|
{
"version": "01-May-2025, 05:40:21 UTC",
"idenum": "CTblLib.Data.IdEnumerator",
"attrid": "InfoText",
"automatic": [
["(11:5xD12).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(11:5xM12):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(13:6xA4).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(13:6xL3(3)).2","35th maximal subgroup of M,\nconstructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(2.A4x2.G2(4)).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(2.A4x3).2","5th maximal subgroup of 2.A7,\nconstructed using `PossibleCharacterTablesOfTypeMGA'"],
["(2.A5x2.J2).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(2.A5x3).2","6th maximal subgroup of 2.A8,\nconstructed using `PossibleCharacterTablesOfTypeMGA'"],
["(2.A5xA5):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(2.A5xD10).2","7th maximal subgroup of 2.J2.2"],
["(2.A6x3).2_1","3rd maximal subgroup of 2.A9,\nconstructed using `PossibleCharacterTablesOfTypeMGA'"],
["(2.A6xU3(3)).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(2.A7x3).2","3rd maximal subgroup of 2.A10,\nconstructed using `PossibleCharacterTablesOfTypeMGA'"],
["(2.A7xL2(7)).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(2.A8x3).2","3rd maximal subgroup of 2.A11,\nconstructed using `PossibleCharacterTablesOfTypeMGA'"],
["(2.A9x3).2","3rd maximal subgroup of 2.A12,\nconstructed using `PossibleCharacterTablesOfTypeMGA'"],
["(2.D10x3.A6).2_3","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(2.D10xA6).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(2^(1+4)x3).GO+(4,2)","origin: Dixon's Algorithm"],
["(2^(1+8).2^3)a.L3(2)","origin: Dixon's Algorithm"],
["(2^(1+8).2^3)b.L3(2)","origin: Dixon's Algorithm"],
["(2^(1+8)x2^6):S6(2)","1st and 2nd maximal subgroup of F4(2),\nconstructed by T. Breuer using the representation on 69615 points\nof F4(2), and the character tables of F4(2) and S6(2),\ntable is sorted w.r.t. (unique) normal series 2.2^6.2^8.S6(2)"],
["(2^2x11:5).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(2^2x13:4):3","Sylow 13 normalizer in Ru,\nof structure (2^2x13:4):3, subdirect product of A4 and 13:12,\ncontained in maximal subgroups of type (2^2xSz(8)):3,\norigin: Dixon's Algorithm"],
["(2^2x2^(1+8)).(3xU4(2)).2","origin: Dixon's Algorithm,\n10th maximal subgroup of Fi23,\ntable is sorted w.r. to normal series 2.2^2.2^8.3.U4(2).2,\ntests:"],
["(2^2x3).(3^(1+4).[2^7.3])","constructed using `PossibleCharacterTablesOfTypeV4G'"],
["(2^2x3).2E6(2)","constructed using `PossibleCharacterTablesOfTypeV4G'"],
["(2^2x3).2E6(2).2","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["(2^2x3).2E6(2)M4","4th maximal subgroup of (2^2x3).2E6(2)"],
["(2^2x3).2E6(2)M5","5th maximal subgroup of (2^2x3).2E6(2)"],
["(2^2x3).2E6(2)M8","8th maximal subgroup of (2^2x3).2E6(2)"],
["(2^2x3).2E6(2)M9","9th maximal subgroup of (2^2x3).2E6(2)"],
["(2^2x3).L3(4)","origin: ATLAS of finite groups, tests: 1.o.r., pow"],
["(2^2x3).L3(4).2_1","constructed using `PossibleCharacterTablesOfTypeV4G'"],
["(2^2x3).L3(4).2_2","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["(2^2x3).L3(4).2_3","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["(2^2x3).L3(4).3","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["(2^2x3).U6(2)","origin: computed in March 2000 from the tables of the factor groups\n2^2.U6(2) and 6.U6(2), the subgroup 3x2^2xU5(2), and the supergroup 6.Fi22"],
["(2^2x3).U6(2).2","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["(2^2x3).U6(2).3","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["(2^2x3).U6(2)M10","10th maximal subgroup of (2^2x3).U6(2),\ndiffers from (2^2x3).U6(2)M8 = 2^2x3xS6(2) only by fusion map"],
["(2^2x3).U6(2)M12","12th maximal subgroup of (2^2x3).U6(2),\ndiffers from (2^2x3).U6(2)M11 = 2x6.M22 only by fusion map"],
["(2^2x3).U6(2)M13","13th maximal subgroup of (2^2x3).U6(2),\ndiffers from (2^2x3).U6(2)M11 = 2x6.M22 only by fusion map"],
["(2^2x3).U6(2)M3","3rd maximal subgroup of (2^2x3).U6(2),\nintersection of a (2^2x3).U6(2) and a 2^11.3M22 in 6.Fi22,\nconstructed in April 2000 by Thomas Breuer using char. theor. methods\nfrom the known tables of 2^2.U6(2)M3, 6.U6(2)M3, and (2^2x3).U6(2)"],
["(2^2x3).U6(2)M5","5th maximal subgroup of (2^2x3).U6(2),\ndiffers from (2^2x3).U6(2)M4 = 2x6_1.U4(3).2_2 only by fusion map"],
["(2^2x3).U6(2)M6","6th maximal subgroup of (2^2x3).U6(2),\ndiffers from (2^2x3).U6(2)M4 = 2x6_1.U4(3).2_2 only by fusion map"],
["(2^2x3).U6(2)M9","9th maximal subgroup of (2^2x3).U6(2),\ndiffers from (2^2x3).U6(2)M8 = 2^2x3xS6(2) only by fusion map"],
["(2^2x3^4).2^3.S4","14th maximal subgroup of 2^2.O8+(2),\nconstructed using `PossibleCharacterTablesOfTypeV4G'"],
["(2^2x4).2^5.S3","origin: Dixon's Algorithm"],
["(2^2xA5):2","origin: Dixon's Algorithm,\n6th maximal subgroup of M12.2,\ntable is sorted w.r.t. normal series 2 < 2xA5 < 2^2xA5 < (2^2xA5):2"],
["(2^2xD14):3","Sylow 7 normalizer in Ru,\nof structure (2^2xD14):3, subdirect product of A4 and 7:6,\ncontained in maximal subgroups of type (2^2xSz(8)):3,\norigin: Dixon's Algorithm"],
["(2^2xF4(2)):2","6th maximal subgroup of B,\nconstructed from the tables of 2^2xF4(2) and 2xF4(2).2"],
["(2^2xSz(8)):3","origin: CAS library,\nmaximal subgroup of Ru,\nsource: received from S.Mattarei,\ntest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly,\ntests: 1.o.r., pow[2,3,5,7,13]"],
["(2^4:A4xA4).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(2^4:S5x3).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(2^5.2^6)a.(S3xL3(2))","origin: Dixon's Algorithm"],
["(2^5.2^6)b.(L3(2)xS3)","origin: Dixon's Algorithm"],
["(2^5.2^6.2^2)a.S3^2","origin: Dixon's Algorithm"],
["(2^5.2^6.2^2)b.S3^2","origin: Dixon's Algorithm"],
["(2^6x2^8):S6(2)","factor group of F4(2)M1 by central involution"],
["(2x12).L3(4)","constructed using `PossibleCharacterTablesOfTypeV4G'"],
["(2x13).6","origin: Dixon's Algorithm"],
["(2x17).8","origin: Dixon's Algorithm"],
["(2x2.(A5xA5)):2^2","15th maximal subgroup of 2^2.O8+(2),\nconstructed using `PossibleCharacterTablesOfTypeV4G'"],
["(2x29).14","origin: Dixon's Algorithm"],
["(2x2^(1+6)_+).A8","constructed using `PossibleCharacterTablesOfTypeV4G'"],
["(2x2^(1+8)):(U4(2):2x2)","6th maximal subgroup of Fi22.2,\norigin: Dixon's Algorithm"],
["(2x2^(1+8)):U4(2):2","origin: Dixon's Algorithm,\n7th maximal subgroup of Fi22,\ntable is sorted w.r.t. normal series 2.2.2^8.U4(2).2,\ntests: 1.o.r., pow[2,3,5]"],
["(2x2^(1+8)_+).2.2^4.(S3xS3)","origin: Dixon's Algorithm"],
["(2x2^(1+8)_+).O8+(2)","origin: Dixon's Algorithm"],
["(2x3.A6).2","2nd maximal subgroup of 2.J2,\nisoclinic table of 2x3.A6_2_2"],
["(2x3^(1+2)_+:8):2","origin: Dixon's Algorithm,\nSylow 3 normalizer in the sporadic simple Janko group J4\n(Note that the table printed in Ostermann's book is not related to J4.),\nmaximal subgroup of 6.L3(4).2_2"],
["(2x3^3).S4","7th maximal subgroup of 2.A9"],
["(2x3^3).S4`","origin: Dixon's Algorithm"],
["(2x3^4:2^3).S4","14th maximal subgroup of 2.O8+(2),\norigin: Dixon's Algorithm"],
["(2x3^5).U4(2).2","origin: Dixon's Algorithm"],
["(2x4).L3(4)","constructed using `PossibleCharacterTablesOfTypeV4G'"],
["(2x4^2).2^4.S3","origin: Dixon's Algorithm"],
["(2x5^2).12","origin: Dixon's Algorithm"],
["(2xA6).2^2","6th maximal subgroup of 2.M22.2"],
