# Group 93312.hk downloaded from the LMFDB on 09 November 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(47492444102771242547311101124093795122543684845700573796168243201719614021764896302684072856189617057317162989147973466174384201677635441634399464292147106446363527206487470472638494387178409710581588964290347983813287115582505475237205,93312); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.6; e := GPC.8; f := GPC.10; g := GPC.12; GPerm := Group( (1,2,4)(3,6,7,9)(5,8)(14,15,17,19)(20,21)(23,24,26,27,29,30)(25,28), (1,3)(2,5)(4,7)(6,8)(10,11,12,13)(14,16)(15,18)(17,20)(19,21)(22,23,25,26,28,29)(24,27,30) ); # Booleans booleans_93312_hk := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := false); # Character Table chartbl_93312_hk:=rec(); chartbl_93312_hk.IsFinite:= true; chartbl_93312_hk.UnderlyingCharacteristic:= 0; chartbl_93312_hk.UnderlyingGroup:= GPC; chartbl_93312_hk.Size:= 93312; chartbl_93312_hk.InfoText:= "Character table for group 93312.hk downloaded from the LMFDB."; chartbl_93312_hk.Identifier:= " C6^3.C6^2:D6 "; chartbl_93312_hk.NrConjugacyClasses:= 234; chartbl_93312_hk.ConjugacyClasses:= [ of ..., f12*f13, f10*f11*f12*f13, f10*f11, f6*f7, f4*f5*f12*f13, f4*f5*f10*f11, f4*f5, f1*f2*f3*f5*f6*f7*f9*f13, f1*f2*f3*f5*f6*f9*f11^2*f12*f13^2, f13, f5^2*f13, f9*f11*f13^2, f7^2*f11*f13^2, f9^2*f13, f5^2*f9*f11, f9*f11^2*f13, f7^2*f11*f13, f11*f13, f5*f11, f5^2*f9^2*f13, f5^2*f11, f5*f7^2*f11, f3*f4*f5*f6*f7^2*f9*f11*f12*f13, f3^2*f4*f5^2*f7^2*f8*f9^2*f13^2, f2*f3*f7^2*f8*f9*f10*f12*f13, f2*f3*f7^2*f8*f9*f10, f1*f2*f5*f6*f9^2*f11^2*f12*f13^2, f1*f2*f3*f5*f6*f8*f9^2*f10*f13, f1*f5^2*f7^2*f10*f11, f1*f5^2*f7^2*f10*f11*f12*f13, f1*f5^2*f7^2*f8*f10*f11^2*f13^2, f1*f5^2*f7^2*f8*f11*f13^2, f1*f2*f4*f5^2*f7^2*f9^2*f12*f13^2, f1*f2*f3*f4*f5^2*f7^2*f9*f12*f13, f1*f4*f6*f7^2*f9*f10*f11^2*f13^2, f1*f4*f7*f9^2*f10*f11^2*f12, f2*f3*f4*f5*f6*f7^2*f9*f11^2*f13, f2*f3*f4*f5*f6*f7^2*f8*f9^2*f11^2*f12*f13^2, f12, f5*f12, f10*f11*f12, f8*f11^2*f13, f5*f10*f11*f13, f7^2*f12*f13, f8*f9^2*f11*f12, f5*f8*f9*f10*f11*f12*f13, f8*f9*f12*f13^2, f7^2*f11*f12, f8, f9*f12, f8*f11^2, f9*f10*f11, f5*f10*f11, f5*f8*f9, f8*f11^2*f12, f5*f8*f11^2, f5^2*f7*f12, f5*f8*f10*f11, f7^2*f9*f12*f13, f9*f10*f13, f7^2*f8*f10*f12*f13^2, f7*f11^2*f12, f10*f12, f8*f13, f8*f12, f5*f8, f5^2*f10, f8*f11*f12, f7*f10*f13, f5*f9*f12, f5*f8*f13, f5*f8*f12, f5*f8*f10, f8*f11*f13^2, f5*f11^2*f12, f5*f8*f13^2, f5^2*f8*f12, f5^2*f8*f11^2, f5*f7*f10*f11, f7*f10*f12*f13^2, f11*f12*f13, f10*f11^2, f5^2*f7^2*f8*f10*f12*f13^2, f8*f11, f7*f10, f5*