# Group 23328.du downloaded from the LMFDB on 22 July 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(1045083736268556626812304653039508791097999859400754713314403644908252782167013454461940423225757228398751968658508025356151037155041542547071668467389356710451253772226716586582387653380773253183660765608879318948127,23328); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.5; e := GPC.7; f := GPC.8; g := GPC.9; h := GPC.10; i := GPC.11;
GPerm := Group( (1,21,17,9,22,13)(2,19,18,7,23,14)(3,20,16,8,24,15)(4,25,11)(5,26,12)(6,27,10), (1,3)(4,16,27,20,7,23,14,10)(5,18,25,19,8,22,15,12)(6,17,26,21,9,24,13,11) );

 
# Booleans 
booleans_23328_du := 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 := false,
solvable := true,
supersolvable := false); 

 
# Character Table 
chartbl_23328_du:=rec(); 
chartbl_23328_du.IsFinite:= true; 
chartbl_23328_du.UnderlyingCharacteristic:= 0; 
chartbl_23328_du.UnderlyingGroup:= GPerm;
chartbl_23328_du.Size:= 23328;
chartbl_23328_du.InfoText:= "Character table for group 23328.du downloaded from the LMFDB."; 
chartbl_23328_du.Identifier:= " C3^3:S3^2.S4 "; 
chartbl_23328_du.NrConjugacyClasses:= 41; 
chartbl_23328_du.ConjugacyClasses:= [(), (1,16)(2,18)(3,17)(4,13)(5,15)(6,14)(7,10)(8,12)(9,11)(19,25)(20,27)(21,26)(23,24), (2,3)(4,6)(7,8)(10,12)(13,14)(17,18)(19,20)(23,24)(25,27), (1,11)(2,12)(3,10)(4,17)(5,18)(6,16)(7,14)(8,15)(9,13)(22,25)(23,26)(24,27), (4,23)(5,24)(6,22)(7,18)(8,16)(9,17)(10,21)(11,19)(12,20), (1,9)(2,8)(3,7)(4,6)(10,16)(11,18)(12,17)(14,15)(19,26)(20,25)(21,27)(22,23), (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), (1,12,20)(2,10,21)(3,11,19)(4,15,23)(5,13,24)(6,14,22)(7,18,26)(8,16,27)(9,17,25), (10,12,11)(13,15,14)(16,18,17)(19,20,21)(22,23,24)(25,26,27), (1,22,16)(2,23,17)(3,24,18)(4,27,11)(5,25,12)(6,26,10)(7,20,15)(8,21,13)(9,19,14), (1,17,24)(2,18,22)(3,16,23)(4,27,11)(5,25,12)(6,26,10), (1,5,9)(2,6,7)(3,4,8)(10,17,15)(11,18,13)(12,16,14)(19,20,21)(22,23,24)(25,26,27), (1,11,19)(2,12,20)(3,10,21)(4,14,22)(5,15,23)(6,13,24)(7,17,25)(8,18,26)(9,16,27), (1,13,26)(2,14,27)(3,15,25)(4,21,16)(5,19,17)(6,20,18)(7,8,9)(10,12,11), (1,25,12)(2,26,10)(3,27,11)(4,19,15)(5,20,13)(6,21,14)(7,22,18)(8,23,16)(9,24,17), (1,15,19,17)(2,13,20,18)(3,14,21,16)(4,22,27,9)(5,23,25,7)(6,24,26,8), (1,19,7,18)(2,21,8,17)(3,20,9,16)(4,5)(10,13,26,23)(11,15,27,22)(12,14,25,24), (1,21,2,19,3,20)(4,26,5,27,6,25)(7,22,8,23,9,24)(10,12,11)(13,17,14,18,15,16), (1,25,2,26,3,27)(4,19,5,20,6,21)(7,22,8,23,9,24)(10,12,11)(13,15,14)(16,18,17), (1,19,2,21,3,20)(4,26,6,27,5,25)(7,24)(8,23)(9,22)(10,12)(13,16,14,18,15,17), (1,16,