["(2xA6).2_3","non-split extension of 2xA6 with 2, factor group of 4.A6.2_3"],
["(2xA6.2^2).2","8th maximal subgroup of HS.2,\norigin: Dixon's Algorithm"],
["(2xL3(2)).2","7th maximal subgroup of 2.J2,\nisoclinic table of 2xL3(2).2"],
["(2xL3(3)).2","14th maximal subgroup of 2.Suz"],
["(2xO8+(3)).S4","12th maximal subgroup of 2.B,\ncontained in a maximal (3^2:2xO8+(3)).S4 type subgroup of the Monster"],
["(3.A6.2_2xA5):2","13th maximal subgroup of 3.Suz.2"],
["(3.A6x2.A5).2","12th maximal subgroup of 6.Suz,\nconstructed in May 2000 by Thomas Breuer, using the known tables of\n3.SuzM12, 2.SuzM12, and 6.Suz"],
["(3.A6xA5):2","12th maximal subgroup of 3.Suz"],
["(3^(1+2)+x3^2):2S4","origin: Dixon's Algorithm,\n3rd maximal subgroup of G2(3)"],
["(3^(1+2):2^2xG2(3)):2","origin: Dixon's Algorithm,\nnormalizer of a defect group of type 3^(1+2) in the Monster"],
["(3^(1+2):4x2.A6).2","13th maximal subgroup of 6.Suz,\norigin: Dixon's Algorithm"],
["(3^(1+2):4xA6).2","13th maximal subgroup of 3.Suz"],
["(3^(1+2):4xD10).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(3^(1+2):8x2.A6).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(3^(1+2):8xA6).2","14th maximal subgroup of 3.Suz.2"],
["(3^(1+2)_+:2x13:6).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(3^(1+2)x2).SD16","origin: Ostermann, tests: 1.o.r., pow[2,3]\nNote that this is NOT the table of the Sylow 3 normalizer J4,\ncontrary to the claim in Ostermann's book"],
["(3^(1+6).3)a.2.S4","origin: Dixon's Algorithm"],
["(3^(1+6).3)b.2.S4","normalizer of a radical 3-subgroup in Fi22,\nisomorphic with (3^(1+6).3)a.2.S4"],
["(3^2:2x13:6).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(3^2:2xG2(3)).2","origin: constructed using tables of G2(3), 3^2:2 and F3+,\n17th maximal subgroup of F3+,\ntests: 1.o.r., pow[2,3,7,13]"],
["(3^2:2xO8+(3)).S4","13th maximal subgroup of M,\ncomputed in September 2023 by Tim Burness, using Magma"],
["(3^2:4x2.A6).2","13th maximal subgroup of 2.Suz,\norigin: Dixon's Algorithm"],
["(3^2:4xA6).2^2","origin: Dixon's Algorithm,\n4th maximal subgroup of ON.2"],
["(3^2:4xD10).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(3^2:4xa6).2","origin: CAS library,\n13th maximal subgroup of Suz,\ntest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly,\ntests: 1.o.r., pow[2,3,5]"],
["(3^2:8xA6).2","14th maximal subgroup of Suz.2,\nnormalizer of a 3C^2 subgroup,\nsorted according to chief series 3^2.2.2.2.A6.2,\norigin: Dixon's Algorithm"],
["(3^2:D8xD10).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(3^2:D8xU4(3).2^2).2","14th maximal subgroup of the sporadic simple group B,\nconstructed by E. O'Brien using Magma, May 2007"],
["(3^2x2).U4(3)","constructed using `CharacterTableOfCommonCentralExtension'"],
["(3^2x2).U4(3).2_3'","origin: ATLAS of finite groups"],
["(3^2x2).U4(3).D8","origin: Dixon's Algorithm"],
["(3^2x4).U4(3)","constructed using `CharacterTableOfCommonCentralExtension'"],
["(3x13:6).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(3x2.D10).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(3x2.U4(2)):2","11th maximal subgroup of 2.O8+(2),\norigin: Dixon's Algorithm"],
["(3x2S5).2","origin: Dixon's Algorithm"],
["(3x2^(1+6)_-.U4(2)).2","5th maximal subgroup of 3.Suz.2"],
["(3x2^(2+8):(A5xS3)).2","10th maximal subgroup of 3.Suz.2"],
["(3x2^(4+6):3A6).2","8th maximal subgroup of 3.Suz.2"],
["(3x3^(1+2)+:2A4).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(3x3^3:S3):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(3xA6).2_1","origin: Dixon's Algorithm\n subgroup of U5(2).2"],
["(3xD10).2","origin: Dixon's Algorithm"],
["(3xG2(3)):2","origin: computed using GAP,\n5th maximal subgroup of Th"],
["(3xG2(4)).2","2nd maximal subgroup of 3.Suz.2"],
["(3xL2(16):2).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(3xL2(25)).2_2","15th maximal subgroup of 3.Suz.2"],
["(3xL3(4).2_2).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(3xM10):2","source: H. Pahlings,\n6th maximal subgroup of J3.2,\ntests: 1.o.r., pow[2,3,5]"],
["(3xMcLN2).2","normalizer of a 2-defect group of order 2^7 in Ly,\nconstructed using `PossibleCharacterTablesOfTypeMGA'"],
["(3xO8+(2)):2","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["(3xO8+(3):3):2","origin: constructed in GAP using tables of O8+(3).3, O8+(3).3.2, F3+,\n3rd maximal subgroup of F3+, 3A normalizer in F3+,\ntests: 1.o.r., pow[2,3,5,7,13]"],
["(3xO8-(2)):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct',\n5th maximal subgroup of O10+(2)"],
["(3xONN2).2","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["(3xSL(2,3)):2","origin: Dixon's Algorithm"],
["(3xU4(2)):2","10th maximal subgroup of O8+(2),\norigin: Dixon's Algorithm"],
["(3xU5(2)).2","4th maximal subgroup of 3.Suz.2"],
["(4^2x2)(2xS4)","origin: Dixon's Algorithm"],
["(4^2x2)S4","origin: Dixon's Algorithm"],
["(4^2x3).L3(4)","constructed using `PossibleCharacterTablesOfTypeV4G'"],
["(4^2x3):S3","origin: Dixon's Algorithm"],
["(4xA6).2_3","subdirect product of M10 and C8,\n7th maximal subgroup of 4.M22"],
["(4xA6):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(5^2:4S4x2.A5):2","origin: Dixon's Algorithm"],
["(5^2:[2^4]xU3(5)).S3","25th maximal subgroup of M"],
["(7:3x2.A7):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(7:3x2.L3(4).2).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(7:3x3):2","origin: Dixon's Algorithm"],
["(7:3x3):4","Sylow 7 normalizer in 2.G2(4),\norigin: Dixon's Algorithm"],
["(7:3xA5):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(7:3xA7):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(7:3xHe):2","17th maximal subgroup of M,\nconstructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(7:3xL2(7)):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(7^2)b:2.L2(7).2","normalizer of a radical 7-subgroup in ON,\ndiffers from 7^2:2.L2(7).2 only by fusion map"],
["(7^2:(3x2A4)xL2(7)).2","34th maximal subgroup of M,\nconstructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(7xL2(7)):2","origin: Dixon's Algorithm"],
["(7xL2(8)).3","maximal subgroup of L6(2)"],
["(9x3).S3","origin: Dixon's Algorithm"],
["(A10x3):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(A4wr2^2):2","factor of O8+(3)M27 by central involution"],
["(A4x11:5).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(A4x3.L3(4)).2","8th maximal subgroup of 3.Suz"],
["(A4x3.L3(4).2_3).2","9th maximal subgroup of 3.Suz.2"],
["(A4x7:3):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(A4xA5):2","origin: Dixon's Algorithm,\n6th maximal subgroup of J2.2"],
["(A4xD10).2","Sylow 5 normalizer in the sporadic simple Mathieu group M24,\norigin: Dixon's Algorithm"],
["(A4xG2(4)):2","origin: computed using GAP from tables of A4, S4, G2(4), G2(4).2, Co1,\n7th maximal subgroup of Co1"],
["(A4xL3(4):2_3):2","9th maximal subgroup of Suz.2,\norigin: Dixon's Algorithm"],
["(A4xO8+(2).3).2","12th maximal subgroup of Fi24'"],
["(A4xU4(2)):2","origin: Dixon's Algorithm,\n18th maximal subgroup of O8+(3)"],
["(A5xA12):2","18th maximal subgroup of M,\nconstructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(A5xA5).(2x4)","15th maximal subgroup of 2.O8+(2)"],
["(A5xA5):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(A5xA5):2^2","origin: Dixon's Algorithm"],
["(A5xA5):4","4th maximal subgroup of A10"],