f10, f8*f9*f10, f7*f10*f12, f5*f11*f12, f5*f8*f11, f5*f7*f8, f5^2*f8*f11, f5^2*f7*f10, f5*f8*f11*f12, f5*f7*f11*f12, f5*f7*f10*f12, f5*f8*f11*f13^2, f5*f8*f10*f11^2, f5^2*f7*f9^2*f10, f5*f7*f10, f5*f7^2*f10, f5*f7*f8*f11, f5*f7^2*f8*f11, f6*f7*f13, f6*f7*f13^2, f4*f12*f13, f4*f8*f10*f13, f6*f7*f11^2*f12, f6*f7*f11^2*f12*f13, f4*f5^2*f7*f9^2*f11^2*f13, f4*f7*f9^2*f11^2*f13, f6, f4*f10*f11, f4*f8*f9, f4*f5*f13, f4*f5*f12, f6*f8*f12*f13, f4*f5*f6*f7^2*f9^2*f10*f11^2*f13^2, f6*f8*f9^2*f10*f12*f13^2, f6*f13, f6*f13^2, f4*f13, f4*f6, f4*f12, f4*f8*f10, f5*f6*f7, f5^2*f6*f7, f4*f11*f12, f4*f8*f10*f11, f4*f9^2*f10, f5*f6*f7*f12, f4*f11^2*f13, f4*f5^2*f9*f11^2*f13, f4*f5*f6*f7*f8*f10*f11^2, f4*f5*f6*f7*f8*f9*f10, f4*f8, f6*f8*f13, f6*f8*f12, f4*f10*f13, f5*f6, f5^2*f6, f4*f11, f5*f6*f8, f4*f10, f5*f6*f12, f4*f9*f12, f5*f6*f8*f12, f1*f2*f3*f5*f6*f7*f11, f1*f2*f3*f6*f9*f11^2*f12*f13, f1*f2*f3^2*f5*f6*f7^2*f9^2*f10*f12, f1*f2*f5^2*f6*f9*f10*f13^2, f3^2*f4*f5*f8*f9*f10*f11*f13^2, f1*f2*f3*f7*f8*f9^2*f11^2*f13^2, f1*f2*f6*f8*f9*f13, f3*f4*f6*f7^2*f8*f9*f10*f12*f13, f3^2*f7*f9^2*f10*f12*f13, f3*f6*f7*f8*f11*f12*f13^2, f3^2*f5^2*f9^2*f10*f11^2*f12, f3^2*f5^2*f7^2*f8*f9*f11*f13, f2*f3*f5^2*f12, f2*f3*f5^2*f7*f11*f13, f2*f3*f8*f10, f2*f3*f7*f9, f2*f3*f9^2*f10, f2*f3*f9^2*f11, f2*f3*f11, f2*f3*f11*f12, f2*f3*f10, f2*f3*f11^2, f2*f3*f9, f2*f3*f9*f12, f1*f2*f5*f6*f7*f8*f9*f10*f11*f12*f13^2, f1*f2*f4*f5*f6*f7*f12*f13^2, f1*f2*f3^2*f6*f7^2*f8*f9^2*f13, f1*f2*f4*f5^2*f6*f7^2*f8*f9^2*f10*f13^2, f1*f5*f6*f7*f8*f9*f13^2, f1*f5*f6*f7*f8*f10*f11^2*f13, f1*f2*f3*f4*f5^2*f6*f7*f8*f9*f10*f13, f1*f2*f3*f4*f5^2*f6*f7^2*f8*f9*f10*f13, f1*f3*f5^2*f6*f7*f9*f10*f11^2*f12*f13^2, f1*f3*f5^2*f6*f7*f9*f10*f11^2*f13^2, f1*f2*f3*f4*f5^2*f7*f9*f10*f11*f12, f1*f2*f3*f4*f5^2*f9*f10*f11*f12, f1*f2*f8*f9*f10*f11^2*f13, f1*f2*f4*f7*f8*f9*f10*f11^2*f13, f1*f2*f3*f4*f6*f8*f10*f13^2, f1*f2*f3*f4*f5*f7^2*f9^2*f11*f12*f13^2, f1*f5^2*f7^2*f9*f11*f12, f1*f5^2*f7^2*f9, f1*f3*f5^2*f6*f9^2, f1*f3*f5^2*f6*f8*f12, f1*f4*f7*f9^2*f10*f11^2*f12*f13^2, f1*f4*f6*f7^2*f9*f10*f11^2, f1*f4*f7*f9^2*f10*f11^2*f12*f13, f1*f4*f6*f7^2*f9*f10*f11^2*f13, f1*f2*f5^2*f7*f11^2*f12, f1*f2*f4*f5*f7^2*f12*f13^2, f1*f2*f7*f9^2*f11^2*f12, f1*f2*f4*f7^2*f9*f12*f13^2, f1*f3*f4*f6*f7*f10*f11*f12*f13, f1*f3*f5^2*f8*f9*f11^2*f12*f13, f1*f3*f4*f6*f7*f9^2*f10*f12*f13, f1*f3*f5^2*f8*f9^2*f12*f13, f1*f3*f4*f6*f8*f13, f1*f3*f5^2*f7^2*f8*f9^2*f10*f13^2, f1*f3*f4*f6*f8*f9^2*f11^2*f13^2, f1*f3*f5^2*f7^2*f8*f10*f11*f13, f1*f2*f3*f4*f6*f7*f10*f11^2*f13^2, f1*f2*f3*f4*f5*f7*f8*f10*f13^2, f1*f2*f3*f4*f5*f6*f