23,2,18,24)(3,17,22)(4,10,26,5,12,27)(6,11,25)(7,13,20,8,15,21)(9,14,19), (1,25,12,9,20,17)(2,27,10,8,21,16)(3,26,11,7,19,18)(4,22,15,6,23,14)(5,24,13), (1,13,25)(2,14,26)(3,15,27)(4,8,19,23,16,11)(5,9,20,24,17,12)(6,7,21,22,18,10), (1,25,17,12,24,5)(2,27,18,11,22,4)(3,26,16,10,23,6)(7,15)(8,14)(9,13)(19,21), (1,16,22)(2,18,23,3,17,24)(4,27,10,6,25,12)(5,26,11)(7,8)(13,14)(19,20), (1,9)(2,7)(3,8)(10,11,12)(13,18,15,17,14,16)(19,22,20,23,21,24)(25,27,26), (1,8,3,9,2,7)(4,6)(10,13,11,15,12,14)(16,18)(19,21)(22,25,23,27,24,26), (1,25,24,5,17,12)(2,26,22,6,18,10)(3,27,23,4,16,11)(13,20)(14,21)(15,19), (1,13,5,11,9,18)(2,14,6,12,7,16)(3,15,4,10,8,17)(19,21,20)(22,27,23,25,24,26), (1,21,13,16,26,4)(2,20,14,18,27,6)(3,19,15,17,25,5)(7,11,8,10,9,12)(23,24), (1,27,11,9,19,16)(2,25,12,7,20,17)(3,26,10,8,21,18)(4,22,14)(5,23,15)(6,24,13), (1,9,22,19,16,14)(2,8,23,21,17,13)(3,7,24,20,18,15)(4,12,27,5,11,25)(6,10,26), (1,11,25,3,12,27)(2,10,26)(4,13,19,5,15,20)(6,14,21)(7,18,22)(8,17,23,9,16,24), (1,8,15,6,19,24,17,26)(2,9,13,4,20,22,18,27)(3,7,14,5,21,23,16,25), (1,26,17,24,19,6,15,8)(2,27,18,22,20,4,13,9)(3,25,16,23,21,5,14,7), (1,13,19,27,8,22,17,11)(2,15,20,26,9,24,18,10)(3,14,21,25,7,23,16,12)(4,6), (1,11,17,22,8,27,19,13)(2,10,18,24,9,26,20,15)(3,12,16,23,7,25,21,14)(4,6), (1,5,24,3,4,23,2,6,22)(7,14,16,9,13,18,8,15,17)(10,27,21,12,26,20,11,25,19), (1,18,21,15,2,16,19,13,3,17,20,14)(4,7,26,22,5,8,27,23,6,9,25,24)(10,11,12), (1,5,18,8,21,27,15,23,2,6,16,9,19,25,13,24,3,4,17,7,20,26,14,22)(10,12,11), (1,22,14,26,20,7,17,4,3,24,13,25,19,9,16,6,2,23,15,27,21,8,18,5)(10,11,12)];
chartbl_23328_du.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];
chartbl_23328_du.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 7, 8, 9, 10, 11, 12, 13, 14, 15, 4, 4, 7, 7, 9, 8, 8, 8, 11, 11, 9, 9, 11, 12, 14, 13, 10, 15, 16, 16, 16, 16, 38, 18, 39, 39], [1, 2, 3, 4, 5, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16, 17, 4, 5, 2, 3, 6, 5, 2, 3, 5, 6, 4, 4, 2, 5, 6, 3, 34, 35, 36, 37, 7, 16, 34, 35]];
chartbl_23328_du.SizesCentralizers:= [23328, 864, 864, 288, 216, 72, 11664, 972, 972, 486, 324, 162, 162, 54, 54, 48, 16, 144, 108, 108, 108, 36, 36, 36, 36, 36, 36, 36, 18, 18, 18, 18, 18, 48, 48, 16, 16, 27, 24, 24, 24];
chartbl_23328_du.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "3A", "3B", "3C", "3D", "3E", "3F", "3G", "3H", "3I", "4A", "4B", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "6H", "6I", "6J", "6K", "6L", "6M", "6N", "6O", "6P", "8A1", "8A-1", "8B1", "8B-1", "9A", "12A", "24A1", "24A-1"];
chartbl_23328_du.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 9, 12, 24, 24];