["(A5xA9):2","origin: constructed in GAP using tables of A5, A5.2, A9, A9.2, F3+,\n18th maximal subgroup of F3+,\ntests: 1.o.r., pow[2,3,5,7]"],
["(A5xD10).2","origin: Dixon's Algorithm,\n7th maximal subgroup of J2.2"],
["(A5xJ2):2","origin: computed using GAP from tables of A5, S5, J2, J2.2, Co1,\n12th maximal subgroup of Co1"],
["(A5xU3(8):3):2","21st maximal subgroup of M,\nconstructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(A5xU4(2)):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct',\n8th maximal subgroup of O10+(2)"],
["(A6:2_2xA5).2","13th maximal subgroup of Suz.2,\norigin: Dixon's Algorithm"],
["(A6x2.A5).2","12th maximal subgroup of 2.Suz,\norigin: Dixon's Algorithm"],
["(A6xA4).2","5th maximal subgroup of A10"],
["(A6xA5):2","origin: Dixon's Algorithm,\n5th maximal subgroup of A11"],
["(A6xA6).D8","origin: Dixon's Algorithm,\n8th maximal subgroup of HN"],
["(A6xA6):2^2","origin: Dixon's Algorithm,\n24th maximal subgroup of O8+(3),\n4th maximal subgroup of A12,\nis of index 2 in 8th maximal subgroup of HN"],
["(A6xA6xA6).(2xS4)","20th maximal subgroup of M"],
["(A6xU3(3)):2","origin: computed using GAP from tables of A6, S6, U3(3), U3(3).2, Co1,\n14th maximal subgroup of Co1,\ntests: 1.o.r., pow[2,3,5,7]"],
["(A7x(A5xA5):2^2):2","27th maximal subgroup of M,\nconstructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(A7x3).2","3rd maximal subgroup of A10,\nconstructed using `PossibleCharacterTablesOfTypeMGA'"],
["(A7xA4):2","origin: Dixon's Algorithm,\n4th maximal subgroup of A11"],
["(A7xA5):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(A7xA6):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(A7xL2(7)):2","origin: computed using GAP from tables of A7, S7, L2(7), L2(7).2, Co1,\n17th maximal subgroup of Co1"],
["(A8x3).2","3rd maximal subgroup of A11,\nconstructed using `PossibleCharacterTablesOfTypeMGA'"],
["(A8xA4):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(A8xA5):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(A9x3):2","3rd maximal subgroup of A12,\nconstructed using `PossibleCharacterTablesOfTypeMGA'"],
["(A9xA4):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(D10x(A5xA5).2).2","origin: Dixon's Algorithm,\n18th maximal subgroup of Co1"],
["(D10x2.(A5xA5).2).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(D10x2^3.L3(2)).2","Sylow 5 normalizer in J4,\nconstructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(D10x3.A6).2_3","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(D10xA5).2","normalizer of a defect 5-subgroup of type 5CD in G2(4).2"],
["(D10xA6).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(D10xA9).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(D10xD10).2^2","origin: Dixon's Algorithm"],
["(D10xHN).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(D10xJ2).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(D10xU3(5)).2","origin: computed in GAP using tables of D10, 5:4, U3(5), U3(5).2, and HN,\n5th maximal subgroup of HN,\n5A normalizer in HN,\ntests: 1.o.r., pow[2,3,5,7]"],
["(D10xU3(5)N2).2","defect normalizer of a 2-block of defect 4 in HN,\nconstructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(D8xA6).2^2","origin: Dixon's Algorithm"],
["(GL(2,3)x2F4(2)').2","origin: Dixon's Algorithm"],
["(L2(11)x3).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(L2(11)xL2(11)):4","32nd maximal subgroup of M,\norigin: Dixon's Algorithm"],
["(L2(11)xM12):2","26th maximal subgroup of M,\nconstructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(L3(2)xL3(2)).4","origin: Dixon's Algorithm"],
["(L3(2)xL3(2)):2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(L3(2)xL3(4)).2","subdirect product of L3(2).2 and L3(4).2_1,\n16th maximal subgroup of 2E6(2)"],
["(L3(2)xL3(4).2_2).2","subdirect product of L3(2).2 and L3(4).2^2,\n16th maximal subgroup of 2E6(2).2"],
["(L3(2)xS4(4):2).2","23rd maximal subgroup of M,\nconstructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(Q16xU3(3)).2","normalizer of a Q16 type defect group in 2.Co1,\nconstructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(Q8x13:4):3","origin: Dixon's Algorithm"],
["(Q8xD14):3","origin: Dixon's Algorithm"],
["(QD16x2F4(2)').2","normalizer of a defect group of type QD16 in 2.B and M,\norigin: Dixon's Algorithm"],
["(S3x2.Fi22).2","9th maximal subgroup of 2.B,\n3rd maximal subgroup of 3.Fi24"],
["(S3x2.U4(3).2_2).2","7th maximal subgroup of 2.Fi22.2,\norigin: constructed in August 2003 by Thomas Breuer,\nusing the M.G.A structure,\n(independently computed using Dixon's Algorithm)"],
["(S3xS3):2xS5","8th maximal subgroup of O8-(2).2"],
["(S3xS3xA5):2","origin: Dixon's Algorithm"],
["(S3xS3xG2(3)):2","16th maximal subgroup of Fi24"],
["(S5xS5xS5):S3","31st maximal subgroup of M"],
["(S6wr2).2","origin: Dixon's Algorithm"],
["(S6xL3(4).2).2","19th maximal subgroup of B,\nconstructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(S6xS6).2^2","9th maximal subgroup of HN.2,\norigin: Dixon's Algorithm"],
["(S6xS6).4","origin: Dixon's Algorithm,\n22nd maximal subgroup of B"],
["(S6xS6):2","10th maximal subgroup of S8(2)"],
["(SL(2,3)x7:3).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(SL2(3)x7:3).2","constructed using `CharacterTableOfIndexTwoSubdirectProduct'"],
["(a4xpsl(3,4)):2","origin: CAS library,\n8th maximal subgroup of Suz,\ntest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3,5,7]"],
["(a6xa5).2","origin: CAS library,\n12th maximal subgroup of Suz,\ntests: 1.o.r., pow[2,3,5]"],
["10^2:S3","origin: Dixon's Algorithm"],
["11+^(1+2):(5x2S4)","origin: Ostermann\ntests: 1.o.r., pow[2,3,5,11]\nMaximal subgroup in sporadic Janko group J4."],
["11:10","origin: CAS library,\nmaximal subgroup of J1,\ntest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly\nconstructions: AGL(1,11),\ntests: 1.o.r., pow[2,5,11]"],
["11:20","origin: Dixon's Algorithm"],
["11:5","3rd maximal subgroup of L2(11)"],
["11:5xS3","Sylow 11 normalizer in 3.McL.2 and Ly"],
["11^(1+2)+:40","origin: Dixon's Algorithm"],
["11^2:(5x2.A5)","origin: Dixon's Algorithm,\nSylow 11 normalizer in the Monster, maximal subgroup of M,\nthe structure is 11^2:(5x2.A5),\nand there is a unique class of 5x2.A5 subgroups in GL(2,11)"],
["11^2:(5x2L2(11).2)","origin: Dixon's Algorithm,\nconstructions: AGL(2,11)"],
["11^2:60","origin: Dixon's Algorithm"],
["12.A6.2_3","origin: ATLAS of finite groups"],
["12.M22","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["12.M22.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["12.M22M2","2nd maximal subgroup of 12.M22,\nconstructed by Stefan Irnich using GAP"],
["12.M22M7","subdirect product of 3.A6.2_3 and C8,\n7th maximal subgroup of 12.M22"],
["12.M22N3","origin: Dixon's Algorithm"],
["127:7","4th maximal subgroup of L7(2)"],
["12_1.L3(4)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["12_1.L3(4).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["12_1.L3(4).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["12_1.L3(4).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["12_1.U4(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["12_1.U4(3).2_1","origin: ATLAS of finite groups, tests: 1.o.r."],
["12_1.U4(3).2_2","origin: ATLAS of finite groups, tests: 1.o.r."],
["12_1.U4(3).2_2'","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructed using `PossibleCharacterTablesOfTypeMGA'"],
