# Group 20736.ig downloaded from the LMFDB on 03 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(599012462365884545933224386505738818633661518116767551769737691155657248361374229952293388591132966860794328601612988551142139957745161315631281089791011668458919323643174185377831940034879720072750068245,20736); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.5; e := GPC.6; f := GPC.7; g := GPC.9; h := GPC.11;
GPerm := Group( (2,4,7,9,8,3)(5,6)(10,12,13,16)(15,17), (1,2,3,5,7,4,6,8,9)(10,11,13,15,16,17)(12,14) );

 
# Booleans 
booleans_20736_ig := 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_20736_ig:=rec(); 
chartbl_20736_ig.IsFinite:= true; 
chartbl_20736_ig.UnderlyingCharacteristic:= 0; 
chartbl_20736_ig.UnderlyingGroup:= GPerm;
chartbl_20736_ig.Size:= 20736;
chartbl_20736_ig.InfoText:= "Character table for group 20736.ig downloaded from the LMFDB."; 
chartbl_20736_ig.Identifier:= " C6:D6^2:S4 "; 
chartbl_20736_ig.NrConjugacyClasses:= 88; 
chartbl_20736_ig.ConjugacyClasses:= [(), (10,12)(11,17)(13,16)(14,15), (10,11)(12,17)(13,14)(15,16), (11,17)(14,15), (10,13)(11,15)(12,16)(14,17), (4,9)(5,6)(10,16)(11,15)(12,13)(14,17), (1,5)(3,4), (5,6)(7,8)(10,13)(11,14)(12,16)(15,17), (5,6)(7,8)(10,16)(11,14)(12,13)(15,17), (2,7)(5,6)(11,17)(14,15), (1,5)(2,8)(10,16)(12,13), (2,7)(5,6)(10,14)(11,13)(12,15)(16,17), (5,6)(7,8)(10,12)(11,15)(13,16)(14,17), (1,9)(2,7)(3,5)(4,6)(10,16)(11,15), (1,8)(2,5)(3,9)(6,7)(10,14)(11,16)(12,15)(13,17), (3,9,4), (1,6,5)(2,8,7)(3,9,4), (2,8,7)(3,9,4), (1,8,3)(2,9,5)(4,6,7)(11,15,14)(12,13,16), (10,17,12,11)(13,15,16,14), (1,6)(3,4)(10,15,16,11)(12,14,13,17), (1,5)(2,9)(3,8)(4,7)(10,12,13,16)(11,17,14,15), (1,3)(4,6,9,5)(10,11,16,15)(12,14,13,17), (1,4)(2,8)(3,5)(6,9)(10,17,16,14)(11,12,15,13), (1,7,6,2)(5,8)(10,16,12,13)(11,15,17,14), (2,7)(4,9)(10,17,16,14)(11,13,15,12), (1,4,5,3)(6,9)(10,11)(12,14)(13,17)(15,16), (2,3,8,9)(4,7)(10,13)(15,17), (1,5)(2,9)(3,7)(4,8)(10,15,16,14)(11,13,17,12), (1,2)(5,8,6,7)(10,11,16,14)(12,17,13,15), (1,8)(2,5,7,6)(10,12)(11,15,17,14), (1,2)(3,9)(5,7)(6,8)(10,12)(11,15,17,14), (3,9,4)(10,12)(11,17)(13,16)(14,15), (3,4,9)(11,17)(14,15), (3,4,9)(10,13)(11,15)(12,16)(14,17), (3,9,4)(10,13)(11,14)(12,16)(15,17), (2,8,7)(3,9,4)(10,13)(11,14)(12,16)(15,17), (3,4,9)(11,14)(15,17), (3,4,9)(10,11)(12,17)(13,14)(15,16), (3,4,9)(10,12)(11,14)(13,16)(15,17), (2,8,7)(3,9,4)(10,12)(11,17)(13,16)(14,15), (1,6,5)(2,8,7)(3,9,4)(10,12)(11,17)(13,16)(14,15), (2,8,7)(3,9,4)(10,16)(11,17)(12,13)(14,15), (1,5,6)(2,7,8)(11,17)(14,15), (1,5,6)(2,8,7)(3,4,9)(10,11)(12,17)(13,14)(15,16), (2,7,8)(3,4,9)(11,15)(14,17), (2,7,8)(3,4,9)(10,11)(12,17)(13,14)(15,16), (2,7,8)(3,4,9)(10,12)(11,14)(13,16)(15,17), (1,5,6)(2,7,8)(3,4,9)(11,14)(15,17), (1,5,6)(2,7,8)(3,4,9)(10,12)(11,14)(13,16)(15,17), (2,7,8)(4,9)(5,6)(10,16)(11,15)(12,13)(14,17), (1,5)(2,7,8)(3,4), (3,4,9)(5,6)(7,8)(10,13)(11,14)(12,16)(15,17), (3,4,9)(5,6)(7,8)(10,16)(11,14)(12,13)(15,17), (2,7)(3,9,4)(5,6)(11,17)(14,15), (1,5)(2,8)(3,4,9)(10,16)(12,13), (2,7)(3,4,9)(5,6)(10,14)(11,13)(12,15)(16,17), (3,9,4)(5,6)(7,8)(10,12)(11,15)(13,16)(14,17), (1,3,6,9,5,4)(2,7)(10,16)(11,15), (1,2,6,8,5,7)(3,9)(10,14)(11,16)(12,15)(13,17), (1,3,8)(2,5,9)(4,7,6)(10,17)(11,16,15,12,14,13), (1,3,8,6,9,2,5,4,7)(10,16,12)(11,15,17), (1,8,4,6,7,9,5,2,3)(10,12,16)(11,14,17), (3,4,9)(10,11,12,17)(13