# Group 128.1935 downloaded from the LMFDB on 29 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(162257263967680180027424265910,128); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.5;
GPerm := Group( (1,2)(3,12)(4,11)(5,10)(6,9)(7,14)(8,13)(15,16)(17,18)(19,24)(20,22)(21,23), (1,3,5,14)(2,7,10,12)(4,15,6,13)(8,9,16,11)(17,19)(18,20)(21,22)(23,24), (1,3)(2,8)(4,13)(5,14)(6,15)(7,11)(9,12)(10,16)(17,20)(18,22)(19,23)(21,24), (1,4,5,6)(2,9,10,11)(3,13,14,15)(7,8,12,16)(17,20)(18,19)(21,24)(22,23), (1,5)(2,10)(3,14)(4,6)(7,12)(8,16)(9,11)(13,15)(17,21)(18,23)(19,22)(20,24), (1,6,5,4)(2,11,10,9)(3,13,14,15)(7,8,12,16), (1,5)(2,10)(3,14)(4,6)(7,12)(8,16)(9,11)(13,15) );

 
# Booleans 
booleans_128_1935 := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true); 

 
# Character Table 
chartbl_128_1935:=rec(); 
chartbl_128_1935.IsFinite:= true; 
chartbl_128_1935.UnderlyingCharacteristic:= 0; 
chartbl_128_1935.UnderlyingGroup:= GPC;
chartbl_128_1935.Size:= 128;
chartbl_128_1935.InfoText:= "Character table for group 128.1935 downloaded from the LMFDB."; 
chartbl_128_1935.Identifier:= " (C2*D4).D4 "; 
chartbl_128_1935.NrConjugacyClasses:= 26; 
chartbl_128_1935.ConjugacyClasses:= [<identity> of ..., f4*f7, f7, f4, f2*f6, f1*f3, f1*f2*f3, f1, f1*f5, f6, f4*f6, f2, f1*f3*f6, f1*f2*f3*f6, f3, f3*f5, f2*f3, f1*f2, f2*f3*f5, f1*f2*f5, f5, f5*f7, f1*f3*f5, f1*f3*f5*f7, f2*f5, f1*f2*f3*f5];
chartbl_128_1935.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];
chartbl_128_1935.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 4, 10, 10, 10, 10, 11, 11]];
chartbl_128_1935.SizesCentralizers:= [128, 128, 128, 128, 32, 32, 32, 16, 16, 64, 64, 32, 32, 32, 16, 16, 16, 16, 16, 16, 32, 32, 32, 32, 16, 16];
chartbl_128_1935.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "4J", "4K", "8A1", "8A3", "8B1", "8B3", "8C", "8D"];
chartbl_128_1935.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8];
chartbl_128_1935.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], [2, 2, 2, 2, -2, -2, -2, 0, 0, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, 2, 2, 0, 0, -2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, -2, 2, 0, 0, -2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, -2, 0, 0, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(8)-2*E(8)^-1, 0, 2*E(8)+2*E(8)^-1, 0, 0], [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*E(8)+2*E(8)^-1, 0, -2*E(8)-2*E(8)^-1, 0, 0], [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(8)-2*E(8)^-1, 0, 2*E(8)+2*E(8)^-1, 0, 0, 0], [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*E(8)+2*E(8)^-1, 0, -2*E(8)-2*E(8)^-1, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_128_1935);