# Group 6144.ze downloaded from the LMFDB on 04 February 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(1614372118149799813814748845874373883761234298927647071458384247669894317222096881983923516752579442428514638772992058596956093255874654916674097690633747580401526930492133385884375101952,6144); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.6; e := GPC.7; f := GPC.8; g := GPC.10; h := GPC.12;
GPerm := Group( (1,9,17)(2,10,18)(3,12,20,4,11,19)(5,13,22,6,14,21)(7,16,23)(8,15,24), (17,18)(19,20)(21,22)(23,24), (7,8)(9,19,10,20)(11,17,12,18)(13,23,14,24)(15,22,16,21), (1,6,2,5)(3,8,4,7)(9,16)(10,15)(11,14)(12,13)(17,20,18,19)(21,23,22,24), (5,8,6,7)(13,16,14,15)(21,23,22,24) );

 
# Booleans 
booleans_6144_ze := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := true,
solvable := true,
supersolvable := false); 

 
# Character Table 
chartbl_6144_ze:=rec(); 
chartbl_6144_ze.IsFinite:= true; 
chartbl_6144_ze.UnderlyingCharacteristic:= 0; 
chartbl_6144_ze.UnderlyingGroup:= GPerm;
chartbl_6144_ze.Size:= 6144;
chartbl_6144_ze.InfoText:= "Character table for group 6144.ze downloaded from the LMFDB."; 
chartbl_6144_ze.Identifier:= " C4^3:(C2^2*S4) "; 
chartbl_6144_ze.NrConjugacyClasses:= 96; 
chartbl_6144_ze.ConjugacyClasses:= [(), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24), (17,18)(19,20)(21,22)(23,24), (9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24), (5,6)(7,8)(13,14)(15,16)(21,22)(23,24), (1,2)(3,4)(13,14)(15,16)(21,22)(23,24), (3,4)(5,6)(11,12)(13,14)(17,18)(23,24), (3,4)(5,6)(9,10)(15,16)(17,18)(23,24), (9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,24)(20,23), (9,13)(10,14)(11,15)(12,16)(17,22)(18,21)(19,23)(20,24), (1,2)(3,4)(5,6)(7,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,24)(20,23), (1,2)(3,4)(5,6)(7,8)(9,13)(10,14)(11,15)(12,16)(17,22)(18,21)(19,23)(20,24), (7,8)(9,21)(10,22)(11,23)(12,24)(13,17)(14,18)(15,20)(16,19), (7,8)(9,23)(10,24)(11,22)(12,21)(13,19)(14,20)(15,17)(16,18), (3,4)(7,8)(9,11)(10,12)(13,16)(14,15)(17,19)(18,20)(21,23)(22,24), (3,4)(7,8)(9,11)(10,12)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23), (3,4)(7,8)(9,13)(10,14)(11,16)(12,15)(17,22)(18,21)(19,24)(20,23), (3,4)(5,6)(7,8)(9,17)(10,18)(11,19)(12,20)(13,22)(14,21)(15,23)(16,24), (3,4)(5,6)(7,8)(9,19)(10,20)(11,18)(12,17)(13,24)(14,23)(15,22)(16,21), (1,3)(2,4)(5,7)(6,8)(9,13)(10,14)(11,16)(12,15)(17,23)(18,24)(19,22)(20,21), (1,5)(2,6)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15)(19,20)(23,24), (1,3)(2,4)(5,8)(6,7)(9,15)(10,16)(11,13)(12,14)(17,22)(18,21)(19,24)(20,23), (1,2)(5,7)(6,8)(9,10)(13,15)(14,16)(19,20)(21,23)(22,24), (1,2)(5,7)(6,8)(9,10)(13,15)(14,16)(17,18)(21,24)(22,23), (7,8)(9,17)(10,18)(11,20)(12,19)(13,21)(14,22)(15,23)(16,24), (5,7)(6,8)(9,17)(10,18)(11,20)(12,19)(13,24)(14,23)(15,21)(16,22), (3,4)(5,6)(7,8)(9,21)(10,22)(11,24)(12,23)(13,18)(14,17)(15,20)(16,19), (1,2)(3,4)(5,7)(6,8)(9,17)(10,18)(11,20)(12,19)(13,23)(14,24)(15,22)(16,21), (1,14,17)(2,13,18)(3,15,19)(4,16,20)(5,9,22)(6,10,21)(7,12,24)(8,11,23), (9,11,10,12)(13,16,14,15)(17,20,18,19)(21,24,22,23), (1,2)(3,4)(5,6)(7,8)(9,11,10,12)(13,16,14,15)(17,19,18,20)(21