# Group 93312.fs downloaded from the LMFDB on 23 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(671989764071074044513394503061920584257971264704498636148889021689545379754044233844615147073053886983023916571023927276404956865976671358124622392069982251720801787183814144554002696476212730590774786094701472161029641763366771771865804384672333718634022553044,93312); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.6; e := GPC.8; f := GPC.10; g := GPC.12; h := GPC.13; GPerm := Group( (1,3)(2,5)(4,8)(6,10)(9,13)(12,16)(20,22)(21,23)(24,26), (1,2,4,7,3,6,8,11,15,16,17,18)(5,9,12,13)(10,14)(19,20,21,22,23,24,25,26) ); # Booleans booleans_93312_fs := 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_fs:=rec(); chartbl_93312_fs.IsFinite:= true; chartbl_93312_fs.UnderlyingCharacteristic:= 0; chartbl_93312_fs.UnderlyingGroup:= GPerm; chartbl_93312_fs.Size:= 93312; chartbl_93312_fs.InfoText:= "Character table for group 93312.fs downloaded from the LMFDB."; chartbl_93312_fs.Identifier:= " C6^4.SO+(4,2) "; chartbl_93312_fs.NrConjugacyClasses:= 107; chartbl_93312_fs.ConjugacyClasses:= [(), (20,22)(24,26), (19,21)(20,22)(23,25)(24,26), (1,6)(2,15)(3,16)(4,5)(7,9)(8,12)(10,17)(11,14)(13,18)(19,24)(20,25)(21,22)(23,26), (1,9)(2,6)(3,14)(5,7)(8,17)(10,11)(12,18)(13,15)(19,21)(20,22), (1,15)(2,11)(4,8)(6,7)(9,13)(16,18)(19,23), (3,15)(5,11)(7,10)(8,17)(12,18)(13,14)(19,21)(20,26)(22,24), (2,16,6)(5,12,10)(7,11,18), (1,15,3)(2,16,6)(4,8,17)(5,12,10)(7,11,18)(9,14,13), (5,12,10)(7,18,11), (4,17,8)(5,12,10)(7,18,11)(9,14,13), (4,17,8)(5,10,12)(7,11,18)(9,14,13), (2,16,6)(4,17,8)(5,12,10)(7,11,18)(9,14,13), (2,7,5)(6,18,10)(9,14,13)(11,12,16)(21,25,23), (2,18,5)(4,17,8)(6,11,10)(7,12,16)(9,13,14)(21,25,23), (1,15,3)(2,11,5)(4,17,8)(6,7,10)(9,14,13)(12,16,18)(21,25,23), (2,11,5)(6,7,10)(9,14,13)(12,16,18)(21,25,23), (2,7,5)(4,17,8)(6,18,10)(9,13,14)(11,12,16)(21,25,23), (1,15,3)(2,7,5)(4,17,8)(6,18,10)(9,14,13)(11,12,16)(21,25,23), (1,13)(2,16)(3,14)(7,11)(9,15)(10,12)(20,24,22,26), (1,9)(3,14)(5,11)(6,16)(7,12)(8,17)(10,18)(13,15)(19,25,21,23)(20,24,22,26), (1,14)(2,5)(3,13)(6,12)(7,18)(8,17)(9,15)(10,16)(19,23,25,21)(20,22), (1,16)(2,15)(3,6)(4,11)(5,9)(7,8)(10,14)(12,13)(17,18)(19,22,25,20)(21,24,23,26), (1,3)(2,11)(6,7)(8,17)(9,13)(16,18)(19,25,23,21)(20,24)(22,26), (1,11,9,10)(2,17,6,8)(3,18,14,12)(4,16)(5,15,7,13)(19,20,21,22)(23,26)(24,25), (2,6,16)(5,10,12)(7,18,11)(20,22)(24,26), (2,6,16)(5,10,12)(7,18,11)(19,23)(21,25), (2,6,16)(7,11,18)(19,23)(21,25), (1,3,15)(2,16,6)(5,10,12)(9,14,13)(19,25)(20,22)(21,23)(24,26), (1,15,3)(5,12,10)(7,18,11)(9,13,14)(19,21)(20,22)(23,25)(24,26), (5,10,12)(7,11,18)(19,23)(21