7^2*f10*f11^2, f1*f2*f3*f4*f8*f10*f13, f1*f4*f7^2*f10*f11^2*f12*f13, f1*f4*f6*f7*f9^2*f10, f1*f4*f10*f11^2*f12*f13^2, f1*f4*f6*f9^2*f10*f13^2, f1*f2*f5^2*f6*f7*f8*f9*f10*f11, f1*f2*f3*f5^2*f6*f8*f11*f12*f13, f1*f5^2*f7^2*f10*f12*f13, f1*f5^2*f7^2*f10*f11^2, f1*f5^2*f7^2*f8*f13^2, f1*f5^2*f7^2*f8*f10*f13^2, f2*f3*f4*f5*f6*f7^2*f8*f9*f11*f12, f2*f3*f4*f5*f6*f7^2*f9^2, f2*f3^2*f4*f6*f8*f10*f11*f13^2, f2*f4*f7^2*f9*f10*f12, f3*f7*f8*f9^2*f10*f11*f12*f13^2, f3^2*f4*f5*f6*f7*f8*f11^2*f12, f3*f5*f7^2*f8*f9^2*f10*f11^2*f12*f13^2, f3*f5*f7*f9*f10*f11^2*f12, f2*f5^2*f7*f9^2*f10*f13, f2*f3^2*f5^2*f7^2*f8*f9^2*f10*f11^2*f12*f13, f2*f3^2*f5*f6*f7*f9*f12*f13, f2*f4*f5^2*f6*f7*f8*f9*f10*f11^2*f12*f13]; chartbl_93312_hk.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, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234]; chartbl_93312_hk.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 2, 2, 3, 3, 2, 2, 4, 4, 8, 8, 7, 7, 4, 4, 11, 12, 11, 13, 12, 13, 13, 12, 11, 14, 13, 15, 15, 13, 12, 12, 15, 16, 16, 16, 17, 17, 17, 18, 19, 15, 15, 16, 20, 17, 14, 21, 21, 21, 16, 17, 20, 21, 21, 21, 21, 14, 19, 19, 20, 19, 18, 22, 19, 18, 22, 20, 22, 22, 23, 22, 23, 23, 22, 20, 22, 23, 23, 23, 23, 11, 11, 12, 12, 11, 11, 12, 12, 13, 12, 12, 11, 11, 13, 13, 13, 15, 15, 12, 12, 12, 12, 12, 12, 16, 16, 12, 12, 16, 16, 15, 15, 16, 15, 15, 16, 21, 21, 21, 21, 21, 21, 21, 21, 17, 12, 17, 12, 24, 20, 20, 25, 157, 158, 159, 160, 49, 49, 60, 60, 60, 60, 49, 49, 45, 45, 60, 60, 62, 47, 47, 62, 61, 61, 120, 120, 40, 40, 120, 120, 111, 112, 111, 112, 60, 60, 48, 48, 109, 110, 110, 109, 133, 134, 134, 133, 135, 136, 136, 135, 119, 119, 119, 119, 133, 134, 134, 133, 135, 136, 136, 135, 84, 84, 82, 82, 83, 83, 46, 46, 153, 153, 157, 158, 159, 160, 227, 227, 228, 228], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 26, 28, 29, 31, 30, 33, 32, 34, 35, 37, 36, 39, 38, 2, 2, 3, 3, 4, 2, 4, 3, 4, 2, 3, 2, 3, 4, 4, 3, 4, 3, 2, 4, 2, 4, 3, 2, 3, 3, 4, 3, 4, 4, 4, 2, 3, 4, 4, 3, 2, 3, 4, 3, 4, 3, 2, 4, 3, 3, 4, 4, 4, 3, 2, 3, 3, 3, 4, 4, 2, 3, 3, 4, 4, 4, 4, 3, 3, 5, 5, 6, 6, 7, 7, 8, 8, 5, 7, 5, 8, 6, 6, 7, 8, 5, 5, 8, 8, 6, 6, 5, 5, 6, 6, 7, 7, 8, 8, 7, 7, 5, 8, 6, 7, 5, 5, 8, 8, 7, 7, 6, 6, 9, 10, 10, 9, 2, 9, 10, 2, 14, 14, 14, 14, 26, 27, 26, 27, 26, 27, 27, 26, 26, 27, 27, 26, 29, 28, 29, 28, 32, 33, 35, 35, 31, 30, 34, 34, 34, 34, 35, 35, 31, 30, 33, 32, 36, 37, 36, 37, 34, 34, 34, 34, 37, 36, 37, 36, 37, 36, 37, 36, 35, 35, 35, 35, 36, 37, 36, 37, 28, 29, 30, 31, 32, 33, 38, 39, 27, 26, 49, 49, 49, 49, 161, 162, 161, 