# Group 5184.ch downloaded from the LMFDB on 24 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(3945553605390473532387329284588938891322275011862088236097158853093101777806304434526248661109449906314846916700964551576859793383072941098389556577229839,5184); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.5; e := GPC.8; f := GPC.9; g := GPC.10;
GPerm := Group( (1,8,7,9)(2,3,6,5)(10,15)(11,17)(12,13)(16,18), (1,12,6,18,5,15)(2,10,7,16,3,13)(4,11,9,17,8,14), (1,15,9,12,2,18)(3,14,5,11,4,17)(6,13,8,10,7,16) );

 
# Booleans 
booleans_5184_ch := 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_5184_ch:=rec(); 
chartbl_5184_ch.IsFinite:= true; 
chartbl_5184_ch.UnderlyingCharacteristic:= 0; 
chartbl_5184_ch.UnderlyingGroup:= GPerm;
chartbl_5184_ch.Size:= 5184;
chartbl_5184_ch.InfoText:= "Character table for group 5184.ch downloaded from the LMFDB."; 
chartbl_5184_ch.Identifier:= " C3^4:D4.D4 "; 
chartbl_5184_ch.NrConjugacyClasses:= 24; 
chartbl_5184_ch.ConjugacyClasses:= [(), (10,17)(11,16)(13,14)(15,18), (1,16)(2,11)(3,10)(4,14)(5,15)(6,17)(7,18)(8,13)(9,12), (1,16)(2,18)(3,15)(4,11)(5,13)(6,10)(7,12)(8,17)(9,14), (1,6)(2,8)(3,4)(7,9)(11,18)(12,17)(13,16)(14,15), (10,14,15)(11,12,16)(13,17,18), (1,6,5)(2,7,3)(4,9,8)(10,11,18)(12,13,14)(15,16,17), (1,2,9)(3,4,5)(6,7,8)(10,12,17)(11,13,15)(14,16,18), (2,8,9,3)(4,6,7,5), (1,6,3,7)(2,4,5,9)(10,18,14,12)(11,16,13,17), (1,6,3,7)(2,4,5,9)(10,13,17,14)(11,15,16,18), (1,2)(3,6)(4,8)(5,7)(10,14,17,13)(11,18,16,15), (1,4,2,8)(3,7,6,5)(10,11,16,15)(12,17,14,18), (1,13,9,10)(2,16)(3,18,7,14)(4,12,6,11)(5,15,8,17), (1,6,4,8)(2,9,3,5)(10,12,11,15)(13,14,17,16), (1,13,7,16)(2,12,6,17)(3,11,5,18)(4,10)(8,15,9,14), (1,7,6,9)(2,4,8,3)(11,15,18,14)(12,16,17,13), (2,9)(3,8)(4,7)(5,6)(10,15,14)(11,16,12)(13,18,17), (1,15,6,16,5,17)(2,10,7,11,3,18)(4,13,9,14,8,12), (1,14,2,16,9,18)(3,13,4,15,5,11)(6,17,7,10,8,12), (1,17,6,11,3,16,7,13)(2,10,4,18,5,14,9,12)(8,15), (1,11,6,15,3,16,7,18)(2,14,4,10,5,13,9,17)(8,12), (2,3,9,8)(4,5,7,6)(10,14,15)(11,12,16)(13,17,18), (2,8,9,3)(4,6,7,5)(10,15,14)(11,16,12)(13,18,17)];
chartbl_5184_ch.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];
chartbl_5184_ch.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 6, 7, 8, 2, 5, 5, 2, 5, 5, 5, 5, 5, 6, 7, 8, 10, 11, 18, 18], [1, 2, 3, 4, 5, 1, 1, 1, 9, 10, 11, 12, 13, 14, 15, 16, 17, 2, 3, 4, 21, 22, 9, 9]];
chartbl_5184_ch.SizesCentralizers:= [5184, 288, 144, 144, 64, 324, 162, 162, 144, 32, 32, 16, 16, 16, 16, 16, 8, 36, 18, 18, 8, 8, 36, 36];
chartbl_5184_ch.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "3A", "3B", "3C", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "6A", "6B", "6C", "8A", "8B", "12A1", "12A-1"];
chartbl_5184_ch.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 8, 8, 12, 12];
chartbl_5184_ch.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], [2, -2, -2, 0, 2, 2, 2, 2, 0, 2, -2, 0, 0, 2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0], [2, -2, 0, -2, 2, 2, 2, 2, 0, -2, 2, 0, 0, 0, 0, 2, 0, -2, 0, -2, 0, 0, 0, 0], [2, -2, 0, 2, 2, 2, 2, 2, 0, -2, 2, 0, 0, 0, 0, -2, 0, -2, 0, 2, 0, 0, 0, 0], [2, -2, 2, 0, 2, 2, 2, 2, 0, 2, -2, 0, 0, -2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0], [2, 2, 0, 0, 2, 2, 2, 2, 0, -2, -2, 0, -2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 2, 2, 2, 2, 0, -2, -2, 0, 2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, -4, 4, 4, 4, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2], [4, 0, 0, 0, -4, 4, 4, 4, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2], [16, 8, 0, 0, 0, 7, -2, -2, 8, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1], [16, 8, 0, 0, 0, 7, -2, -2, -8, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1], [16, -8, 0, 0, 0, 7, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -3*E(4), 3*E(4)], [16, -8, 0, 0, 0, 7, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3*E(4), -3*E(4)], [32, 0, 0, 8, 0, -4, -4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [32, 0, 8, 0, 0, -4, 5, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [32, 0, -8, 0, 0, -4, 5, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [32, 0, 0, -8, 0, -4, -4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_5184_ch);