chartbl_23328_du.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], [2, 2, 2, 2, 0, 0, 2, 2, 2, 2, -1, -1, 2, -1, -1, 2, 2, 2, 0, 2, 2, 0, 0, -1, -1, 0, 0, -1, -1, -1, 0, 0, -1, 0, 0, 0, 0, -1, 2, 0, 0], [2, -2, -2, 2, 0, 0, 2, 2, 2, 2, -1, -1, 2, -1, -1, 2, -2, 2, 0, -2, -2, 0, 0, 1, 1, 0, 0, -1, -1, 1, 0, 0, 1, 0, 0, 0, 0, -1, 2, 0, 0], [2, -2, 2, -2, 0, 0, 2, 2, 2, 2, -1, -1, 2, -1, -1, 0, 0, -2, 0, -2, 2, 0, 0, 1, -1, 0, 0, 1, 1, 1, 0, 0, -1, -1*E(8)-E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3, -1, 0, -1*E(8)-E(8)^3, E(8)+E(8)^3], [2, -2, 2, -2, 0, 0, 2, 2, 2, 2, -1, -1, 2, -1, -1, 0, 0, -2, 0, -2, 2, 0, 0, 1, -1, 0, 0, 1, 1, 1, 0, 0, -1, E(8)+E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3, -1, 0, E(8)+E(8)^3, -1*E(8)-E(8)^3], [2, 2, -2, -2, 0, 0, 2, 2, 2, 2, -1, -1, 2, -1, -1, 0, 0, -2, 0, 2, -2, 0, 0, -1, 1, 0, 0, 1, 1, -1, 0, 0, 1, -1*E(8)-E(8)^3, E(8)+E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3, -1, 0, -1*E(8)-E(8)^3, E(8)+E(8)^3], [2, 2, -2, -2, 0, 0, 2, 2, 2, 2, -1, -1, 2, -1, -1, 0, 0, -2, 0, 2, -2, 0, 0, -1, 1, 0, 0, 1, 1, -1, 0, 0, 1, E(8)+E(8)^3, -1*E(8)-E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3, -1, 0, E(8)+E(8)^3, -1*E(8)-E(8)^3], [3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 0, 0, 3, 0, 0, -1, -1, 3, 1, 3, 3, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, -1, -1, -1, -1, 0, -1, -1, -1], [3, 3, 3, 3, -1, -1, 3, 3, 3, 3, 0, 0, 3, 0, 0, -1, -1, 3, -1, 3, 3, -1, -1, 0, 0, -1, -1, 0, 0, 0, -1, -1, 0, 1, 1, 1, 1, 0, -1, 1, 1], [3, -3, -3, 3, -1, 1, 3, 3, 3, 3, 0, 0, 3, 0, 0, -1, 1, 3, -1, -3, -3, 1, -1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 1, 1, -1, -1, 0, -1, 1, 1], [3, -3, -3, 3, 1, -1, 3, 3, 3, 3, 0, 0, 3, 0, 0, -1, 1, 3, 1, -3, -3, -1, 1, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, -1, -1, 1, 1, 0, -1, -1, -1], [4, -4, 4, -4, 0, 0, 4, 4, 4, 4, 1, 1, 4, 1, 1, 0, 0, -4, 0, -4, 4, 0, 0, -1, 1, 0, 0, -1, -1, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [4, 4, -4, -4, 0, 0, 4, 4, 4, 4, 1, 1, 4, 1, 1, 0, 0, -4, 0, 4, -4, 0, 0, 1, -1, 0, 0, -1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0], [8, 0, 8, 0, 2, 2, 8, -1, 8, -1, 2, 2, -1, 2, -1, 0, 0, 0, 2, 0, -1, -1, -1, 0, 2, 2, 2, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0], [8, 8, 0, 0, 2, 2, 8, 8, -1, -1, 2, 2, -1, -1, 2, 0, 0, 0, 2, -1, 0, 2, 2, 2, 0, -1, -1, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0], [8, 0, 8, 0, -2, -2, 8, -1, 8, -1, 2, 2, -1, 2, -1, 0, 0, 0, -2, 0, -1, 1, 1, 0, 2, -2, -2, 0, 0, 0, 1, 1, -1, 0, 0, 0, 0, -1, 0, 0, 0], [8, 8, 0, 0, -2, -2, 