)^3, -2*E(24)^3, 2*E(24)^3, 2*E(24)^9, 2*E(24)^9, -2*E(24)^9, 2*E(24)^3, -2*E(24)^9, 0, 0, 0, 0, 2*E(24)^3, -2*E(24)^3, -2*E(24)^9, -2*E(24)^3, 2*E(24)^9, 2*E(24)^9, 2*E(24)^3, -2*E(24)^9, 0, 0, 0, 0, E(24)^6, E(24)^2+E(24)^-2, E(24)^6, -1*E(24)^2-E(24)^-2, E(24)^2+E(24)^-2, -1*E(24)^2-E(24)^-2, -1*E(24)^6, -1*E(24)^6, 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, -1*E(24)^9, -1*E(24)-E(24)^5, E(24)^3, -1*E(24)^3+2*E(24)^7, -1*E(24)^3+2*E(24)^7, E(24)+E(24)^5, E(24)^9, E(24)^3-2*E(24)^7, -1*E(24)^9, E(24)^9, E(24)^3, E(24)^3-2*E(24)^7, -1*E(24)^3, -1*E(24)-E(24)^5, E(24)+E(24)^5, -1*E(24)^3], [2, -2, 2, -2, 0, 0, 2, -2, 2, -2, 0, 0, -1, 2*E(24)^6, -2*E(24)^6, -2*E(24)^6, 2*E(24)^6, 0, 0, -2*E(24)^6, -2*E(24)^6, 2*E(24)^6, 2*E(24)^6, 0, 0, -1+2*E(24)^4, -1, 1-2*E(24)^4, 1-2*E(24)^4, 1, -1+2*E(24)^4, 1, 2*E(24)^9, 2*E(24)^9, -2*E(24)^9, -2*E(24)^3, -2*E(24)^3, 2*E(24)^3, -2*E(24)^9, 2*E(24)^3, 0, 0, 0, 0, -2*E(24)^9, 2*E(24)^9, 2*E(24)^3, 2*E(24)^9, -2*E(24)^3, -2*E(24)^3, -2*E(24)^9, 2*E(24)^3, 0, 0, 0, 0, -1*E(24)^6, E(24)^2+E(24)^-2, -1*E(24)^6, -1*E(24)^2-E(24)^-2, E(24)^2+E(24)^-2, -1*E(24)^2-E(24)^-2, E(24)^6, E(24)^6, 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, E(24)^3, -1*E(24)^3+2*E(24)^7, -1*E(24)^9, -1*E(24)-E(24)^5, -1*E(24)-E(24)^5, E(24)^3-2*E(24)^7, -1*E(24)^3, E(24)+E(24)^5, E(24)^3, -1*E(24)^3, -1*E(24)^9, E(24)+E(24)^5, E(24)^9, -1*E(24)^3+2*E(24)^7, E(24)^3-2*E(24)^7, E(24)^9], [2, -2, 2, -2, 0, 0, 2, -2, 2, -2, 0, 0, -1, -2*E(24)^6, 2*E(24)^6, 2*E(24)^6, -2*E(24)^6, 0, 0, 2*E(24)^6, 2*E(24)^6, -2*E(24)^6, -2*E(24)^6, 0, 0, 1-2*E(24)^4, -1, -1+2*E(24)^4, -1+2*E(24)^4, 1, 1-2*E(24)^4, 1, 2*E(24)^3, 2*E(24)^3, -2*E(24)^3, -2*E(24)^9, -2*E(24)^9, 2*E(24)^9, -2*E(24)^3, 2*E(24)^9, 0, 0, 0, 0, -2*E(24)^3, 2*E(24)^3, 2*E(24)^9, 2*E(24)^3, -2*E(24)^9, -2*E(24)^9, -2*E(24)^3, 2*E(24)^9, 0, 0, 0, 0, E(24)^6, E(24)^2+E(24)^-2, E(24)^6, -1*E(24)^2-E(24)^-2, E(24)^2+E(24)^-2, -1*E(24)^2-E(24)^-2, -1*E(24)^6, -1*E(24)^6, 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, E(24)^9, E(24)+E(24)^5, -1*E(24)^3, E(24)^3-2*E(24)^7, E(24)^3-2*E(24)^7, -1*E(24)-E(24)^5, -1*E(24)^9, -1*E(24)^3+2*E(24)^7, E(24)^9, -1*E(24)^9, -1*E(24)^3, -1*E(24)^3+2*E(24)^7, E(24)^3, E(24)+E(24)^5, -1*E(24)-E(24)^5, E(24)^3], [2, -2, 2, -2, 0, 0, 2, -2, 2, -2, 0, 0, -1, 2*E(24)^6, -2*E(24)^6, -2*E(24)^6, 2*E(24)^6, 