["12_2.L3(4)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["12_2.L3(4).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["12_2.L3(4).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["12_2.L3(4).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]\n2nd power map determined in 4_2.L3(4).2_3 (see there)"],
["12_2.U4(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3]\n3rd power map determined only up to matrix automorphisms\n(138,142)(139,143)(140,144)(141,145), (130,134)(131,135)(132,136)(133,137)"],
["12_2.U4(3).2_1","origin: ATLAS of finite groups, tests: 1.o.r."],
["12_2.U4(3).2_3","origin: ATLAS of finite groups, tests: 1.o.r.,\n3rd power map determined only up to matrix automorphism\n(86,90)(88,92)(87,91)(89,93)"],
["12_2.U4(3).2_3'","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructed using `PossibleCharacterTablesOfTypeMGA',\n3rd power map determined only up to matrix automorphism\n(20,22)(74,76)(78,80)"],
["13:12","3rd maximal subgroup of Sz(8).3,\nconstructions: AGL(1,13)"],
["13:4","9th maximal subgroup of 3D4(2)"],
["13^(1+2):(3x4S4)","Sylow 13 normalizer in the sporadic simple group M,\nstructure: 13^{1+2}_+:(3x4S4),\norigin: Dixon's Algorithm,\nconstructed by Thomas Breuer using the Atlas' structure information"],
["13^2:2.L2(13).4","33rd maximal subgroup of M,\norigin: Dixon's Algorithm"],
["17:16","constructions: AGL(1,17)"],
["19:18","3rd maximal subgroup of J3.2,\nconstructions: AGL(1,19)"],
["19:6","origin: CAS library,\nmaximal subgroup of J1,\ntest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly,\ntests: 1.o.r., pow[2,3,19]"],
["19:9","1st maximal subgroup of L2(19)"],
["2(A4xA4).2^2","origin: Dixon's Algorithm,\n2A normalizer in U4(3)"],
["2(A4xA4).4.2","origin: Dixon's Algorithm"],
["2(A4xA4).4.2^2","origin: Dixon's Algorithm"],
["2(L2(11)x2).2","origin: Dixon's Algorithm"],
["2(L2(7)x4).2","origin: Dixon's Algorithm"],
["2(S4xS4)","factor group of 3^(3+4):2(S4xS4) < Co1"],
["2.(13:6xA4).2","origin: Dixon's Algorithm"],
["2.(2.(A4xA4).2)","origin: Dixon's Algorithm"],
["2.(2.(A4xA4).2.2)","origin: Dixon's Algorithm"],
["2.(2^2xSz(8)):3","origin: computed by J\"urgen M\"uller using GAP,\n3rd maximal subgroup of 2.Ru,"],
["2.(2^2xU4(2)).2","origin: Dixon's Algorithm"],
["2.(2^4:A5)","origin: Dixon's Algorithm"],
["2.(2^5:S6)","origin: Dixon's Algorithm"],
["2.(2x2^(1+8)):U4(2):2","7th maximal subgroup of 2.Fi22,\norigin: Dixon's Algorithm"],
["2.(2x3.A7)","3rd and 4th maximal subgroup of 12.M22"],
["2.(2x3^4:A6)","1st maximal subgroup of 4.U4(3), contributed by G. Hiss"],
["2.(2xA7)","3rd and 4th maximal subgroup of 4.M22"],
["2.(2xF4(2)).2","4B centralizer in the Monster group,\nconstructed by Simon Norton, Dec. 2000"],
["2.(2xL2(11))","8th maximal subgroup of 4.M22"],
["2.(3^(1+6):2^(3+4):3^2:2)","origin: Dixon's Algorithm"],
["2.(3^2:D8xU4(3).2^2).2","origin: Dixon's Algorithm"],
["2.(3^3:(S4x2))","origin: Dixon's Algorithm"],
["2.(A4x2(A4xA4).2).2","origin: Dixon's Algorithm"],
["2.(A4xA4)","origin: Dixon's Algorithm,\nnormal subgroup of index 2 in U4(2)M5"],
["2.(A4xL3(4)).2","8th maximal subgroup of 2.Suz,\nstructure (SL(2,3) Y 2.L3(4)).2,\norigin: Dixon's Algorithm"],
["2.(A4xU4(2))","4th maximal subgroup of S6(3),\norigin: Dixon's Algorithm"],
["2.(A5wr2)","origin: Dixon's Algorithm"],
["2.(A5xA4).2","6th maximal subgroup of 2.A9"],
["2.(A5xA5).2","origin: Dixon's Algorithm,\n5th maximal subgroup of G2(5)"],
["2.(A5xA5).2^2","16th maximal subgroup of 2.O8+(2),\norigin: Dixon's Algorithm"],
["2.(A5xA5).4","4th maximal subgroup of 2.A10"],
["2.(A6xA4).2","5th maximal subgroup of 2.A10"],
["2.(A6xA5).2","origin: Dixon's Algorithm,\n5th maximal subgroup of 2.A11"],
["2.(A7xA4).2","origin: Dixon's Algorithm,\n4th maximal subgroup of 2.A11"],
["2.(D10xJ2).2","origin: Dixon's Algorithm"],
["2.(D8x2^2).S3","origin: Dixon's Algorithm"],
["2.(D8x3^(1+2)_+:Q8)","origin: Dixon's Algorithm"],
["2.(D8x3^2:Q8)","origin: Dixon's Algorithm"],
["2.(S3x5:4)","origin: Dixon's Algorithm"],
["2.(S3xS6)","origin: Dixon's Algorithm"],
["2.(S4xS5)","origin: Dixon's Algorithm"],
["2.(S6x2)","origin: Dixon's Algorithm"],
["2.(S6xS4)","origin: Dixon's Algorithm"],
["2..11.m23","origin: CAS library,\nnames:= 2..11.m23\n order: 2^18.3^2.5.7.11.23 = 20,891,566,080\n number of classes: 56\n source:gabrysch, thomas\n ein computerprogramm zur berechnung\n von charakterentafeln und einige anwendungen,\n diplomarbeit, univ. of bielefeld [1977]\n comments:non-split extension of m23 with an\n elementar-abelian group of order 2..11.m23 \n test: 1. o.r., sym 2 decompose correctly \n2nd power map determined by subgroup fusion into Fi23\ntests: 1.o.r., pow[2,3,5,7,11,23]"],
["2.2.2^4+6:S5","origin: Dixon's Algorithm,\n6th maximal subgroup of 2.Ru"],
["2.2E6(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.2E6(2).2","origin: ATLAS of finite groups"],
["2.2E6(2)M5","5th maximal subgroup of 2.2E6(2)"],
["2.2E6(2)M9","9th maximal subgroup of 2.2E6(2)"],
["2.2^(1+8)_+:(S3xS3xS3)","13th maximal subgroup of 2.O8+(2),\norigin: Dixon's Algorithm"],
["2.2^(2+12):(A8xS3)","origin: Dixon's Algorithm"],
["2.2^(2+2).2^(1+1+2+2):S4","origin: Dixon's Algorithm,\none type of solvable subgroups of maximal order in Ru"],
["2.2^(2+8).(3xA5)","2nd maximal subgroup of 2.G2(4), of structure 2.2^{2+8}.(3xA5),\nconstructed by S. Irnich and J. M\"uller using the tables of G2(4)M2,\nG2(4), 2.G2(4), and the splitting of classes computed from a perm. repr.,\ntests: 1.o.r., pow[2,3,5]"],
["2.2^(3+3):7","origin: Dixon's Algorithm"],
["2.2^(4+12).(S3x3S6)","origin: Dixon's Algorithm"],
["2.2^(4+6).2.S3","origin: Dixon's Algorithm"],
["2.2^11:M24","origin: computed by Thomas Breuer using tables of 2.Co1 and 2^11:M24,\n3rd maximal subgroup of 2.Co1,\ntests: 1.o.r., pow[2,3]"],
["2.2^3+8:L3(2)","origin: Dixon's Algorithm,\n4th maximal subgroup of 2.Ru,"],
["2.2^3.2^5.S3","origin: Dixon's Algorithm"],
["2.2^4+6:S5","maximal subgroup of Ru,\nnormalizer of a 2A involution, tests: 1.o.r., pow[2,3,5]"],
["2.2^4.(S3x3^2:2)","origin: Dixon's Algorithm"],
["2.2^4.2.S3","origin: Dixon's Algorithm"],
["2.2^4.2^4.S3","origin: Dixon's Algorithm"],
["2.2^4.S6","6th maximal subgroup of 2.HS,\norigin: Dixon's Algorithm"],
["2.2^5.S6","origin: Dixon's Algorithm"],
["2.2^6.L3(2)","origin: Dixon's Algorithm"],
["2.2^6:u3(3):2","origin: Dixon's Algorithm,\n2nd maximal subgroup of 2.Ru,"],
["2.2^8.f20","origin: CAS library,\nmaximal subgroup of 2F4(2)',\n centralizer of 2a-element\n structure:= 2*[2^8]:f20 [f20: frobenius group of order 20]\n 1st & 2nd orthogonality relations are satisfied\n symmetric squares decompose properly\n created August 1984,\n test: 1. o.r., sym 2 decompose correctly,\ntests: 1.o.r., pow[2,5]"],
["2.3^4.2^3.S4","origin: Dixon's Algorithm"],
["2.4^3.L3(2)","7th maximal subgroup of 2.HS"],
["2.A10","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.A10.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.A11","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["2.A11.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["2.A11M7","7th maximal subgroup of 2.A11,\ndiffers from 2.A11M6 = 2xM11 only by fusion map"],
["2.A12","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["2.A12.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["2.A12M8","8th maximal subgroup of 2.A12,\ndiffers from 2.A12M7 = 2.M12 only by fusion map"],