8, 8, -1, -1, 2, 2, -1, -1, 2, 0, 0, 0, -2, -1, 0, -2, -2, 2, 0, 1, 1, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0], [8, -8, 0, 0, -2, 2, 8, 8, -1, -1, 2, 2, -1, -1, 2, 0, 0, 0, -2, 1, 0, 2, -2, -2, 0, 1, -1, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0], [8, -8, 0, 0, 2, -2, 8, 8, -1, -1, 2, 2, -1, -1, 2, 0, 0, 0, 2, 1, 0, -2, 2, -2, 0, -1, 1, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0], [8, 0, -8, 0, -2, 2, 8, -1, 8, -1, 2, 2, -1, 2, -1, 0, 0, 0, -2, 0, 1, -1, 1, 0, -2, -2, 2, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0], [8, 0, -8, 0, 2, -2, 8, -1, 8, -1, 2, 2, -1, 2, -1, 0, 0, 0, 2, 0, 1, 1, -1, 0, -2, 2, -2, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, -1, 0, 0, 0], [16, 0, 0, 0, 0, 4, 16, -2, -2, 7, 4, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [16, 0, 16, 0, 0, 0, 16, -2, 16, -2, -2, -2, -2, -2, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0], [16, 16, 0, 0, 0, 0, 16, 16, -2, -2, -2, -2, -2, 1, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [16, 0, 0, 0, 0, -4, 16, -2, -2, 7, 4, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [16, -16, 0, 0, 0, 0, 16, 16, -2, -2, -2, -2, -2, 1, -2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [16, 0, -16, 0, 0, 0, 16, -2, 16, -2, -2, -2, -2, -2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0], [18, 0, 0, 2, 6, 0, -9, 0, 0, 0, 6, -3, 0, 0, 0, 2, 0, -1, -3, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 2, 2, 0, 0, 0, -1, -1, -1], [18, 0, 0, 2, -6, 0, -9, 0, 0, 0, 6, -3, 0, 0, 0, 2, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, -2, -2, 0, 0, 0, -1, 1, 1], [32, 0, 0, 0, 0, 0, 32, -4, -4, 14, -4, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [36, 0, 0, 4, 0, 0, -18, 0, 0, 0, -6, 3, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0], [36, 0, 0, -4, 0, 0, -18, 0, 0, 0, -6, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, -2*E(8)-2*E(8)^3, 2*E(8)+2*E(8)^3, 0, 0, 0, 0, E(8)+E(8)^3, -1*E(8)-E(8)^3], [36, 0, 0, -4, 0, 0, -18, 0, 0, 0, -6, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 2*E(8)+2*E(8)^3, -2*E(8)-2*E(8)^3, 0, 0, 0, 0, -1*E(8)-E(8)^3, E(8)+E(8)^3], [48, 0, 0, 0, 4, 0, 48, -6, -6, -6, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [48, 0, 0, 0, -4, 0, 48, -6, -6, -6, 0, 0, 3, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [54, 0, 0, 6, 6, 0, -27, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 1, 1, 1], [54, 0, 0, 6, -6, 0, -27, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, -1, -1], [72, 0, 0, -8, 0, 0, -36, 0, 0, 0, 6, -3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_23328_du);