162]]; chartbl_93312_hk.SizesCentralizers:= [93312, 93312, 31104, 31104, 1728, 1728, 1728, 1728, 288, 288, 46656, 15552, 15552, 11664, 7776, 7776, 7776, 5832, 3888, 3888, 3888, 1944, 1944, 108, 54, 2592, 2592, 288, 288, 288, 288, 288, 288, 144, 144, 144, 144, 96, 96, 46656, 15552, 15552, 15552, 15552, 15552, 15552, 15552, 15552, 11664, 7776, 7776, 7776, 7776, 7776, 7776, 7776, 7776, 7776, 7776, 7776, 7776, 7776, 5832, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 3888, 1944, 1944, 1944, 1944, 1944, 1944, 1944, 1944, 1944, 1944, 1944, 1944, 1944, 1944, 1944, 1944, 1944, 1944, 1944, 1944, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 432, 432, 432, 432, 432, 432, 432, 432, 432, 432, 432, 432, 144, 144, 144, 144, 108, 72, 72, 54, 108, 108, 54, 54, 1296, 1296, 864, 864, 864, 864, 432, 432, 432, 432, 432, 432, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 72, 72, 72, 72, 72, 72, 48, 48, 36, 36, 108, 108, 54, 54, 36, 36, 36, 36]; chartbl_93312_hk.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "3A", "3B", "3C", "3D", "3E", "3F", "3G", "3H", "3I", "3J", "3K", "3L", "3M", "3N", "3O", "4A1", "4A-1", "4B", "4C", "4D1", "4D-1", "4E1", "4E-1", "4F", "4G", "4H1", "4H-1", "4I1", "4I-1", "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", "6AD", "6AE", "6AF", "6AG", "6AH", "6AI", "6AJ", "6AK", "6AL", "6AM", "6AN", "6AO", "6AP", "6AQ", "6AR", "6AS", "6AT", "6AU", "6AV", "6AW", "6AX", "6AY", "6AZ", "6BA", "6BB", "6BC", "6BD", "6BE", "6BF", "6BG", "6BH", "6BI", "6BJ1", "6BJ-1", "6BK1", "6BK-1", "6BL1", "6BL-1", "6BM1", "6BM-1", "6BN1", "6BN-1", "6BO1", "6BO-1", "6BP", "6BQ", "6BR", "6BS", "6BT", "6BU", "6BV", "6BW", "6BX1", "6BX-1", "6BY1", "6BY-1", "6BZ1", "6BZ-1", "6CA1", "6CA-1", "6CB1", "6CB-1", "6CC1", "6CC-1", "6CD1", "6CD-1", "6CE1", "6CE-1", "6CF", "6CG", "6CH", "6CI", "6CJ1", "6CJ-1", "6CK1", "6CK-1", "6CL1", "6CL-1", "6CM1", "6CM-1", "6CN", "6CO", "6CP", "6CQ", "6CR", "6CS", "6CT", "6CU", "9A", "9B", "9C", "9D", "12A1", "12A-1", "12B1", "12B-1", "12B5", "12B-5", "12C1", "12C-1", "12D1", "12D-1", "12E1", "12E-1", "12F", "12G", "12H", "12I", "12J1", "12J-1", "12K1", "12K5", "12L1", "12L-1", "12M1", "12M5", "12N1", "12N-1", "12O1", "12O-1", "12P1", "12P-1", "12Q1", "12Q-1", "12R1", "12R-1", "12R5", "12R-5", "12S1", "12S-1", "12S5", "12S-5", "12T1", "12T-1", "12T5", "12T-5", "12U1", "12U-1", "12U5", "12U-5", "12V1", "12V-1", "12V5", "12V-5", "12W1", "12W-1", "12W5", "12W-5", "12X", "12Y", "12Z1", "12Z-1", "12AA1", "12AA-1", "12AB1", "12AB-1", "12AC1", 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