# Group 1728.47306 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(3698911848691991278430874763685306070689642047449129,1728); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.5; e := GPC.7;
GPerm := Group( (2,3)(4,5)(9,10)(12,14), (4,5)(7,8)(11,13)(15,16), (4,5)(9,11)(10,13)(12,16)(14,15)(18,19), (4,5)(9,10)(11,13)(12,14)(15,16), (9,12,10,14)(11,15,13,16), (9,10)(11,13)(12,14)(15,16), (6,7,8), (1,2,3), (17,18,19) );
GLZN := Group([[[ZmodnZObj(1,78), ZmodnZObj(26,78)], [ZmodnZObj(0,78), ZmodnZObj(1,78)]],[[ZmodnZObj(25,78), ZmodnZObj(0,78)], [ZmodnZObj(0,78), ZmodnZObj(25,78)]],[[ZmodnZObj(25,78), ZmodnZObj(33,78)], [ZmodnZObj(0,78), ZmodnZObj(1,78)]],[[ZmodnZObj(55,78), ZmodnZObj(8,78)], [ZmodnZObj(0,78), ZmodnZObj(61,78)]],[[ZmodnZObj(53,78), ZmodnZObj(0,78)], [ZmodnZObj(0,78), ZmodnZObj(53,78)]],[[ZmodnZObj(73,78), ZmodnZObj(52,78)], [ZmodnZObj(0,78), ZmodnZObj(47,78)]],[[ZmodnZObj(61,78), ZmodnZObj(18,78)], [ZmodnZObj(36,78), ZmodnZObj(43,78)]],[[ZmodnZObj(31,78), ZmodnZObj(39,78)], [ZmodnZObj(0,78), ZmodnZObj(31,78)]],[[ZmodnZObj(40,78), ZmodnZObj(39,78)], [ZmodnZObj(39,78), ZmodnZObj(1,78)]]]);

 
# Booleans 
booleans_1728_47306 := 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_47306:=rec(); 
chartbl_1728_47306.IsFinite:= true; 
chartbl_1728_47306.UnderlyingCharacteristic:= 0; 
chartbl_1728_47306.UnderlyingGroup:= GLZN;
chartbl_1728_47306.Size:= 1728;
chartbl_1728_47306.InfoText:= "Character table for group 1728.47306 downloaded from the LMFDB."; 
chartbl_1728_47306.Identifier:= " C12.D6^2 "; 
chartbl_1728_47306.NrConjugacyClasses:= 162; 
chartbl_1728_47306.ConjugacyClasses:= [[1, 0, 0, 1], [53, 0, 0, 53], [77, 0, 0, 77], [25, 0, 0, 25], [25, 33, 0, 1], [77, 20, 0, 1], [38, 33, 39, 14], [25, 46, 0, 53], [61, 18, 36, 43], [5, 30, 72, 47], [35, 18, 36, 17], [31, 30, 72, 73], [53, 65, 0, 1], [77, 65, 0, 25], [40, 13, 39, 14], [64, 13, 39, 38], [50, 67, 57, 28], [55, 73, 12, 23], [73, 35, 6, 5], [29, 21, 12, 49], [40, 39, 39, 1], [61, 18, 0, 55], [1, 52, 0, 1], [22, 57, 39, 55], [40, 13, 39, 1], [61, 70, 0, 55], [22, 31, 39, 55], [47, 48, 0, 5], [73, 48, 0, 31], [5, 39, 0, 5], [47, 39, 0, 47], [31, 52, 0, 5], [73, 52, 0, 47], [70, 39, 39, 70], [34, 39, 39, 34], [47, 26, 0, 73], [5, 26, 0, 31], [73, 61, 0, 5], [8, 35, 39, 70], [43, 3, 42, 61], [47, 39, 6, 5], [56, 3, 3, 74], [17, 16, 42, 61], [43, 68, 42, 35], [34, 39, 45, 70], [73, 26, 6, 5], [47, 52, 6, 31], [53, 39, 39, 14], [77, 39, 39, 38], [29, 60, 0, 35], [17, 60, 0, 23], [53, 52, 0, 53], [77, 52, 0, 77], [43, 60, 0, 49], [25, 52, 0, 25], [25, 39, 39, 64], [29, 21, 39, 74], [17, 21, 39, 62], [53, 13, 39, 14], [77, 13, 39, 38], [29, 34, 0, 35], [17, 34, 0, 23], [43, 34, 0, 49], [43, 21, 39, 10], [25, 13, 39, 64], [49, 3, 0, 61], [43, 3, 0, 55], [23, 68, 0, 61], [17, 68, 0, 55], [62, 3, 39, 74], [56, 3, 39, 68], [49, 16, 0, 35], [43, 16, 0, 29], [29, 73, 39, 