["2.A13","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"],
["2.A13.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"],
["2.A14.2","Schur cover of S14,\nconstructed by Gunter Malle"],
["2.A15.2","Schur cover of S15,\nconstructed by Gunter Malle"],
["2.A16.2","Schur cover of S16,\nconstructed by Gunter Malle"],
["2.A17.2","Schur cover of S17,\nconstructed by Gunter Malle"],
["2.A18.2","Schur cover of S18,\nconstructed by Gunter Malle"],
["2.A4xS3","11th maximal subgroup of 2.M12"],
["2.A5","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["2.A5.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["2.A5.2xS3","3B-normalizer in 2.G2(4).2"],
["2.A6","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["2.A6.2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5],\nconstructions: SigmaL(2,9)"],
["2.A6.2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["2.A6M2","2nd maximal subgroup of 2.A6,\ndiffers from 2.A6M1 = 2.A5 only by fusion map"],
["2.A6M5","5th maximal subgroup of 2.A6,\ndiffers from 2.A6M4 = 2.Symm(4) only by fusion map"],
["2.A7","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.A7.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.A8","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.A8.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.A8N3","origin: Dixon's Algorithm"],
["2.A9","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.A9.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.A9M5","5th maximal subgroup of 2.A9,\ndiffers from 2.A9M4 only by fusion map"],
["2.B","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.BN7","origin: Dixon's Algorithm,\nSylow 7 normalizer in 2.B"],
["2.Co1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13,23]"],
["2.D10xA5","5CD-normalizer in 2.G2(4)"],
["2.D12","origin: Dixon's Algorithm"],
["2.D14","origin: Dixon's Algorithm"],
["2.D16","origin: Dixon's Algorithm"],
["2.D18","origin: Dixon's Algorithm"],
["2.D20","origin: Dixon's Algorithm"],
["2.D22","origin: Dixon's Algorithm"],
["2.D24","origin: Dixon's Algorithm"],
["2.D26","origin: Dixon's Algorithm"],
["2.D28","origin: Dixon's Algorithm"],
["2.D30","origin: Dixon's Algorithm"],
["2.D32","origin: Dixon's Algorithm"],
["2.D8.S5","origin: Dixon's Algorithm"],
["2.F4(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.F4(2).2","origin: ATLAS of finite groups\nthe 2nd power map had been incorrect up to version 1.3,\n(the map had 85,85,86,86 instead of 86,86,85,85)"],
["2.F4(2)M1","computed using Magma V2.23-4 Thu Oct 19 2017 17:46:11 on schedir\n[Seed = 1959126426]\nTotal time: 2871.289 seconds, Total memory usage: 2133.88MB"],
["2.F4(2)M2","2nd maximal subgroup of 2.F4(2),\ndiffers from 2.F4(2)M1 only by fusion map"],
["2.F4(2)M5","computed using Magma V2.23-4 Thu Oct 19 2017 17:21:28 on schedir\n[Seed = 3681173513]\nTotal time: 475.949 seconds, Total memory usage: 150.62MB"],
["2.F4(2)M6","6th maximal subgroup of 2.F4(2),\ndiffers from 2.F4(2)M5 only by fusion map"],
["2.Fi22","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.Fi22.2","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.Fi22M13","13th maximal subgroup of 2.Fi22,\ndiffers from 2.Fi22M12 = S10x2 only by fusion map"],
["2.Fi22M3","3rd maximal subgroup of 2.Fi22"],
["2.Fi22M5","origin: computed from the character tables of Fi22M5, Fi22, and 2.Fi22,\nthe table is sorted w.r.t. the normal series 2 < 2^11 < 2^11.M22"],
["2.Fi22N2","origin: Dixon's Algorithm"],
["2.G2(4)","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.G2(4).2","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.G2(4)N2","origin: Dixon's Algorithm"],
["2.HS","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["2.HS.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["2.HS.2N2","origin: Dixon's Algorithm"],
["2.HS.2N3","origin: Dixon's Algorithm"],
["2.HS.2N5","origin: Dixon's Algorithm,\nSylow 5 normalizer in 2.HS.2,\nmaximal subgroup of 2.HS.2,\ntable is sorted w.r. to normal series 2.5.5^2.8.2.2,\ntests: 1.o.r., pow[2,5]"],
["2.HSM10","preimage in 2.HS of the 2A centralizer in HS,\norigin: Dixon's Algorithm"],
["2.HSM11","origin: Dixon's Algorithm"],
["2.HSM3","3rd maximal subgroup of 2.HS,\ndiffers from 2.HSM2 only by fusion map"],
["2.HSM9","9th maximal subgroup of 2.HS,\ndiffers from 2.HSM8 only by fusion map"],
["2.HSN2","origin: Dixon's Algorithm"],
["2.HSN3","origin: Dixon's AlgorithmSylow 3 normalizer in 2.HS"],
["2.HSN3A","3A normalizer in 2.HS, isoclinic with S5xS3x2"],
["2.J2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.J2.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.J2.2N5","origin: Dixon's Algorithm"],
["2.J2M8","8th maximal subgroup of 2.J2,\nisoclinic table of 2x5^2:D12"],
["2.J2N2","origin: Dixon's Algorithm"],
["2.J2N3","origin: Dixon's Algorithm"],
["2.L2(11)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11]"],
["2.L2(11).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11]"],
["2.L2(13)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13]"],
["2.L2(13).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13]"],
["2.L2(17)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,17]"],
["2.L2(17).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,17]"],
["2.L2(19)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,19]"],
["2.L2(19).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,19]"],
["2.L2(23)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,11,23]"],
["2.L2(23).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,11,23]"],
["2.L2(25)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"],
["2.L2(25).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"],
["2.L2(25).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\nconstructions: SigmaL(2,25)"],
["2.L2(25)M3","3rd maximal subgroup of 2.L2(25),\ndiffers from 2.L2(25)M2 = Isoclinic(2.A5.2) only by fusion map"],
["2.L2(27)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13]"],
["2.L2(27).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13]"],
["2.L2(27).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13],\nconstructions: SigmaL(2,27)"],
["2.L2(27).6","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13]"],
["2.L2(29)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,29]"],
["2.L2(29).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,29]"],
["2.L2(3)","origin: Dixon's Algorithm"],
["2.L2(31)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,31]"],
["2.L2(31).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,31]"],
["2.L2(49)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.L2(49).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.L2(49).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.L2(81)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,41]"],
["2.L2(81).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,41]"],
["2.L2(81).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["2.L2(81).4_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,41]"],
["2.L3(2)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7]"],
["2.L3(2).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7]"],