,23,22,24), (1,2)(3,4)(5,6)(7,8)(9,11,10,12)(13,16,14,15)(17,20,18,19)(21,24,22,23), (9,11,10,12)(13,16,14,15)(17,19,18,20)(21,23,22,24), (1,4,2,3)(13,15,14,16)(17,20,18,19), (1,4,2,3)(5,6)(7,8)(9,11,10,12)(13,14)(15,16)(17,18)(19,20)(21,23,22,24), (5,6)(7,8)(9,11,10,12)(13,15,14,16)(17,20,18,19)(21,23,22,24), (5,6)(7,8)(9,11,10,12)(13,15,14,16)(17,19,18,20)(21,24,22,23), (7,8)(9,21,10,22)(11,23,12,24)(13,17,14,18)(15,20,16,19), (7,8)(9,23,10,24)(11,22,12,21)(13,19,14,20)(15,17,16,18), (5,6)(7,8)(9,13,10,14)(11,15,12,16)(17,21,18,22)(19,24,20,23), (5,6)(7,8)(9,13,10,14)(11,15,12,16)(17,22,18,21)(19,23,20,24), (5,7,6,8)(13,15,14,16)(17,18)(19,20)(21,23,22,24), (5,7,6,8)(9,10)(11,12)(13,16,14,15)(17,18)(19,20)(21,23,22,24), (3,4)(7,8)(9,15,10,16)(11,13,12,14)(17,23,18,24)(19,22,20,21), (3,4)(7,8)(9,15,10,16)(11,13,12,14)(17,24,18,23)(19,21,20,22), (3,4)(5,6)(7,8)(9,17,10,18)(11,19,12,20)(13,22,14,21)(15,23,16,24), (3,4)(5,6)(7,8)(9,19,10,20)(11,18,12,17)(13,24,14,23)(15,22,16,21), (1,3)(2,4)(5,7)(6,8)(9,15,10,16)(11,13,12,14)(17,21,18,22)(19,23,20,24), (1,4)(2,3)(5,7)(6,8)(9,14,10,13)(11,15,12,16)(17,24,18,23)(19,21,20,22), (7,8)(9,17,10,18)(11,20,12,19)(13,21,14,22)(15,23,16,24), (5,7)(6,8)(9,17,10,18)(11,20,12,19)(13,24,14,23)(15,21,16,22), (3,4)(5,6)(7,8)(9,21,10,22)(11,24,12,23)(13,18,14,17)(15,20,16,19), (1,2)(3,4)(5,7)(6,8)(9,17,10,18)(11,20,12,19)(13,23,14,24)(15,22,16,21), (1,3,2,4)(5,7,6,8)(9,13)(10,14)(11,15)(12,16)(17,23,18,24)(19,21,20,22), (1,3,2,4)(5,7,6,8)(9,13)(10,14)(11,15)(12,16)(17,24,18,23)(19,22,20,21), (1,15,5,12)(2,16,6,11)(3,13,8,10)(4,14,7,9)(17,21)(18,22)(19,23,20,24), (1,20,2,19)(3,17,4,18)(5,22)(6,21)(7,23)(8,24)(11,12)(13,15,14,16), (1,13,5,9)(2,14,6,10)(3,15,8,11)(4,16,7,12)(17,21,18,22)(19,24)(20,23), (1,12,8,13)(2,11,7,14)(3,9,6,15)(4,10,5,16)(17,23)(18,24)(19,22,20,21), (1,7)(2,8)(3,5,4,6)(9,18,16,24)(10,17,15,23)(11,20,14,21)(12,19,13,22), (1,12,5,15)(2,11,6,16)(3,10,8,13)(4,9,7,14)(17,22)(18,21)(19,23,20,24), (1,19,5,24)(2,20,6,23)(3,18,7,22)(4,17,8,21)(9,14,10,13)(11,16)(12,15), (1,8)(2,7)(3,5,4,6)(9,18,15,23)(10,17,16,24)(11,19,13,21)(12,20,14,22), (1,11)(2,12)(3,9)(4,10)(5,13,6,14)(7,15,8,16)(19,20)(21,24,22,23), (1,8)(2,7)(3,5,4,6)(9,17,16,23)(10,18,15,24)(11,20,14,21)(12,19,13,22), (1,8,3,5)(2,7,4,6)(9,20,15,23)(10,19,16,24)(11,18,13,21)(12,17,14,22), (1,24,7,19)(2,23,8,20)(3,21,6,17)(4,22,5,18)(9,14,12,15)(10,13,11,16), (1,18,14,2,17,13)(3,20,15,4,19,16)(5,22,9)(6,21,10)(7,24,12)(8,23,11), (1,20,15,2,19,16)(3,17,13,4,18,14)(5,23,11,6,24,12)(7,22,9,8,21,10), (1,23,13,2,24,14)(3,22,15,4,21,16)(5,20,9)(6,19,10)(7,17,11)(8,18,12), (1,10,19)(2,9,20)(3,11,17,4,12,18)(5,13,23,6,14,24)(7,16,21)(8,15,22), (1,10,19,2,9,20)(3,11,17)(4,12,18)(5,15,23,7,13,21)(6,16,24,8,14,22), (1,21,14)(2,22,13)(3,24,16,4,23,15)(5,17,9,6,18,10)(7,20,11)(8,19,12), (1,10,18,2,9,17)(3,11,19)(4,12,20)(5,16,21,7,14,24)(6,15,22,8,13,23), (5,7)(6,8)(9,21,11,23,10,22,12,24)(13,19,16,18,14,20,15,17), (5,7)(6,8)(9,21,12,24,10,22,11,23)(13,19,15,17,14,20,16,18), (5,7,6,8)(9,13,11,15,10,14,12,16)(17,21,19,24,18,22,20,23), (5,7,6,8)(9,13,11,15,10,14,12,16)(17,22,19,23,18,21,20,24), (1,2)(3,4)(5,7)