,25), (2,6,16)(4,8,17)(5,10,12)(7,18,11)(9,13,14)(20,26)(22,24), (1,3,15)(2,6,16)(4,17,8)(5,10,12)(7,18,11)(9,13,14)(20,22)(24,26), (2,6,16)(4,8,17)(5,10,12)(7,18,11)(9,13,14)(20,22)(24,26), (2,6,16)(4,8,17)(5,10,12)(7,18,11)(9,13,14)(20,24)(22,26), (2,6,16)(5,10,12)(7,18,11)(19,21)(20,22)(23,25)(24,26), (1,3,15)(2,16,6)(5,10,12)(9,14,13)(19,25)(21,23), (4,17,8)(5,12,10)(7,18,11)(9,14,13)(20,26)(22,24), (2,16,6)(7,18,11)(19,23)(20,26)(21,25)(22,24), (2,6,16)(7,11,18)(20,26)(22,24), (1,3,15)(2,6,16)(4,17,8)(5,10,12)(7,18,11)(9,13,14)(19,23)(20,26)(21,25)(22,24), (1,15,3)(2,6,16)(5,12,10)(9,13,14)(19,23)(20,24)(21,25)(22,26), (1,3,15)(2,16,6)(5,10,12)(9,14,13)(19,23)(20,24)(21,25)(22,26), (5,10,12)(7,11,18)(19,23)(20,22)(21,25)(24,26), (4,8,17)(5,10,12)(7,11,18)(9,13,14)(20,22)(24,26), (4,8,17)(5,10,12)(7,11,18)(9,13,14)(19,21)(20,22)(23,25)(24,26), (4,8,17)(5,10,12)(7,11,18)(9,13,14)(19,23)(20,22)(21,25)(24,26), (4,8,17)(5,12,10)(7,18,11)(9,13,14)(20,22)(24,26), (4,8,17)(5,12,10)(7,18,11)(9,13,14)(19,21)(20,22)(23,25)(24,26), (2,6,16)(4,8,17)(5,10,12)(7,18,11)(9,13,14)(19,21)(23,25), (2,6,16)(4,8,17)(5,10,12)(7,18,11)(9,13,14)(19,21)(20,26)(22,24)(23,25), (2,6,16)(4,8,17)(5,10,12)(7,18,11)(9,13,14)(19,21)(20,22)(23,25)(24,26), (2,6,16)(4,8,17)(5,10,12)(7,18,11)(9,13,14)(19,21)(20,24)(22,26)(23,25), (1,3,15)(2,7,12)(5,6,18)(9,13,14)(10,16,11)(19,23,25)(20,22)(24,26), (2,10,11)(5,18,16)(6,12,7)(9,13,14)(19,25,23)(20,24)(22,26), (1,4,13)(2,6,16)(3,17,14)(5,12,10)(7,18,11)(8,9,15)(19,23)(20,24,22)(21,25), (2,5,7)(6,10,18)(9,13,14)(11,16,12)(20,22)(21,23,25)(24,26), (2,5,11)(6,10,7)(9,13,14)(12,18,16)(20,22)(21,23,25)(24,26), (2,5,11)(6,10,7)(9,13,14)(12,18,16)(20,24)(21,23,25)(22,26), (2,5,11)(6,10,7)(9,13,14)(12,18,16)(20,26)(21,23,25)(22,24), (2,5,7)(4,8,17)(6,10,18)(9,14,13)(11,16,12)(20,22)(21,23,25)(24,26), (2,5,7)(4,8,17)(6,10,18)(9,14,13)(11,16,12)(20,24)(21,23,25)(22,26), (2,5,7)(4,8,17)(6,10,18)(9,14,13)(11,16,12)(20,26)(21,23,25)(22,24), (2,5,18)(4,8,17)(6,10,11)(7,16,12)(9,14,13)(20,22)(21,23,25)(24,26), (1,3,15)(2,5,7)(4,8,17)(6,10,18)(9,13,14)(11,16,12)(20,22)(21,23,25)(24,26), (1,3,15)(2,5,7)(4,8,17)(6,10,18)(9,13,14)(11,16,12)(20,24)(21,23,25)(22,26), (1,3,15)(2,5,7)(4,8,17)(6,10,18)(9,13,14)(11,16,12)(20,26)(21,23,25)(22,24), (1,3,15)(2,5,11)(4,8,17)(6,10,7)(9,13,14)(12,18,16)(20,24)(21,23,25)(22,26), (1,2,3,6,15,16)(4,12,17,5,8,10)(7,14,18,9,11,13)(19,24)(20,25)(21,22)(23,26), (1,13,3,9,15,14)(2,6)(5,18,10,7,12,11)(8,17)(19,21)(20,22), (1,14,3,13,15,9)(2,12,16,5,6,10)(4,8)(7,18)(21,23)(24,26), (2,16,6)(3,15)(4,8)(5,11,10,7,12,18)(9,13)(23,25), (1,6)(2,15)(3,16)(4,12,8,10,17,5)(7,9,18,13,11,14)