["2.L3(4)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.L3(4).(2^2)_{1*2*3*}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.L3(4).(2^2)_{1*2*3}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.L3(4).(2^2)_{1*23*}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.L3(4).(2^2)_{1*23}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.L3(4).(2^2)_{12*3*}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.L3(4).(2^2)_{12*3}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.L3(4).(2^2)_{123*}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.L3(4).(2^2)_{123}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.L3(4).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.L3(4).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.L3(4).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.L3(4)M4","4th maximal subgroup of 2.L3(4),\ndiffers from 2xA6 = 2.L3(4)M3 only by fusion map"],
["2.L3(4)M5","5th maximal subgroup of 2.L3(4),\ndiffers from 2xA6 = 2.L3(4)M3 only by fusion map"],
["2.L3(4)M7","7th maximal subgroup of 2.L3(4),\ndiffers from 2xL3(2) = 2.L3(4)M6 only by fusion map"],
["2.L3(4)M8","8th maximal subgroup of 2.L3(4),\ndiffers from 2xL3(2) = 2.L3(4)M6 only by fusion map"],
["2.L4(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"],
["2.L4(3).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\nconstructions: GL(4,3)"],
["2.L4(3).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"],
["2.L4(3).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"],
["2.L4(5)","computed by Thomas Breuer in December 2005,\nusing the character table of the factor group, Dixon's algorithm,\nand character theoretic methods"],
["2.M12","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11]"],
["2.M12.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11]"],
["2.M12M10","origin: Dixon's Algorithm,\n10th maximal subgroup of 2.M12"],
["2.M12M2","2nd maximal subgroup of 2.M12,\ndiffers from 2.M12M1 = 2xM11 only by fusion map"],
["2.M12M4","4th maximal subgroup of 2.M12,\ndiffers from 2.M12M3 = A6.D8 only by fusion map"],
["2.M12M7","7th maximal subgroup of 2.M12,\ndiffers from 2.M12M6 = 2x3^2.2.S4 only by fusion map"],
["2.M12M8","origin: Dixon's Algorithm,\n8th maximal subgroup of 2.M12,\nstructure is 4Y(2xA5):2"],
["2.M12M9","origin: Dixon's Algorithm,\n9th maximal subgroup of 2.M12,\nstructure is (2xQ8).S4"],
["2.M12N2","origin: Dixon's Algorithm"],
["2.M12N5","origin: Dixon's Algorithm"],
["2.M22","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["2.M22.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["2.M22M2","2nd maximal subgroup of 2.M22,\nconstructed by Stefan Irnich using GAP"],
["2.M22M5","5th maximal subgroup of 2.M22,\nconstructed by S. Irnich using tables of M22, 2.M22, M22M5"],
["2.M22N2","origin: Dixon's Algorithm"],
["2.O10-(3)","computed by Eamonn O'Brien using Magma, November 2007"],
["2.O7(3)","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.O7(3).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2.3.5.7.13]"],
["2.O7(3)M8","8th maximal subgroup of 2.O7(3),\ndiffers from 2.O7(3)M7 = 2.S6(2) only by fusion map"],
["2.O7(3)M9","origin: Dixon's Algorithm"],
["2.O8+(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.O8+(2).2","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.O8+(2)M12","12th maximal subgroup of 2.O8+(2),\ndiffers from 2.O8+(2)M11 = (3x2.U4(2)):2 only by fusion map"],
["2.O8+(2)M17","17th maximal subgroup of 2.O8+(2),\ndiffers from 2.O8+(2)M16 = 2.(A5xA5).2^2 only by fusion map"],
["2.O8+(2)M3","3rd maximal subgroup of 2.O8+(2),\ndiffers from 2.O8+(2)M2 = 2.S6(2) only by fusion map"],
["2.O8+(2)M6","6th maximal subgroup of 2.O8+(2),\ndiffers from 2.O8+(2)M5 = 2^(1+6)_+.A8 only by fusion map"],
["2.O8+(2)M9","9th maximal subgroup of 2.O8+(2),\ndiffers from 2.O8+(2)M8 = 2.A9 only by fusion map"],
["2.O8+(3)","constructed by Max Neunh\"offer, April 2008"],
["2.O8+(7)","computed by Eamonn O'Brien using Magma, December 2011"],
["2.O8-(3)","constructed by Max Neunh\"offer, April 2008"],
["2.O9(3)","constructed by Max Neunh\"offer, April 2008"],
["2.Ru","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13,29]"],
["2.RuM1","1st maximal subgroup of 2.Ru"],
["2.RuN2","origin: Dixon's Algorithm"],
["2.S4","origin: CAS library, tests: 1.o.r., pow[2,3]"],
["2.S4(5)","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Sp(4,5)"],
["2.S4(5).2","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.S6(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.S6(3)","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.S6(3).2","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.Suz","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"],
["2.Suz.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"],
["2.SuzM11","11th maximal subgroup of 2.Suz,\norigin: Dixon's Algorithm"],
["2.SuzM4","table of the 4th maximal subgroup of 2.Suz, structure 2.2^(1+6).U4(2),\nconstructed by Thomas Breuer 1997/03/17 using the tables of Suz, 2.Suz,\nand SuzM4\n"],
["2.SuzM7","7th maximal subgroup of 2.Suz,\nstructure (2.2^4.2^6):3A6,\norigin: Dixon's Algorithm"],
["2.SuzM9","9th maximal subgroup of 2.Suz,\norigin: Dixon's Algorithm"],
["2.SuzN2","origin: Dixon's Algorithm"],
["2.Sz(8)","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.U4(2)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5],\nconstructions: Sp(4,3)"],
["2.U4(2).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["2.U4(2)N2","origin: Dixon's Algorithm"],
["2.U4(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.U4(3).(2^2)_{1*2*2*}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.U4(3).(2^2)_{1*2*2}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.U4(3).(2^2)_{1*22}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.U4(3).(2^2)_{1*3*3*}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.U4(3).(2^2)_{1*3*3}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.U4(3).(2^2)_{1*33}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.U4(3).(2^2)_{12*2*}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.U4(3).(2^2)_{12*2}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.U4(3).(2^2)_{122}","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.U4(3).(2^2)_{13*3*}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.U4(3).(2^2)_{13*3}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.U4(3).(2^2)_{133}","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.U4(3).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.U4(3).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.U4(3).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.U4(3).4","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2.U4(3).D8","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["2.U6(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["2.U6(2).2","origin: ATLAS of finite groups"],
["2.U6(2)M10","10th maximal subgroup of 2.U6(2),\ndiffers from 2.U6(2)M9 = 2xS6(2) only by fusion map"],
["2.U6(2)M13","13th maximal subgroup of 2.U6(2),\ndiffers from 2.U6(2)M12 = 2.M22 only by fusion map"],
["2.U6(2)M3","3rd maximal subgroup of 2.U6(2),\nintersection of a 2.U6(2) and a 2^10:M22 in Fi22,\nstructure 2^10:L3(4),\nconstructed in March 2000 by Thomas Breuer using char. theor. methods\nfrom the known tables of 2.U6(2) and 2^9.L3(4)"],
["2.U6(2)M6","6th maximal subgroup of 2.U6(2),\ndiffers from 2.U6(2)M5 = 2.U4(3).2_2 only by fusion map"],
["2.U6(2)M9","9th maximal subgroup of 2.U6(2),\ndiffers from 2.U6(2)M8 = 2xS6(2) only by fusion map"],
