Quelle  attr_text.json   Sprache: unbekannt

{
"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"],
["2^2+4.3xs3","origin: CAS library,\n9th maximal subgroup of J3,\n test: 1. o.r., sym 2 decompose correctly \ntests: 1.o.r., pow[2,3]"],
["2^2+8(a5xs3)","origin: CAS library,\n9th maximal subgroup of Suz,\ntest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly,\ntests: 1.o.r., pow[2,3,5]"],
["2^2.(2^(1+8)_+:(S3xS3xS3))","13th maximal subgroup of 2^2.O8+(2),\nconstructed using `PossibleCharacterTablesOfTypeV4G'"],
["2^2.(3^2:2A4)","origin: Dixon's Algorithm"],
["2^2.(3^2:Q8)","origin: Dixon's Algorithm"],
["2^2.(3^2:Q8.2)","origin: Dixon's Algorithm"],
["2^2.(U3(3).2xS4)","origin: Dixon's Algorithm,\nmaximal subgroup of O8+(3).S4"],
["2^2.2E6(2)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13,17,19]"],
["2^2.2E6(2).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13,17,19]\nthe 2nd power map is determined only up to automorphisms of the characters"],
["2^2.2E6(2).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13,17,19]"],
["2^2.2E6(2).3.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13,17,19]"],
["2^2.2E6(2)M4","4th maximal subgroup of 2^2.2E6(2)"],
["2^2.2E6(2)M5","5th maximal subgroup of 2^2.2E6(2)"],
["2^2.2E6(2)M8","8th maximal subgroup of 2^2.2E6(2)"],
["2^2.2E6(2)M9","9th maximal subgroup of 2^2.2E6(2)"],
["2^2.2^(1+8)_+:U4(2)","origin: Dixon's Algorithm"],
["2^2.2^(3+3):7","constructed using `PossibleCharacterTablesOfTypeV4G'"],
["2^2.2^(4+8):(S3xA5)","origin: Dixon's Algorithm"],
["2^2.2^8:s3","origin: CAS library,\nmaximal subgroup of 2F4(2)',\n  normalizer of klein four group contained in class 2b\n  structure:= 2^2.[2^8]:s3 [s3: symmetric group on 3 elements]\n  1st & 2nd orthogonality relations are satisfied\n  symmetric squares decompose properly\n  created august 1984\ntests: 1.o.r., pow[2,3]"],
["2^2.Fi22.2","table of a factor group of 2.BM9, of structure (2x2.Fi22).2,\nmaximal subgroup of Fi24"],
["2^2.L3(4)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2^2.L3(4).2^2","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["2^2.L3(4).2_1","constructed using `PossibleCharacterTablesOfTypeV4G'"],
["2^2.L3(4).2_2","origin: ATLAS of Finite Groups"],
["2^2.L3(4).2_3","origin: ATLAS of Finite Groups"],
["2^2.L3(4).3","origin: ATLAS of Finite Groups"],
["2^2.L3(4).3.2_2","origin: ATLAS of Finite Groups"],
["2^2.L3(4).3.2_3","origin: ATLAS of Finite Groups"],
["2^2.L3(4).6","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["2^2.L3(4).D12","constructed using `CharacterTableOfTypeGS3'"],
["2^2.O8+(2)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2^2.O8+(2).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2^2.O8+(2).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2^2.O8+(2).3.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["2^2.O8+(2)M11","11th maximal subgroup of 2^2.O8+(2),\ndiffers from 2^2.O8+(2)M10 = 2x(3x2.U4(2)):2 only by fusion map"],
["2^2.O8+(2)M12","12th maximal subgroup of 2^2.O8+(2),\ndiffers from 2^2.O8+(2)M10 = 2x(3x2.U4(2)):2 only by fusion map"],
["2^2.O8+(2)M16","16th maximal subgroup of 2^2.O8+(2),\ndiffers from 2^2.O8+(2)M15 = (2x2.(A5xA5)):2^2 only by fusion map"],