(6,8)(9,21,12,24,10,22,11,23)(13,20,15,18,14,19,16,17), (1,2)(3,4)(5,7)(6,8)(9,21,11,23,10,22,12,24)(13,20,16,17,14,19,15,18), (1,2)(3,4)(5,7,6,8)(9,13,12,16,10,14,11,15)(17,21,20,23,18,22,19,24), (1,2)(3,4)(5,7,6,8)(9,13,12,16,10,14,11,15)(17,22,20,24,18,21,19,23), (1,3)(2,4)(5,7,6,8)(9,17,11,19,10,18,12,20)(13,22,15,23,14,21,16,24), (1,3)(2,4)(5,7,6,8)(9,17,12,20,10,18,11,19)(13,22,16,24,14,21,15,23), (1,3)(2,4)(5,7,6,8)(9,19,11,18,10,20,12,17)(13,24,15,22,14,23,16,21), (1,3)(2,4)(5,7,6,8)(9,19,12,17,10,20,11,18)(13,24,16,21,14,23,15,22), (1,8,4,5,2,7,3,6)(9,15,11,14,10,16,12,13)(19,20)(21,24)(22,23), (1,9,3,11,2,10,4,12)(5,16,7,14,6,15,8,13)(17,19,18,20)(21,22), (1,13,3,15,2,14,4,16)(5,9,7,12,6,10,8,11)(17,19)(18,20)(21,23,22,24), (1,18,4,20,2,17,3,19)(5,22,7,24,6,21,8,23)(9,11,10,12)(13,16)(14,15), (1,20,3,18,2,19,4,17)(5,22,8,23,6,21,7,24)(9,11,10,12)(13,14), (1,6,3,8,2,5,4,7)(11,12)(13,16)(14,15)(17,22,19,23,18,21,20,24), (1,7,4,5)(2,8,3,6)(9,22,14,19,10,21,13,20)(11,24,15,18,12,23,16,17), (1,8,4,5)(2,7,3,6)(9,17,16,22,10,18,15,21)(11,19,14,24,12,20,13,23), (1,15,18,4,14,19,2,16,17,3,13,20)(5,9,22)(6,10,21)(7,12,24)(8,11,23), (1,12,21,4,9,23,2,11,22,3,10,24)(5,13,17,6,14,18)(7,16,20,8,15,19)];
chartbl_6144_ze.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];
chartbl_6144_ze.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 29, 4, 4, 4, 4, 5, 5, 4, 4, 4, 4, 4, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 21, 5, 21, 21, 21, 21, 21, 21, 5, 21, 22, 22, 29, 29, 29, 29, 29, 29, 29, 33, 33, 37, 37, 33, 33, 37, 37, 37, 37, 37, 37, 33, 37, 37, 37, 37, 33, 49, 49, 68, 68], [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, 1, 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, 5, 2, 6, 7, 23, 8, 24, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 34, 35]];
chartbl_6144_ze.SizesCentralizers:= [6144, 6144, 2048, 2048, 1536, 1536, 768, 768, 512, 512, 512, 512, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 192, 192, 128, 128, 128, 128, 48, 1024, 1024, 1024, 1024, 768, 768, 512, 512, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 128, 128, 128, 128, 128, 128, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 32, 32, 48, 48, 48, 24, 24, 24, 24, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 64, 64, 64, 64, 64, 64, 32, 32, 24, 24];
chartbl_6144_ze.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "2N", "2O", "2P", "2Q", "2R", "2S", "2T", "2U", "2V", "2W", "2X", "2Y", "2Z", "2AA", "3A", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "4J", "4K", "4L", "4M", "4N", "4O", "4P", "4Q", "4R", "4S", "4T", "4U", "4V", "4W", "4X", "4Y", "4Z", "4AA", "4AB", "4AC", "4AD", "4AE", "4AF", "4AG", "4AH", "4AI", "4AJ", "4AK", "4AL", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "8A", "8B", "8C", "8D", "8E", "8F", "8G", "8H", "8I", "8J", "8K", "8L", "8M", "8N", "8O", "8P", "8Q", "8R", "8S", "8T", "12A", "12B"];
chartbl_6144_ze.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 12, 12];
chartbl_6144_ze.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, 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ConvertToLibraryCharacterTableNC(chartbl_6144_ze);