74], [17, 73, 39, 62], [43, 73, 39, 10], [61, 70, 36, 43], [5, 56, 72, 47], [25, 59, 0, 1], [38, 59, 39, 1], [25, 7, 39, 14], [22, 57, 75, 43], [35, 57, 75, 56], [35, 44, 36, 17], [38, 7, 39, 14], [44, 69, 33, 47], [31, 69, 33, 34], [31, 4, 72, 73], [49, 29, 0, 61], [43, 29, 0, 55], [62, 29, 39, 61], [56, 29, 39, 55], [49, 55, 39, 74], [43, 55, 39, 68], [62, 55, 39, 74], [56, 55, 39, 68], [29, 47, 0, 61], [17, 47, 0, 49], [16, 73, 39, 74], [4, 73, 39, 62], [22, 31, 75, 43], [35, 5, 75, 56], [44, 17, 33, 47], [31, 43, 33, 34], [41, 24, 0, 59], [71, 24, 0, 11], [67, 24, 0, 7], [19, 24, 0, 37], [47, 22, 0, 5], [8, 9, 39, 5], [73, 9, 39, 70], [73, 74, 0, 31], [41, 76, 0, 59], [71, 76, 0, 11], [2, 63, 39, 59], [32, 63, 39, 11], [67, 63, 39, 46], [19, 63, 39, 76], [67, 50, 0, 7], [19, 50, 0, 37], [11, 51, 0, 59], [41, 27, 0, 71], [37, 64, 0, 59], [67, 40, 0, 71], [76, 51, 39, 46], [28, 27, 39, 58], [5, 13, 0, 5], [47, 13, 0, 47], [70, 13, 39, 5], [34, 13, 39, 47], [5, 65, 39, 70], [47, 65, 39, 34], [11, 38, 0, 7], [41, 14, 0, 19], [70, 65, 39, 70], [34, 65, 39, 34], [8, 61, 39, 5], [73, 35, 39, 70], [2, 37, 39, 59], [32, 37, 39, 11], [67, 11, 39, 46], [19, 11, 39, 76], [11, 25, 0, 59], [41, 1, 0, 71], [76, 25, 39, 59], [28, 1, 39, 71], [11, 77, 39, 46], [41, 53, 39, 58], [76, 77, 39, 46], [28, 53, 39, 58], [67, 37, 0, 59], [19, 37, 0, 11], [2, 11, 39, 46], [32, 11, 39, 76], [61, 49, 36, 43], [5, 65, 72, 47], [74, 23, 75, 56], [74, 49, 75, 43], [61, 23, 75, 56], [70, 13, 33, 34], [70, 65, 33, 47], [5, 13, 33, 34]];
chartbl_1728_47306.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_47306.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 21, 22, 23, 24, 25, 26, 27, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 21, 21, 22, 22, 23, 23, 22, 23, 21, 24, 24, 25, 25, 26, 26, 26, 24, 25, 22, 22, 22, 22, 22, 22, 22, 22, 27, 27, 27, 23, 23, 23, 21, 21, 21, 21, 23, 23, 21, 21, 23, 26, 26, 24, 24, 24, 24, 26, 26, 22, 22, 22, 22, 25, 25, 25, 25, 54, 54, 54, 54, 55, 56, 56, 55, 63, 63, 64, 64, 64, 64, 63, 63, 54, 54, 54, 54, 54, 54, 55, 55, 56, 56, 56, 56, 54, 54, 55, 55, 65, 65, 76, 76, 76, 76, 63, 63, 64, 64, 64, 64, 63, 63, 54, 54, 54, 54, 55, 55, 55, 56, 56, 55, 56, 56], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 1, 1, 1, 1, 1, 1, 28, 29, 31, 30, 33, 32, 35, 34, 37, 36, 38, 39, 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, 5, 6, 6, 7, 7, 8, 8, 2, 3, 4, 9, 10, 5, 6, 8, 9, 11, 11, 7, 10, 12, 12, 5, 5, 6, 6, 8, 8, 7, 7, 13, 14, 15, 16, 9, 11, 10, 12, 28, 28, 29, 29, 28, 28, 29, 29, 28, 28, 28, 28, 29, 29, 29, 29, 30, 31, 32, 33, 34, 35, 31, 30, 33, 32, 36, 37, 37, 36, 35, 34, 28, 29, 28, 28, 29, 29, 30, 31, 32, 33, 37, 36, 34, 35, 38, 38, 39, 39, 40, 41, 42, 43, 44, 45, 46, 47]];