["2^2.O8+(2)M17","17th maximal subgroup of 2^2.O8+(2),\ndiffers from 2^2.O8+(2)M15 = (2x2.(A5xA5)):2^2 only by fusion map"],
["2^2.O8+(2)M2","2nd maximal subgroup of 2^2.O8+(2),\ndiffers from 2^2.O8+(2)M1 = 2x2.S6(2) only by fusion map"],
["2^2.O8+(2)M3","3rd maximal subgroup of 2^2.O8+(2),\ndiffers from 2^2.O8+(2)M1 = 2x2.S6(2) only by fusion map"],
["2^2.O8+(2)M5","5th maximal subgroup of 2^2.O8+(2),\ndiffers from 2^2.O8+(2)M4 = (2x2^(1+6)_+).A8 only by fusion map"],
["2^2.O8+(2)M6","6th maximal subgroup of 2^2.O8+(2),\ndiffers from 2^2.O8+(2)M4 = (2x2^(1+6)_+).A8 only by fusion map"],
["2^2.O8+(2)M8","8th maximal subgroup of 2^2.O8+(2),\ndiffers from 2^2.O8+(2)M7 = 2x2.A9 only by fusion map"],
["2^2.O8+(2)M9","9th maximal subgroup of 2^2.O8+(2),\ndiffers from 2^2.O8+(2)M7 = 2x2.A9 only by fusion map"],
["2^2.O8+(3)","group Spin8+(3),\nconstructed using `PossibleCharacterTablesOfTypeV4G'"],
["2^2.O8+(3).3","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["2^2.S6","origin: Dixon's Algorithm"],
["2^2.Sz(8)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["2^2.Sz(8).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11],\n(all possibilities of an order 3 table automorphism of 2^2.Sz(8)\nto represent a group automorphism of Sz(8) lead to equivalent tables)"],
["2^2.U6(2)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["2^2.U6(2).2","origin: ATLAS of finite groups,\n3rd maximal subgroup of Fi23"],
["2^2.U6(2).3","origin: ATLAS of finite groups"],
["2^2.U6(2).3.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["2^2.U6(2):S3x2","9th maximal subgroup of Fi24\n(the subgroup is really a direct product, the ATLAS does not state this)"],
["2^2.U6(2)M10","10th maximal subgroup of 2^2.U6(2),\ndiffers from 2^2.U6(2)M8 = 2^2xS6(2) only by fusion map"],
["2^2.U6(2)M12","12th maximal subgroup of 2^2.U6(2),\ndiffers from 2^2.U6(2)M11 = 2x2.M22 only by fusion map"],
["2^2.U6(2)M13","13th maximal subgroup of 2^2.U6(2),\ndiffers from 2^2.U6(2)M11 = 2x2.M22 only by fusion map"],
["2^2.U6(2)M3","3rd maximal subgroup of 2^2.U6(2),\nintersection of a 2^2.U6(2) and a 2^11.M22 in 2.Fi22,\nthe structure 2^10:2.L3(4),\nconstructed in April 2000 by Thomas Breuer using char. theor. methods\nfrom the known tables of 2^2.U6(2), 2.U6(2)M3, and 2^11.M22"],
["2^2.U6(2)M5","5th maximal subgroup of 2^2.U6(2),\ndiffers from 2^2.U6(2)M4 = 2x2.U4(3).2_2 only by fusion map"],
["2^2.U6(2)M6","6th maximal subgroup of 2^2.U6(2),\ndiffers from 2^2.U6(2)M4 = 2x2.U4(3).2_2 only by fusion map"],
["2^2.U6(2)M9","9th maximal subgroup of 2^2.U6(2),\ndiffers from 2^2.U6(2)M8 = 2^2xS6(2) only by fusion map"],
["2^2.[2^6].(S3xS3)","origin: Dixon's Algorithm"],
["2^2.[2^7*3^2].S3","origin: CAS library,\nmaximal subgroup of Co3,\nComputed using CAYLEY.\nTest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3]"],
["2^2.[2^9]:(7:3xS3)","origin: Dixon's Algorithm"],
["2^2.[2^9]:(7xS3)","origin: Dixon's Algorithm,\nmaximal subgroup in 3D4(2)"],
["2^2.[2^9]:S3","origin: Dixon's Algorithm"],
["2^2.psl(3,4).s3","origin: CAS library,\nmaximal subgroup of He,\ntest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3,5,7]"],
["2^24.Co1","central factor group of the maximal subgroup 2^(1+24).Co1 of the Monster,\nconstructed by Simon Norton, Dec. 2000"],