0, 0, -2*E(24)^6, -2*E(24)^6, 2*E(24)^6, 2*E(24)^6, 0, 0, -1+2*E(24)^4, -1, 1-2*E(24)^4, 1-2*E(24)^4, 1, -1+2*E(24)^4, 1, -2*E(24)^9, -2*E(24)^9, 2*E(24)^9, 2*E(24)^3, 2*E(24)^3, -2*E(24)^3, 2*E(24)^9, -2*E(24)^3, 0, 0, 0, 0, 2*E(24)^9, -2*E(24)^9, -2*E(24)^3, -2*E(24)^9, 2*E(24)^3, 2*E(24)^3, 2*E(24)^9, -2*E(24)^3, 0, 0, 0, 0, -1*E(24)^6, E(24)^2+E(24)^-2, -1*E(24)^6, -1*E(24)^2-E(24)^-2, E(24)^2+E(24)^-2, -1*E(24)^2-E(24)^-2, E(24)^6, E(24)^6, 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, -1*E(24)^3, E(24)^3-2*E(24)^7, E(24)^9, E(24)+E(24)^5, E(24)+E(24)^5, -1*E(24)^3+2*E(24)^7, E(24)^3, -1*E(24)-E(24)^5, -1*E(24)^3, E(24)^3, E(24)^9, -1*E(24)-E(24)^5, -1*E(24)^9, E(24)^3-2*E(24)^7, -1*E(24)^3+2*E(24)^7, -1*E(24)^9], [2, -2, 2, -2, 0, 0, 2, -2, 2, -2, 0, 0, -1, -2*E(24)^6, 2*E(24)^6, 2*E(24)^6, -2*E(24)^6, 0, 0, 2*E(24)^6, 2*E(24)^6, -2*E(24)^6, -2*E(24)^6, 0, 0, -1+2*E(24)^4, -1, 1-2*E(24)^4, 1-2*E(24)^4, 1, -1+2*E(24)^4, 1, -2*E(24)^3, -2*E(24)^3, 2*E(24)^3, 2*E(24)^9, 2*E(24)^9, -2*E(24)^9, 2*E(24)^3, -2*E(24)^9, 0, 0, 0, 0, 2*E(24)^3, -2*E(24)^3, -2*E(24)^9, -2*E(24)^3, 2*E(24)^9, 2*E(24)^9, 2*E(24)^3, -2*E(24)^9, 0, 0, 0, 0, E(24)^6, -1*E(24)^2-E(24)^-2, E(24)^6, E(24)^2+E(24)^-2, -1*E(24)^2-E(24)^-2, E(24)^2+E(24)^-2, -1*E(24)^6, -1*E(24)^6, 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, -1*E(24)^9, E(24)+E(24)^5, E(24)^3, E(24)^3-2*E(24)^7, E(24)^3-2*E(24)^7, -1*E(24)-E(24)^5, E(24)^9, -1*E(24)^3+2*E(24)^7, -1*E(24)^9, E(24)^9, E(24)^3, -1*E(24)^3+2*E(24)^7, -1*E(24)^3, E(24)+E(24)^5, -1*E(24)-E(24)^5, -1*E(24)^3], [2, -2, 2, -2, 0, 0, 2, -2, 2, -2, 0, 0, -1, 2*E(24)^6, -2*E(24)^6, -2*E(24)^6, 2*E(24)^6, 0, 0, -2*E(24)^6, -2*E(24)^6, 2*E(24)^6, 2*E(24)^6, 0, 0, 1-2*E(24)^4, -1, -1+2*E(24)^4, -1+2*E(24)^4, 1, 1-2*E(24)^4, 1, 2*E(24)^9, 2*E(24)^9, -2*E(24)^9, -2*E(24)^3, -2*E(24)^3, 2*E(24)^3, -2*E(24)^9, 2*E(24)^3, 0, 0, 0, 0, -2*E(24)^9, 2*E(24)^9, 2*E(24)^3, 2*E(24)^9, -2*E(24)^3, -2*E(24)^3, -2*E(24)^9, 2*E(24)^3, 0, 0, 0, 0, -1*E(24)^6, -1*E(24)^2-E(24)^-2, -1*E(24)^6, E(24)^2+E(24)^-2, -1*E(24)^2-E(24)^-2, E(24)^2+E(24)^-2, E(24)^6, E(24)^6, 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, E(24)^3, E(24)^3-2*E(24)^7, -1*E(24)^9, E(24)+E(24)^5, E(24)+E(24)^5, -1*E(24)^3+2*E(24)^7, -1*E(24)^3, -1*E(24)-E(24)^5, E(24)^3, -1*E(24)^3, -1*E(24)^9, -1*E(24)-E(24)^5, E(24)^9, E(24)^3-2*E(24)^7, -1*E(24)^3+2*E(24)^7, E(24)^9], [2, -2, 