chartbl_1728_47306.SizesCentralizers:= [1728, 1728, 1728, 1728, 288, 288, 288, 288, 288, 288, 288, 288, 192, 192, 192, 192, 32, 32, 32, 32, 864, 864, 864, 432, 432, 432, 216, 864, 864, 576, 576, 576, 576, 576, 576, 576, 576, 96, 96, 96, 96, 96, 96, 96, 96, 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, 216, 216, 216, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 96, 96, 96, 96, 72, 72, 72, 72, 864, 864, 864, 864, 432, 432, 432, 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, 216, 216, 216, 144, 144, 144, 144, 144, 144, 144, 144, 96, 96, 96, 96, 48, 48, 48, 48, 48, 48, 48, 48];
chartbl_1728_47306.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "2N", "2O", "2P", "2Q", "2R", "2S", "3A", "3B", "3C", "3D", "3E", "3F", "3G", "4A", "4B", "4C1", "4C-1", "4D1", "4D-1", "4E1", "4E-1", "4F1", "4F-1", "4G", "4H", "4I", "4J", "4K", "4L", "4M", "4N", "4O", "4P", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "6H", "6I", "6J", "6K", "6L", "6M", "6N", "6O", "6P", "6Q", "6R", "6S1", "6S-1", "6T1", "6T-1", "6U1", "6U-1", "6V1", "6V-1", "6W", "6X", "6Y", "6Z", "6AA", "6AB", "6AC", "6AD", "6AE", "6AF", "6AG", "6AH", "6AI", "6AJ", "6AK", "6AL1", "6AL-1", "6AM1", "6AM-1", "6AN1", "6AN-1", "6AO1", "6AO-1", "6AP", "6AQ", "6AR", "6AS", "6AT", "6AU", "6AV", "6AW", "12A1", "12A5", "12B1", "12B5", "12C", "12D", "12E", "12F", "12G1", "12G5", "12H1", "12H5", "12I1", "12I5", "12J1", "12J5", "12K1", "12K-1", "12L1", "12L-1", "12M1", "12M-1", "12N1", "12N-1", "12O1", "12O-1", "12P1", "12P-1", "12Q1", "12Q-1", "12R1", "12R-1", "12S", "12T", "12U1", "12U5", "12V1", "12V5", "12W1", "12W-1", "12X1", "12X-1", "12Y1", "12Y-1", "12Z1", "12Z-1", "12AA1", "12AA5", "12AB1", "12AB5", "12AC", "12AD", "12AE", "12AF", "12AG", "12AH", "12AI", "12AJ"];
chartbl_1728_47306.OrderClassRepresentatives:= [1, 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, 4, 4, 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, 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, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12];
chartbl_1728_47306.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, 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, 0, 0, 0, 0, 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, 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, -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, 0, 2*E(12)+2*E(12)^-1, 0, -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, -2*E(12)-2*E(12)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(12)-E(12)^-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, 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, -4, -4, -4, 2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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, 0, -2*E(12)-2*E(12)^-1, 0, 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, 2*E(12)+2*E(12)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(12)+E(12)^-1, -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, 0, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_1728_47306);