["2^2x11:5","Sylow 11 normalizer in 2.Fi22"],
["2^2xU5(2)","1st maximal subgroup of 2^2.U6(2)"],
["2^3+8:L3(2)","maximal subgroup of Ru,\norigin: computed by K.Lux using Clifford matrices,\ntests: 1.o.r., pow[2,3,7]"],
["2^3.(2x2^(1+3+3+3).L3(2))","origin: Dixon's Algorithm"],
["2^3.(2x2^3.L3(2))","origin: Dixon's Algorithm"],
["2^3.(S4x2)","origin: Dixon's Algorithm,\n7th maximal subgroup of M12.2,\ntable is sorted w.r.t. normal series 2<2^3<2^3.2^2<2^3.A4<2^3.S4<2^3.(S4x2)"],
["2^3.2^2.2^6.(3xL3(2))","origin: computed by Klaus Lux using Dixon's Algorithm,\n9th maximal subgroup of HN,\ntable is sorted w.r. to normal series 2^3.2^2.2^6.3.L3(2),\ntests: 1.o.r., pow[2,3,7]"],
["2^3.2^2.2^6.(S3xL3(2))","10th maximal subgroup of HN.2,\norigin: Dixon's Algorithm"],
["2^3.7.3","origin: Ostermann, tests: 1.o.r., pow[2,3,7]\nSylow 2 normalizer in sporadic Janko group J1"],
["2^3.D8","Sylow 2 subgroup of 2^3:sl(3,2)"],
["2^3.L3(2)","nonsplit extension of 2^3 with L3(2),\nmaximal subgroup of G2(3),\nconstructed as factor of the subgroup 4^3.L3(2) of ON"],
["2^3.L3(2):2","origin: Dixon's Algorithm"],
["2^3.S3","subgroup of 2^3:sl(3,2)"],
["2^3.S4v1","subgroup of 2^3:sl(3,2)"],
["2^3.S4v2","subgroup of 2^3:sl(3,2)"],
["2^3:7","constructions: AGL(1,8)"],
["2^3:L3(2)xS3","maximal subgroup of 3.M22.2"],
["2^3:sl(3,2)","origin: CAS library,\nmaximal subgroup of M22,\ntest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly,\nconstructions: AGL(3,2),\ntests: 1.o.r., pow[2,3,7]"],
["2^4+6:3a6","origin: CAS library,\n7th maximal subgroup of Suz,\ntest:     TEST, JAMES, JAMES,n=3,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3,5]"],
["2^4.(S4x2)","stabilizer of chain (2A^4 < 2A^4.[2^3]) in HS,\norigin: Dixon's Algorithm"],
["2^4.a8","origin: CAS library,\nmaximal subgroup of Co3,\nnon-split extension\ncomputed using ordinary characters of the inertia group 2^3:gl(3,2)\n(there must be a degree-15-character extended from 2^4 to restrict\nthe degree-23-character of c3 properly), the irreducible character\nof degree 23 of c3 and Clifford matrices which differ from those\nin split-case by representative orders and, for the 3x3-Matrices,\nsome signs.\ntests: 1.o.r., pow[2,3,5,7]"],
["2^4.s6","origin: CAS library,\n6th maximal subgroup of HS,\ntests: 1.o.r., pow[2,3,5]"],
["2^4:(3xA5).2","source: H. Pahlings,\n6th maximal subgroup of M23,\n4th maximal subgroup of J3.2,\ntable is sorted w.r. to normal series 2^4.3.A5.2,\ntests: 1.o.r., pow[2,3,5]"],
["2^4:(S3xS3)","origin: CAS library,\nnames:=mo61p; m6[1]+\n order: 2^6.3^2 = 576\n number of classes: 16\n source:dye, r.h.\n        the classes and characters of\n        certain maximal and other subgroups\n        of o 2n+2(2)\n        ann.mat.pura appl.(4) 107\n        (1975), 13-47\n comments:semidirect product of an elementary\n          abelian group of order 2^4 and o4+,\n          table blown up using cas-system\ntests: 1.o.r., pow[2,3]"],
["2^4:3.S6","origin: Dixon's Algorithm,\n3rd maximal subgroup of 3.M22.2"],
["2^4:3^2:4","origin: Dixon's Algorithm,\nsolvable subgroup of maximal order in M22"],
["2^4:A4b","origin: Dixon's Algorithm"],