,14,16,15), (3,4,9)(10,11,13,14)(12,17,16,15), (2,7,8)(3,4,9)(10,11,13,14)(12,17,16,15), (2,7,8)(3,4,9)(10,11,12,17)(13,14,16,15), (1,5,6)(2,7,8)(3,4,9)(10,11,12,17)(13,14,16,15), (1,6)(2,8,7)(3,4)(10,11,16,15)(12,17,13,14), (1,3)(2,8,7)(4,5,9,6)(10,15,16,11)(12,17,13,14), (1,3)(2,7,8)(4,5,9,6)(10,15,16,11)(12,17,13,14), (1,2,6,7)(3,9,4)(5,8)(10,13,12,16)(11,14,17,15), (1,2,6,7)(3,4,9)(5,8)(10,13,12,16)(11,14,17,15), (1,3,5,4)(2,8,7)(6,9)(10,11)(12,14)(13,17)(15,16), (1,3,5,4)(2,7,8)(6,9)(10,11)(12,14)(13,17)(15,16), (1,6,5)(2,9,8,3)(4,7)(10,13)(15,17), (1,5,6)(2,9,8,3)(4,7)(10,13)(15,17), (1,5)(2,3,7,9,8,4)(10,16,13,12)(11,15,14,17), (1,9,5,4,6,3)(2,8)(10,14,16,17)(11,13,15,12), (1,6,5)(2,7)(4,9)(10,14,16,17)(11,12,15,13), (1,2)(3,9,4)(5,7,6,8)(10,14,16,11)(12,15,13,17), (1,2)(3,4,9)(5,7,6,8)(10,14,16,11)(12,15,13,17), (1,8)(2,6,7,5)(3,4,9)(10,12)(11,14,17,15), (1,8)(2,6,7,5)(3,9,4)(10,12)(11,14,17,15), (1,5)(2,3,8,9,7,4)(10,14,16,15)(11,12,17,13), (1,8,5,2,6,7)(3,9)(10,12)(11,14,17,15), (1,2,3,5,8,4,6,7,9)(10,17,16,11,12,15)(13,14), (1,9,8,5,4,2,6,3,7)(10,14,12,17,16,11)(13,15)];
chartbl_20736_ig.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];
chartbl_20736_ig.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16, 17, 18, 19, 2, 2, 2, 6, 2, 6, 2, 7, 7, 5, 9, 10, 4, 16, 16, 16, 16, 18, 16, 16, 16, 18, 17, 18, 18, 17, 18, 18, 18, 17, 17, 16, 16, 16, 16, 16, 16, 16, 16, 18, 18, 19, 62, 63, 33, 36, 37, 41, 42, 33, 51, 51, 51, 51, 52, 52, 52, 52, 37, 37, 36, 54, 54, 55, 55, 43, 44, 62, 63], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 1, 1, 1, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 2, 4, 5, 2, 2, 4, 3, 5, 2, 2, 5, 4, 3, 4, 3, 5, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 3, 17, 17, 20, 20, 20, 20, 20, 21, 23, 23, 25, 25, 27, 27, 28, 28, 22, 24, 26, 30, 30, 31, 31, 29, 32, 45, 45]];
chartbl_20736_ig.SizesCentralizers:= [20736, 6912, 5184, 3456, 3456, 768, 768, 384, 384, 384, 192, 192, 192, 96, 96, 3456, 2592, 1728, 18, 1728, 192, 96, 96, 96, 96, 96, 96, 96, 48, 48, 48, 48, 3456, 1728, 1728, 1728, 1728, 864, 864, 864, 864, 864, 864, 864, 648, 432, 432, 432, 432, 432, 384, 384, 192, 192, 192, 96, 96, 96, 48, 48, 18, 18, 18, 864, 432, 432, 216, 216, 96, 96, 96, 96, 96, 96, 96, 96, 96, 48, 48, 48, 48, 48, 48, 48, 24, 24, 18, 18];
chartbl_20736_ig.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "2N", "3A", "3B", "3C", "3D", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "4J", "4K", "4L", "4M", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "6H", "6I", "6J", "6K", "6L", "6M", "6N", "6O", "6P", "6Q", "6R", "6S", "6T", "6U", "6V", "6W", "6X", "6Y", "6Z", "6AA", "6AB", "6AC", "9A", "9B", "12A", "12B", "12C", "12D", "12E", "12F", "12G1", "12G5", "12H1", "12H5", "12I1", "12I5", "12J1", "12J5", "12K", "12L", "12M", "12N1", "12N5", "12O1", "12O5", "12P", "12Q", "18A", "18B"];
chartbl_20736_ig.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 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, 9, 9, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 18, 18];