["2.[2^6].(2xS3)","origin: Dixon's Algorithm"],
["2.[2^6]:(S3xS3)","origin: Dixon's Algorithm,\n6th maximal subgroup of S6(2),\ntable is sorted w.r.t. normal series 2.2^2.2^4.3.2.3.2,\nmodule for S3xS3 is 2^2 x 2^{1+4}_+"],
["2.[2^9]:5:4","origin: Dixon's Algorithm"],
["23:11","origin: CAS library,\nmaximal subgroup of M23,\ntest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[11,23]"],
["23:22","23 normalizer in J4,\nconstructions: AGL(1,23)"],
["25:4","3rd maximal subgroup of Sz(32),\norigin: Dixon's Algorithm"],
["29:14","25th maximal subgroup of F3+"],
["2A4xA5","5th maximal subgroup of 2.J2"],
["2A5xD10","6th maximal subgroup of 2.J2"],
["2E6(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["2E6(2).2","origin: ATLAS of finite groups, tests: 1.o.r."],
["2E6(2).2N3C","origin: Dixon's Algorithm,\ncomputed from a permutation representation of the underlying group,\nwhich was determined using `CyclicExtensions` (from the GrpConst package)\nfor the 3C normalizer in 2E6(2);\nthere is exactly one such extension apart from the direct product.\nThe table is sorted w.r.t. a normal series\nwith factors 3.3^6.2^3.2^6.(S3xS3)."],
["2E6(2).3","origin: constructed by Simon Norton, Jan. 1996, tests: 1.o.r., pow"],
["2E6(2).3.2","origin: constructed from tables of 2E6(2).3 and 2E6(2).2,\ntests: 1.o.r., pow[2,3,5,7,11,13,17,19],\nconstructions: Aut(2E6(2))"],
["2E6(2)M4","4th maximal subgroup of 2E6(2)"],
["2E6(2)M5","5th maximal subgroup of 2E6(2)"],
["2E6(2)M8","8th maximal subgroup of 2E6(2)"],
["2E6(2)M9","9th maximal subgroup of 2E6(2)"],
["2E6(2)N3C","origin: Dixon's Algorithm,\ncomputed by Frank L\"ubeck in December 2018,\nusing a permutation representation of 2E6(2),\nthe table is sorted w.r.t. the derived series,\nwith factors 3.3^6.2^3.2^6.3^2.2,\nnote that the structure claimed in the ATLAS of Finite Groups is wrong"],
["2F4(2)'","origin: ATLAS of finite groups, tests: 1.o.r."],
["2F4(2)'.2","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(2F4(2)')"],
["2F4(2)'.2N2","origin: Dixon's Algorithm"],
["2F4(2)'M2","2nd maximal subgroup of 2F4(2)',\ndiffers from 2F4(2)'M1 only by fusion map"],
["2F4(2)'M7","7th maximal subgroup of 2F4(2)',\ndiffers from 2F4(2)'M6 only by fusion map"],
["2F4(2)'N2","origin: Dixon's Algorithm"],
["2F4(2)x2","4th maximal subgroup of F4(2).2"],
["2F4(8)","source: Gunter Malle, tests: 1.o.r., pow[2,3,5,7,13,19,37,109]"],
["2S5.2","origin: Dixon's Algorithm"],
["2^(1+1+2+2):S3","origin: Dixon's Algorithm,\ntable of the intersection of maximal subgroups 2^4:A7, 2^4:A7, and 2.A8\nin McL"],
["2^(1+1+2+4).(2x2^(2+4).S3^2)","origin: Dixon's Algorithm"],
["2^(1+1+3+3).(2x2^(3+3).L3(2))","origin: Dixon's Algorithm"],
["2^(1+12).3_1.U4(3).2_2'","9th maximal subgroup of F3+,\nconstructed in September 2000 by Thomas Breuer, using a permutation\nrepresentation and the table of F3+, sorted according to the chain\n2 < 2^(1+12) < 2^(1+12).3 < 2^(1+12).3.U4(3) < 2^(1+12).3.U4(3).2,\ntests: 1.o.r., pow[2,3,5,7]"],
["2^(1+12)_+.3_1.U4(3).2^2_{122}","10th maximal subgroup of Fi24"],
["2^(1+22).Co2","maximal subgroup in the sporadic simple group B,\nconstructed by H. Pahlings in March 2005 using Clifford matrices"],
["2^(1+3):L3(2)","origin: Dixon's Algorithm,\ntable of the intersection of maximal subgroups 2.A8 and 2^4:A7 in McL"],
["2^(1+4)+.(S3xS3)","origin: Dixon's Algorithm"],
["2^(1+4)+:3^2.2","origin: Dixon's Algorithm\n10th maximal subgroup of G2(3)"],
["2^(1+4).S3","origin: Dixon's Algorithm,\nmaximal subgroup of U3(3).2"],
["2^(1+4).S3^2","origin: Dixon's Algorithm"],
["2^(1+4).S5","source: H. Pahlings,\n4th maximal subgroup of J2.2,\n8th maximal subgroup of J3.2,\ntests: 1.o.r., pow[2,3,5]"],
["2^(1+4)_+.(S3x3^2:2)","origin: Dixon's Algorithm"],
["2^(1+5+8).(S3xA6)","origin: Dixon's Algorithm"],
["2^(1+6)_+.A8","origin: Dixon's Algorithm,\n5th maximal subgroup of 2.O8+(2)"],
["2^(1+6)_+.L3(2).2","origin: Dixon's Algorithm"],
["2^(1+6)_+:A7","origin: Dixon's Algorithm"],
["2^(1+6)_+:S5","7th maximal subgroup of HS.2,\norigin: Dixon's Algorithm"],
["2^(1+6)_-.2^4.A5","origin: Dixon's Algorithm"],
["2^(1+6)_-.3^3.S4","origin: Dixon's Algorithm"],
["2^(1+6)_-.U4(2).2","2A normalizer in Suz.2, 5th maximal subgroup of Suz.2,\nsorted according to chief series 2.2^6.U4(2).2,\norigin: Dixon's Algorithm"],
["2^(1+6)_-3.3.3^2:2","origin: Dixon's Algorithm\n subgroup of U5(2).2"],
["2^(1+8)+.O8+(2)","origin: CAS library,\nmaximal subgroup (involution centralizer) in Co1,\ntests: 1.o.r., pow[2,3,5,7]"],
["2^(1+8)+:L2(8)","origin: Dixon's Algorithm"],
["2^(1+8).(A5xA5).2","origin: Dixon's Algorithm,\n4th maximal subgroup of HN,\ntable is sorted w.r. to normal series 2.2^8.(A5xA5).2,\ntests: 1.o.r., pow[2,3,5]"],
["2^(1+8).2^(1+4).S3","origin: Dixon's Algorithm"],
["2^(1+8).2^2.(3xA5).2","origin: Dixon's Algorithm"],
["2^(1+8).2^2.S3^2","origin: Dixon's Algorithm"],
["2^(1+8).2^3.2^2.S3","origin: Dixon's Algorithm"],
["2^(1+8).2^4.2.S3","origin: Dixon's Algorithm"],
["2^(1+8).2^4.S3^2","origin: Dixon's Algorithm"],
["2^(1+8).D8.S3","origin: Dixon's Algorithm"],
["2^(1+8):S8","maximal subgroup of 2^(1+8).S6(2), which is maximal in Co2,\nthe group occurs as an inertia factor group of the maximal subgroup\n2^(1+22).Co2 of the Baby Monster;\nconstructed by H. Pahlings in March 2005"],
["2^(1+8)_+.(2xA5)","origin: Dixon's Algorithm"],
["2^(1+8)_+.(A4xA4).2","origin: Dixon's Algorithm"],
["2^(1+8)_+.(A4xA5)","origin: Dixon's Algorithm"],
["2^(1+8)_+.(A5xA5).2^2","5th maximal subgroup of HN.2,\norigin: Dixon's Algorithm"],
["2^(1+8)_+.2^2.2^2.2^4.S3","origin: Dixon's Algorithm"],
["2^(1+8)_+.2^3.2^2.2^3.S3","origin: Dixon's Algorithm"],
["2^(1+8)_+.2^3.2^5.S3","origin: Dixon's Algorithm"],
["2^(1+8)_+.2^5.S4(2)","origin: Dixon's Algorithm"],
["2^(1+8)_+:(S3xS3xS3)","13th maximal subgroup of O8+(2),\norigin: Dixon's Algorithm"],
["2^(1+8)_+:L2(8):3","origin: Dixon's Algorithm"],
["2^(10+16).O10+(2)","5th maximal subgroup of M,\ncomputed in September 2023 by Alexander Hulpke"],
["2^(2+1+2).2^(1+1+2).2^2.S4","origin: Dixon's Algorithm,\none type of solvable subgroups of maximal order in Ru"],
["2^(2+1+2+4+2).(3xS4)","origin: Dixon's Algorithm"],
["2^(2+10+20).(M22.2xS3)","7th maximal subgroup of B,\ncomputed by Eamonn O'Brien using Magma, March 2007"],
["2^(2+11+22).(M24xS3)","6th maximal subgroup of the Monster group,\ncomputed using Magma V2.27-3, Dec 14 2023 on schedir\nTotal time: 32375.099 seconds, Total memory usage: 20383.66MB"],
["2^(2+12):(A8xS3)","origin: Dixon's Algorithm,\n8th maximal subgroup of Co1,\ntable is sorted w.r. to normal series 2^2.2^12.3.2.A8,\ntests: 1.o.r., pow[2,3,5,7]"],
["2^(2+2+4).(S3xS3)","normalizer of a radical 2-subgroup in M24 and He,\norigin: Dixon's Algorithm"],
["2^(2+4).(S3x2)","origin: Dixon's Algorithm"],
["2^(2+4).S3","origin: Dixon's Algorithm"],
["2^(2+4):(3x3):2","origin: Dixon's Algorithm,\ntable of the intersection of (nonconjugate) maximal subgroups\n2^4:A7 and 2^4:A7 in McL"],
["2^(2+4):(3xD10)","origin: Dixon's Algorithm"],
["2^(2+4):(S3xS3)","source: H. Pahlings,\n5th maximal subgroup of L3(4).D12,\n4th maximal subgroup of J2.2,\n9th maximal subgroup of J3.2,\n8th maximal subgroup of McL.2,\ntable is sorted w.r. to normal series 2^2.2^4.3.2.3.2,\ntests: 1.o.r., pow[2,3]"],
["2^(2+4):15","origin: Dixon's Algorithm"],