["2^4:D8","origin: Ostermann, tests: 1.o.r., pow[2],\n2nd power map determined only up to matrix automorphisms,\nSylow 2 normalizer in sporadic Mathieu group M22\nSylow 2 normalizer in sporadic Mathieu group M23"],
["2^4:a6","origin: CAS library,\nmaximal subgroup of M22,\ntest: OR.1, JAMES, JAMES,n=3,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3,5]"],
["2^4:a7","origin: CAS library,\nmaximal subgroup of M23,\nmaximal subgroup of McL,\ntest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly\ntests: 1.o.r., pow[2,3,5,7]"],
["2^4:a8","origin: CAS library,\nnames:= 2^4:a8\n order: 322,560 = 2^10 . 3^2 . 5 . 7\n number of classes: 25\nsource: todd,j.a.\n        a representation of the mathieu-group m24\n        as a collineation group\n        ann.mat.pura appl [4] 71\n        (1966),199-238\n comments: 2^4:a8 is maximal subgroup of m24\n test: orth.1, min, sym(3)\nconstructions: AGL(4,2),\ntests: 1.o.r., pow[2,3,5,7]"],
["2^4:s5","origin: CAS library,\nmaximal subgroup of M22,\ntest: 1.OR,JAMES,JAMES,n=3,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3,5]"],
["2^5.2^4.L4(2)","origin: Dixon's Algorithm"],
["2^5.2^6.(2xL3(2))","origin: Dixon's Algorithm"],
["2^5.2^6.D8.S3","origin: Dixon's Algorithm"],
["2^5.S6","5th maximal subgroup of HS.2,\norigin: Dixon's Algorithm"],
["2^5.psl(5,2)","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[2,3,5,7,31]"],
["2^5:A6","origin: Dixon's Algorithm"],
["2^5:L5(2)","origin: Dixon's algorithm and character theory programs in GAP,\nmaximal subgroup of L6(2), sorted according to normal series 2^5:L5(2),\nconstructions: AGL(5,2)"],
["2^5:S6","origin: Dixon's Algorithm,\n3rd maximal subgroup of S6(2)"],
["2^6.2^5.S6","origin: Dixon's Algorithm"],
["2^6.U4(2)","origin: Dixon's Algorithm,\n7th maximal subgroup of HN,\nequal to Aut(2^{1+6}_-)',\nnon-split extension (table is very similar to that of split extension),\ntable is sorted w.r. to normal subgroup 2^6,\ntests: 1.o.r., pow[2,3,5]"],
["2^6.U4(2).2","origin: Dixon's Algorithm,\n7th maximal subgroup of HN.2,\nequal to Aut(2^{1+6}_-),\ntests: 1.o.r., pow[2,3,5]"],
["2^6:(3xA5)","origin: Dixon's Algorithm"],
["2^6:(3xA5):2","origin: Dixon's Algorithm"],
["2^6:(7xL2(8))","origin: Dixon's Algorithm,\nconstructions: AGL(2,8)"],
["2^6:(psl(3,2)xs3)","origin: CAS library,\nnames:= 2^6:[psl(3,2]xs3)\n order: 64,512 = 2^10 . 3^2 . 7\n number of classes: 33\n source/origin: pahlings,h.\n comments: 2^6:(psl(3,2)xs3) is maximal subgroup of m24\n test: orth.1, min, sym(3)\ntests: 1.o.r., pow[2,3,7]"],
["2^6:3.s6","origin: CAS library,\nmaximal subgroup of M24,\nmaximal subgroup of He,\nnames:= 2^6:3.s6\norder: 138,240 = 2^10 . 3^3 . 5\nnumber of classes: 33\nsource/origin: pahlings,h.\ntest: orth.1, min, sym[3]\ntests: 1.o.r., pow[2,3,5]"],
["2^6:3A7","origin: Dixon's Algorithm"],
["2^6:3^(1+2).D8","origin: Dixon's Algorithm,\nsolvable subgroup of maximal order in M24 and He"],
["2^6:3^3:S4","origin: Dixon's Algorithm"],
["2^6:A7","origin: Dixon's Algorithm"],
["2^6:A8","origin: CAS library,\nmaximal subgroup of O8+(2),\ntests: 1.o.r., pow[2,3,5,7]"],
["2^6:L3(2)","origin: Dixon's Algorithm,\n5th maximal subgroup of S6(2)"],
["2^6:L6(2)","origin: CAS library,\nconstructions: AGL(6,2),tests: 1.o.r., pow[2,3,5,7,31]"],