(19,20)(21,26)(22,23)(24,25), (1,6)(2,15)(3,16)(4,5,17,10,8,12)(7,14,11,13,18,9)(19,20)(21,26)(22,23)(24,25), (1,4)(2,11,6,18,16,7)(3,8)(5,10)(9,14)(15,17)(20,24)(21,25), (2,6,16)(3,15)(5,7,12,11,10,18)(8,17)(13,14)(19,21)(20,26)(22,24), (1,9,4,15,13,8)(2,11)(3,14,17)(5,12,10)(6,7)(16,18)(19,23)(20,22,24), (1,17,13,3,4,14)(2,7,16,11,6,18)(5,12,10)(8,9,15)(21,25)(22,24,26), (1,17,15,4,3,8)(2,7,12,16,18,10)(5,6,11)(19,23,25)(20,24), (1,7,9,12)(2,4)(3,11,14,5)(6,17,16,8)(10,15,18,13)(19,22,25,26,21,20,23,24), (1,4,13,3,17,14,15,8,9)(2,12,7,6,5,18,16,10,11)(19,25,23)(20,22,26), (1,17,13,3,8,14,15,4,9)(2,5,7,6,10,18,16,12,11)(19,23,21)(22,24,26), (1,9,4,15,14,8,3,13,17)(2,11,12,16,18,10,6,7,5)(19,21,23)(22,26,24), (1,14,15,9,3,13)(5,18,12,11,10,7)(6,16)(8,17)(19,23,21,25)(20,26,22,24), (1,9,3,14,15,13)(2,6)(4,8)(5,11,12,7,10,18)(19,23,21,25)(20,26,22,24), (1,15)(2,5,6,10,16,12)(7,11,18)(8,17)(9,14)(19,23,25,21), (1,2,3,16,15,6)(4,11)(5,13,10,9,12,14)(7,8)(17,18)(19,20,25,22)(21,26,23,24), (1,6,15,16,3,2)(4,11)(5,14,12,9,10,13)(7,8)(17,18)(19,22,25,20)(21,24,23,26), (1,9,3,14,15,13)(2,12,16,5,6,10)(7,18)(8,17)(19,21,25,23)(20,22), (1,15)(2,6)(4,9,17,14,8,13)(5,18,12,11,10,7)(19,21)(20,24,26,22), (1,15)(2,7,16,18,6,11)(4,9)(8,13)(10,12)(14,17)(19,25,23,21)(20,22,26,24), (1,3)(2,7,6,11,16,18)(4,14)(5,10)(8,9)(13,17)(19,21,23,25)(20,26), (2,7,6,11,16,18)(3,15)(4,13)(5,10)(8,14)(9,17)(19,23)(20,22,26,24), (1,10,3,12,15,5)(2,14,6,9,16,13)(4,7,17,18,8,11)(19,20,23,26)(21,24,25,22), (1,2,15,6,3,16)(4,7)(5,14,12,9,10,13)(8,18)(11,17)(19,26,23,22)(20,25,24,21), (1,16,3,6,15,2)(4,7)(5,13,10,9,12,14)(8,18)(11,17)(19,22,23,26)(20,21,24,25), (1,3)(2,18,6,11,16,7)(5,12,10)(8,17)(9,13)(19,21,23,25)(20,24)(22,26), (1,9,3,13,15,14)(2,10,7,16,12,11)(5,18,6)(19,25,23)(20,26,22,24), (1,8)(2,11,10)(3,4)(5,6,18,12,16,7)(9,14,13)(15,17)(19,23,25)(20,22,24,26), (1,13,4)(2,11,6,7,16,18)(3,9,17,15,14,8)(5,10,12)(19,21,23,25)(20,22,24), (1,12,13,11,3,5,9,18,15,10,14,7)(2,8,6,17)(4,16)(19,22,21,20)(23,26)(24,25), (1,5,14,11,15,12,9,7,3,10,13,18)(2,8,6,17)(4,16)(19,22,21,20)(23,26)(24,25), (1,18,4,16,13,10,3,11,17,2,14,12,15,7,8,6,9,5)(19,20,25,22,23,26)(21,24), (1,11,17,2,13,5,3,7,8,6,14,10,15,18,4,16,9,12)(19,22,23,24,21,26)(20,25), (1,12,9,16,4,18,15,10,14,6,8,7,3,5,13,2,17,11)(19,26,21,24,23,22)(20,25), (1,10,14,7,15,5,9,18,3,12,13,11)(2,4)(6,8,16,17)(19,26,23,22,21,24,25,20), (1,5,13,7,3,10,9,11,15,12,14,18)(2,4)(6,8,16,17)(19,24,23,20,21,26,25,22)]; chartbl_93312_fs.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]; chartbl_93312_fs.