2, -2, 0, 0, 2, -2, 2, -2, 0, 0, -1, -2*E(24)^6, 2*E(24)^6, 2*E(24)^6, -2*E(24)^6, 0, 0, 2*E(24)^6, 2*E(24)^6, -2*E(24)^6, -2*E(24)^6, 0, 0, -1+2*E(24)^4, -1, 1-2*E(24)^4, 1-2*E(24)^4, 1, -1+2*E(24)^4, 1, 2*E(24)^3, 2*E(24)^3, -2*E(24)^3, -2*E(24)^9, -2*E(24)^9, 2*E(24)^9, -2*E(24)^3, 2*E(24)^9, 0, 0, 0, 0, -2*E(24)^3, 2*E(24)^3, 2*E(24)^9, 2*E(24)^3, -2*E(24)^9, -2*E(24)^9, -2*E(24)^3, 2*E(24)^9, 0, 0, 0, 0, E(24)^6, -1*E(24)^2-E(24)^-2, E(24)^6, E(24)^2+E(24)^-2, -1*E(24)^2-E(24)^-2, E(24)^2+E(24)^-2, -1*E(24)^6, -1*E(24)^6, 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, E(24)^9, -1*E(24)-E(24)^5, -1*E(24)^3, -1*E(24)^3+2*E(24)^7, -1*E(24)^3+2*E(24)^7, E(24)+E(24)^5, -1*E(24)^9, E(24)^3-2*E(24)^7, E(24)^9, -1*E(24)^9, -1*E(24)^3, E(24)^3-2*E(24)^7, E(24)^3, -1*E(24)-E(24)^5, E(24)+E(24)^5, E(24)^3], [2, -2, 2, -2, 0, 0, 2, -2, 2, -2, 0, 0, -1, 2*E(24)^6, -2*E(24)^6, -2*E(24)^6, 2*E(24)^6, 0, 0, -2*E(24)^6, -2*E(24)^6, 2*E(24)^6, 2*E(24)^6, 0, 0, 1-2*E(24)^4, -1, -1+2*E(24)^4, -1+2*E(24)^4, 1, 1-2*E(24)^4, 1, -2*E(24)^9, -2*E(24)^9, 2*E(24)^9, 2*E(24)^3, 2*E(24)^3, -2*E(24)^3, 2*E(24)^9, -2*E(24)^3, 0, 0, 0, 0, 2*E(24)^9, -2*E(24)^9, -2*E(24)^3, -2*E(24)^9, 2*E(24)^3, 2*E(24)^3, 2*E(24)^9, -2*E(24)^3, 0, 0, 0, 0, -1*E(24)^6, -1*E(24)^2-E(24)^-2, -1*E(24)^6, E(24)^2+E(24)^-2, -1*E(24)^2-E(24)^-2, E(24)^2+E(24)^-2, E(24)^6, E(24)^6, 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, 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-6*E(8)^2, 6*E(8)^2, -6*E(8)^2, 0, 0, 2*E(8)^2, -2*E(8)^2, 2*E(8)^2, -2*E(8)^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6*E(8)^3, -6*E(8)^3, -6*E(8)^3, 6*E(8), -6*E(8), 6*E(8), 6*E(8)^3, -6*E(8), 0, 0, 0, 0, 2*E(8)^3, 2*E(8)^3, -2*E(8), -2*E(8)^3, -2*E(8), 2*E(8), -2*E(8)^3, 2*E(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, 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], [6, -6, -6, 6, 0, 0, 2, -2, -2, 2, 0, 0, 0, -6*E(8)^2, 6*E(8)^2, -6*E(8)^2, 6*E(8)^2, 0, 0, -2*E(8)^2, 2*E(8)^2, -2*E(8)^2, 2*E(8)^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6*E(8), -6*E(8), -6*E(8), 6*E(8)^3, -6*E(8)^3, 6*E(8)^3, 6*E(8), -6*E(8)^3, 0, 0, 0, 0, 2*E(8), 2*E(8), -2*E(8)^3, -2*E(8), -2*E(8)^3, 2*E(8)^3, -2*E(8), 2*E(8)^3, 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, 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], [6, -6, -6, 