["2^(2+6):3^3:S3","5th maximal subgroup of S6(3),\norigin: Dixon's Algorithm"],
["2^(2+8).2^2.(3xS3)","origin: Dixon's Algorithm"],
["2^(2+8):(3xA5)","maximal subgroup of G2(4), of structure 2^2+8:(3xA5),\ntests: 1.o.r., pow[2,3,5]"],
["2^(2+8):(3xA5):2","origin: Dixon's Algorithm"],
["2^(2+8):(S5xS3)","10th maximal subgroup of Suz.2,\norigin: Dixon's Algorithm"],
["2^(3+1+3).L3(2)","normalizer of a radical 2-subgroup in M24,\norigin: Dixon's Algorithm"],
["2^(3+12).(L3(2)xA6)","origin: Computed by A. Hulpke, using Dixon's Algorithm"],
["2^(3+12).(L3(2)xS6)","14th maximal subgroup of Fi24,\norigin: Dixon's Algorithm"],
["2^(3+3):7","origin: Dixon's Algorithm,\n1st maximal subgroup of Sz(8)"],
["2^(3+3):7:3","origin: Dixon's Algorithm,\n2nd maximal subgroup of Sz(8).3"],
["2^(3+3+3).L3(2)","origin: Dixon's Algorithm"],
["2^(3+6):21","origin: Dixon's Algorithm"],
["2^(3+8):(S3xS6)","5th maximal subgroup of S8(2),\norigin: Dixon's Algorithm"],
["2^(4+10)(S5xS3)","origin: Dixon's Algorithm,\n8th maximal subgroup of Co2,\ntable is sorted w.r. to normal series 2^4.2^10.(S5xS3),\ntests: 1.o.r., pow[2,3,5]"],
["2^(4+10).(S4xS3)","origin: Dixon's Algorithm,\nsolvable subgroup of maximal order in Co2"],
["2^(4+12).(S3x3S6)","origin: computed by Alexander Hulpke using Dixon's algorithm,\n9th maximal subgroup of Co1,\ntable is sorted w.r. to normal series 2^4.2^12.S3.3S6,\ntests: 1.o.r., pow[2,3,5]"],
["2^(4+12).(S3x3^(1+2)_+:D8)","origin: Dixon's Algorithm,\nsolvable subgroup of maximal order in Co1"],
["2^(4+4).(S3xS3).2","origin: Dixon's Algorithm,\nmaximal subgroup in He.2,\nsolvable subgroup of maximal order in He.2"],
["2^(4+4):(3xA5)","origin: Dixon's Algorithm,\n3rd maximal subgroup of U5(2)"],
["2^(4+6).2^2.(3xS3)","origin: Dixon's Algorithm"],
["2^(4+6):(A5x3)","maximal subgroup of G2(4), of structure 2^(4+6):(A5x3),\n2nd power map determined only up to matrix automorphisms,\ntests: 1.o.r., pow[2,3,5]"],
["2^(4+6):(A5x3):2","origin: Dixon's Algorithm"],
["2^(4+6):3S6","8th maximal subgroup of Suz.2,\norigin: Dixon's Algorithm"],
["2^(4+8).(2xA4)","origin: Dixon's Algorithm"],
["2^(4+8):(A4xS3)","origin: Dixon's Algorithm"],
["2^(4+8):(S3xA5)","origin: Dixon's Algorithm,\n7th maximal subgroup of U6(2),\ntable is sorted w.r. to normal series 2^4.2^8.(S3xA5),\n2nd power map is not uniquely determined by the characters,\ntests: 1.o.r., pow[2,3,5]"],
["2^(5+10+20).(S3xL5(2))","8th maximal subgroup of the Monster group,\ncomputed by Anthony Pisani in 2025"],
["2^(5+5):31","1st maximal subgroup of Sz(32),\norigin: Dixon's Algorithm"],
["2^(5+8):(2x3.A6)","origin: Dixon's Algorithm"],
["2^(5+8):(2xA6)","origin: Dixon's Algorithm"],
["2^(5+8):(2xS4)","origin: Dixon's Algorithm"],
["2^(5+8):(S3x3.A6)","origin: Dixon's Algorithm"],
["2^(5+8):(S3xA6)","origin: Dixon's Algorithm,\n10th maximal subgroup of Fi22,\ntable sorted w.r. to normal series given by 2^4.2.2^8.3.2.A6,\ntests: 1.o.r., pow[2,3,5]"],
["2^(5+8):(S3xD8)","origin: Dixon's Algorithm"],
["2^(5+8):(S3xS4)","origin: Dixon's Algorithm"],
["2^(5+8):(S3xS6)","9th maximal subgroup of Fi22.2,\norigin: Dixon's Algorithm"],
["2^(6+6):(S3xL3(2))","7th maximal subgroup of S8(2),\norigin: Dixon's Algorithm"],
["2^(6+8).(S3xA8)","origin: Computed by A. Hulpke, using Dixon's Algorithm"],
["2^(6+8):(A7xS3)","origin: Dixon's Algorithm,\n11th maximal subgroup of Fi23,\ntable is sorted w.r. to normal series given by 2^6.2^8.A7.3.2,\ntests: 1.o.r., pow[2,3,5]"],
["2^(7+8).(S3xA8)","15th maximal subgroup of Fi24,\norigin: Dixon's Algorithm"],
["2^(9+16).S8(2)","4th maximal subgroup of B,\nsorted w.r.t. normal series 2^9 < 2^(9+16) < 2^(9+16).S8(2),\ncomputed by Eamonn O'Brien using Magma, March 2007"],
["2^1+24.2.Co1","double cover of the maximal subgroup 2^1+24.Co1,\nconstructed by Simon Norton, Dec. 2000"],
["2^1+24.Co1","maximal subgroup and 2B centralizer in the Monster,\nconstructed by Simon Norton, Dec. 2000"],
["2^1+4+6.a8","origin: CAS library,\nmaximal subgroup of Co2,\nReceived from Bielefeld 18.01.89\nTest: JAMES, JAMES,n=3,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3,5,7]"],
["2^1+4b:a5","origin: CAS library,\n8th maximal subgroup of J3,\n3rd maximal subgroup of J2\ntests: 1.o.r., pow[2,3,5]"],
["2^1+6.psl(3,2)","origin: CAS library,\nmaximal subgroup of He,\ntest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3,7]"],
["2^1+6.u4q2","origin: CAS library,\nmaximal subgroup of Suz,\ntest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly,\ntests: 1.o.r., pow[2,3,5]"],
["2^1+8.2.A9","a double cover of the maximal subgroup 2^1+8.A9 of the Thompson group,\ncomputed by Simon Norton, Dec. 2000"],
["2^1+8.a9","origin: CAS library,\nmaximal subgroup of Th,\nReceived from Bielefeld 18.1.1989\nTest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3,5,7]"],
["2^1+8:s6f2","origin: CAS library,\nmaximal subgroup of Co2,\nSource: Table from Birmingham.\nTest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3,5,7]"],
["2^10.2^2.2^2.S4","origin: Dixon's Algorithm"],
["2^10.2^3.2^3.S3","origin: Dixon's Algorithm"],
["2^10.2^3.L3(2)","origin: Dixon's Algorithm"],
["2^10.2^3.S4","origin: Dixon's Algorithm"],
["2^10.2^4.S5","origin: Dixon's Algorithm"],
["2^10.A8","origin: Dixon's Algorithm"],
["2^10:(2^5:s5)","origin: CAS library,\nOne intersection between a Co2M8 and a Co2M2, has index 3 in Co2M8.\nComputed using Clifford matrices and lots of information from Co2M2.\nTest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters from Co2M2 (and Co2) decompose properly.\ntests: 1.o.r., pow[2,3,5]"],
["2^10:(L5(2)xS3)","origin: CAS library,\ntests: 1.o.r., pow[2,3,5,7,31]"],
["2^10:L5(2)","origin: CAS library,\ntests: 1.o.r., pow[2,3,5,7,31]"],
["2^10:M22'","constructed using Dixon's algorithm and character theoretic methods\nin July 2010"],
["2^10:m22","origin: CAS library,\n2..10.m22\n2nd power map determined only up to matrix automorphisms,\ntests: 1.o.r., pow[2,3,5,7,11],"],
["2^10:m22:2","origin: CAS library,\ntests: 1.o.r., pow[2,3,5,7,11]"],
["2^11.2^6.3^(1+2).D8","origin: Dixon's Algorithm,\nsolvable subgroup of maximal order in J4,\nsorted w.r.t. normal series 2.2^6.2^4.2^6.3.3^2.D8"],
["2^11:M24","origin: computed by C. Jansen using B. Fischer's Clifford matrices,\nmaximal subgroup of Co1,\nthe 2nd power map is determined only up to matrix automorphisms,\ntests: 1.o.r., pow[2,3,5,7,11,23]"],
["2^12.(2^2xD8)","origin: Dixon's Algorithm,\nfactor group of Co1N2"],
["2^12.(S3x3S6)","factor group of 2^(4+12).(S3x3S6) < Co1"],
["2^12.3^2.U4(3).2_2'","factor group of the 3B normalizer in 3.F3+,\nconstructed in January 2004 by Thomas Breuer, using a permutation\nrepresentation on 1512 points, sorted according to the chain\n3 < 3x2^12 < (3x2^12).3.U4(3) < (3x2^12).3.U4(3).2,\ntests: 1.o.r., pow[2,3,5,7]"],
["2^12.3_1.U4(3).2_2'","occurs as factor group of F3+M9"],
["2^12.M24","8th maximal subgroup of Fi24,\nsorted w.r.t. the normal series 2^11.2.M24,\ncomputed by T. Breuer in July 2005 using Dixon's algorithm and\ncharacter theoretic methods"],
["2^12:(L4(2)xL3(2))","origin: CAS library,\ntests: 1.o.r., pow[2,3,5,7]"],
["2^12:J2","constructed using Dixon's algorithm and character theoretic methods\nin July 2010"],
["2^12:Sz(8)","constructed using Dixon's algorithm and character theoretic methods\nin July 2010"], |