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 3, 2, 3, 2, 5, 8, 8, 10, 12, 11, 10, 13, 9, 13, 13, 8, 12, 11, 10, 10, 9, 12, 12, 10, 11, 11, 11, 12, 12, 13, 13, 13, 13, 15, 14, 16, 14, 17, 17, 17, 18, 18, 18, 15, 19, 19, 19, 16, 9, 11, 12, 8, 12, 12, 10, 8, 14, 16, 15, 21, 81, 83, 82, 30, 29, 27, 29, 29, 37, 38, 39, 28, 40, 41, 42, 43, 27, 54, 55, 56, 70, 70, 81, 82, 83, 84, 84], [1, 2, 3, 4, 5, 6, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 20, 21, 22, 23, 24, 25, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 3, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 5, 5, 6, 4, 4, 5, 7, 6, 6, 6, 80, 9, 9, 9, 21, 21, 20, 23, 23, 22, 22, 21, 22, 22, 23, 23, 23, 24, 20, 20, 20, 25, 25, 69, 69, 69, 80, 80]]; chartbl_93312_fs.SizesCentralizers:= [93312, 15552, 10368, 432, 288, 288, 96, 23328, 23328, 7776, 5184, 5184, 3888, 648, 648, 648, 324, 324, 324, 288, 288, 144, 144, 96, 24, 7776, 7776, 7776, 5184, 5184, 3888, 3888, 3888, 3888, 3888, 2592, 2592, 2592, 2592, 2592, 2592, 2592, 2592, 1296, 1296, 1296, 1296, 1296, 1296, 1296, 1296, 1296, 1296, 648, 648, 648, 324, 324, 324, 324, 324, 324, 324, 324, 324, 324, 324, 324, 216, 144, 144, 144, 144, 144, 72, 48, 36, 36, 36, 24, 54, 54, 54, 144, 144, 144, 144, 144, 72, 72, 72, 72, 72, 72, 72, 72, 48, 36, 36, 36, 24, 24, 18, 18, 18, 24, 24]; chartbl_93312_fs.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "3A", "3B", "3C", "3D", "3E", "3F", "3G", "3H", "3I", "3J", "3K", "3L", "4A", "4B", "4C", "4D", "4E", "4F", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "6H", "6I1", "6I-1", "6J", "6K", "6L", "6M", "6N", "6O", "6P1", "6P-1", "6Q", "6R", "6S", "6T", "6U", "6V", "6W", "6X", "6Y1", "6Y-1", "6Z", "6AA", "6AB", "6AC", "6AD", "6AE", "6AF", "6AG", "6AH", "6AI", "6AJ", "6AK", "6AL", "6AM", "6AN", "6AO", "6AP", "6AQ", "6AR", "6AS1", "6AS-1", "6AT", "6AU", "6AV", "6AW", "6AX", "8A", "9A", "9B1", "9B-1", "12A", "12B", "12C", "12D1", "12D-1", "12E", "12F", "12G", "12H", "12I", "12J", "12K1", "12K-1", "12L", "12M", "12N", "12O", "12P1", "12P5", "18A", "18B1", "18B-1", "24A1", "24A5"]; chartbl_93312_fs.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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, 8, 9, 9, 9, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 18, 18, 18, 24, 24]; chartbl_93312_fs.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], [2, 2, 2, 2, 2, 0, 0, 2, 2, -1, 2, -1, -1, 2, 2, 2, -1, -1, -1, 0, 2, 2, 2, 0, 0, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, 0, -1, 2, -1, 0, 0, 0, 0, 0, -1, -1, 2, -1, -1, 2, 0, -1, -1, -1, 2, -1, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0], [2, 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0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_93312_fs);