chartbl_20736_ig.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], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, -1, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 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, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, -1], [2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 0, 0, 2, 2, 2, -1, -2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 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, 0, 0, 1, -1, -1, -2, -2, -2, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 1], [3, 3, 3, -1, -1, -1, -1, 3, 3, -1, -1, -1, -1, 1, 1, 3, 3, 3, 0, -1, 3, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 3, 3, -1, -1, 3, -1, -1, -1, 3, 3, -1, 3, 3, -1, 3, -1, -1, -1, -1, -1, 3, -1, 3, -1, -1, -1, 1, 1, 0, 0, 0, -1, -1, -1, -1, -1, -1, 3, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 0, 0], [3, 3, 3, -1, -1, 3, 3, -1, -1, 3, -1, 3, -1, 1, 1, 3, 3, 3, 0, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 3, 3, -1, -1, 3, -1, -1, -1, 3, 3, -1, 3, 3, -1, 3, -1, -1, -1, 3, 3, -1, 3, -1, 3, -1, -1, 1, 1, 0, 0, 0, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 0, 0], [3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 3, 3, 3, 0, 3, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 0, 0], [3, 3, 3, -1, -1, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, 3, 3, 3, 0, -1, 3, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 3, 3, -1, -1, 3, -1, -1, -1, 3, 3, -1, 3, 3, -1, 3, -1, -1, -1, -1, -1, 3, -1, 3, -1, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, -1, -1, 1, 3, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 0, 0], [3, 3, 3, -1, -1, 3, 3, -1, -1, 3, -1, 3, -1, -1, -1, 3, 3, 3, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 3, 3, -1, -1, 3, -1, -1, -1, 3, 3, -1, 3, 3, -1, 3, -1, -1, -1, 3, 3, -1, 3, -1, 3, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 0, 0], [3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, 3, 0, 3, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 3, 3, 3, 3, 3, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 0, 0], [3, 3, -3, -1, -1, -1, -1, 3, 3, -1, -1, 1, -1, -1, 1, 3, 3, 3, 0, 1, -3, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 3, 3, -1, -1, 3, -1, -1, -1, 3, 3, -1, -3, -3, -1, -3, -1, -1, -1, -1, -1, 3, -1, 3, 1, -1, -1, -1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, -3, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 0, 0], [3, 3, -3, -1, -1, -1, -1, 3, 3, -1, -1, 1, -1, 1, -1, 3, 3, 3, 0, 1, -3, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 3, 3, -1, -1, 3, -1, -1, -1, 3, 3, -1, -3, -3, -1, -3, -1, -1, -1, -1, -1, 3, -1, 3, 1, -1, -1, 1, -1, 0, 0, 0, 1, 1, 1, 1, 1, -1, -3, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 0, 0], [3, 3, -3, -1, -1, 3, 3, -1, -1, 3, -1, -3, -1, -1, 1, 3, 3, 3, 0, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 3, 3, -1, -1, 3, -1, -1, -1, 3, 3, -1, -3, -3, -1, -3, -1, -1, -1, 3, 3, -1, 3, -1, -3, -1, -1, -1, 1, 0, 0, 0, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 0, 0], [3, 3, -3, -1, -1, 3, 3, -1, -1, 3, -1, -3, -1, 1, -1, 3, 3, 3, 0, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 3, 3, -1, -1, 3, -1, -1, -1, 3, 3, -1, -3, -3, -1, -3, -1, -1, -1, 3, 3, -1, 3, -1, -3, -1, -1, 1, -1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 0, 0], [3, 3, -3, 3, 3, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 3, 3, 3, 0, -3, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -3, -3, 3, -3, 3, 3, 3, -1, 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ConvertToLibraryCharacterTableNC(chartbl_20736_ig);