6, 0, 0, 2, -2, -2, 2, 0, 0, 0, 6*E(8)^2, -6*E(8)^2, 6*E(8)^2, -6*E(8)^2, 0, 0, 2*E(8)^2, -2*E(8)^2, 2*E(8)^2, -2*E(8)^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6*E(8)^3, 6*E(8)^3, 6*E(8)^3, -6*E(8), 6*E(8), -6*E(8), -6*E(8)^3, 6*E(8), 0, 0, 0, 0, -2*E(8)^3, -2*E(8)^3, 2*E(8), 2*E(8)^3, 2*E(8), -2*E(8), 2*E(8)^3, -2*E(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, 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], [6, -6, 6, -6, 0, 0, -2, 2, -2, 2, 0, 0, 0, -6*E(8)^2, 6*E(8)^2, 6*E(8)^2, -6*E(8)^2, 0, 0, -2*E(8)^2, -2*E(8)^2, 2*E(8)^2, 2*E(8)^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6*E(8), -6*E(8), 6*E(8), 6*E(8)^3, 6*E(8)^3, -6*E(8)^3, 6*E(8), -6*E(8)^3, 0, 0, 0, 0, -2*E(8), 2*E(8), 2*E(8)^3, 2*E(8), -2*E(8)^3, -2*E(8)^3, -2*E(8), 2*E(8)^3, 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, 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], [6, -6, 6, -6, 0, 0, -2, 2, -2, 2, 0, 0, 0, 6*E(8)^2, -6*E(8)^2, -6*E(8)^2, 6*E(8)^2, 0, 0, 2*E(8)^2, 2*E(8)^2, -2*E(8)^2, -2*E(8)^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6*E(8)^3, 6*E(8)^3, -6*E(8)^3, -6*E(8), -6*E(8), 6*E(8), -6*E(8)^3, 6*E(8), 0, 0, 0, 0, 2*E(8)^3, -2*E(8)^3, -2*E(8), -2*E(8)^3, 2*E(8), 2*E(8), 2*E(8)^3, -2*E(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, 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], [6, -6, 6, -6, 0, 0, -2, 2, -2, 2, 0, 0, 0, -6*E(8)^2, 6*E(8)^2, 6*E(8)^2, -6*E(8)^2, 0, 0, -2*E(8)^2, -2*E(8)^2, 2*E(8)^2, 2*E(8)^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6*E(8), 6*E(8), -6*E(8), -6*E(8)^3, -6*E(8)^3, 6*E(8)^3, -6*E(8), 6*E(8)^3, 0, 0, 0, 0, 2*E(8), -2*E(8), -2*E(8)^3, -2*E(8), 2*E(8)^3, 2*E(8)^3, 2*E(8), -2*E(8)^3, 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, 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], [6, -6, 6, -6, 0, 0, -2, 2, -2, 2, 0, 0, 0, 6*E(8)^2, -6*E(8)^2, -6*E(8)^2, 6*E(8)^2, 0, 0, 2*E(8)^2, 2*E(8)^2, -2*E(8)^2, -2*E(8)^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6*E(8)^3, -6*E(8)^3, 6*E(8)^3, 6*E(8), 6*E(8), -6*E(8), 6*E(8)^3, -6*E(8), 0, 0, 0, 0, -2*E(8)^3, 2*E(8)^3, 2*E(8), 2*E(8)^3, -2*E(8), -2*E(8), -2*E(8)^3, 2*E(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, 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]];
ConvertToLibraryCharacterTableNC(chartbl_768_1088504);