["2^6:S4a","origin: Dixon's Algorithm"],
["2^6:S4b","origin: Dixon's Algorithm"],
["2^6:S5","origin: Dixon's Algorithm"],
["2^6:S6","maximal subgroup of S12,\norigin: Dixon's Algorithm"],
["2^6:S7","origin: Dixon's Algorithm"],
["2^6:S8","subgroup of the maximal subgroup 2^6:S6(2) of Fi22,\ncomputed by Faryad Ali using Clifford Matrices,\ntests: 1.o.r., pow[2,3,5,7]"],
["2^6:U4(2)","origin: computed using Clifford matrices\n1st maximal subgroup of O8-(2), tests: 1.o.r., pow[2,3,5]"],
["2^6:U4(2).2","origin: computed in 1997 by E. Mpono using Clifford theory,\nmaximal subgroup of 2^6:S6(2),\ndiffers from table of nonsplit extension (HN.2M8)\nonly by 2nd power map and representative orders,\ntests: 1.o.r., pow[2,3,5]"],
["2^6:s6f2","origin: CAS library,\nmaximal subgroup of Fi22,\n1987   O.B.\ntests: 1.o.r., pow[2,3,5,7]"],
["2^6:u3(3)","origin: CAS library,\nsubgroup of index 2 in maximal subgroup of ru\n  structure:= 2^6:u[3,3]\n  1st & 2nd orthogonality relations are satisfied\n  symmetric squares decompose properly\n  created september 1984\ntests: 1.o.r., pow[2,3,7]"],
["2^6:u3(3):2","origin: CAS library,\nmaximal subgroup of Ru,\n  structure:= 2^6:U(3,3):2\n  1st & 2nd orthogonality relations are satisfied\n  symmetric squares decompose properly\n  created september 1984,\ntests: 1.o.r., pow[2,3,7]"],
["2^7:S6(2)","origin: computed in 1997 by E. Mpono using Clifford theory,\nmaximal subgroup of Fi22.2,\ntests: 1.o.r., pow[2,3,5,7]"],
["2^8.A9","origin: Dixon's Algorithm,\nbase stabilizer in O9(3)"],
["2^8:O8+(2)","table computed with CliffordTable( O8+(2) -> 2^8:O8+(2) )"],
["2^8:O8+(2):2","origin: Dixon's Algorithm"],
["2^8:O8-(2)","origin: computed using Clifford matrices,\n1st maximal subgroup of O10-(2),\ntests: 1.o.r., pow[2,3,5,7,17]"],
["2^8:O8-(2):2","origin: Dixon's Algorithm"],
["2^8:S6(2)","maximal subgroup of 2^8:O8+(2),\ncomputed by Faryad Ali\n(Note that the group is *not* contained in 2^8:O8-(2),\n2^8:O8-(2) contains a subgroup of type 2^8:S6(2) with orbits lengths\n1+1+56+63+63+72 on the 2^8, which has 168 conjugacy classes),\ntests: pow[2,3,5,7]"],
["2^8:S8","factor group of 2^(1+8).S8,\nconstructed by H. Pahlings"],
["2^8:S8(2)","table computed with CliffordTable( S8(2) -> 2^8:S8(2) )"],
["2^9.2^4.A5a","origin: Dixon's Algorithm"],
["2^9.2^4.A5b","origin: Dixon's Algorithm"],
["2^9.L3(4)","3rd maximal subgroup of U6(2),\ntests: 1.o.r."],
["2^[39].(L3(2)x3.S6)","10th maximal subgroup of the Monster group,\ncomputed using Magma V2.27-3, Dec 17 2023 on schedir\nTotal time: 101832.550 seconds, Total memory usage: 139972.41MB"],
["2^{1+4}_-:2A5","origin: Dixon's Algorithm,\n3rd maximal subgroup of 2.J2"],
["2^{1+6}:3^{1+2}:2A4","1st maximal subgroup of U5(2), origin: CAYLEY"],
["2^{1+8}_+:(S3xA5)","4th maximal subgroup of O8-(2),\norigin: Dixon's Algorithm"],
["2^{3+4}:(3xS3)","origin: Dixon's Algorithm,\n4th maximal subgroup of 2.J2"],
["2^{3+6}:(L3(2)x3)","3rd maximal subgroup of O8-(2),\norigin: Dixon's Algorithm"],
["2_1.O12+(3)","computed by Eamonn O'Brien using Magma, February 2014"],
["2x(3.A7)","3rd and 4th maximal subgroup of 6.M22"],
["2x(3^(1+6).3)a.2.S4","normalizer of a radical 3-subgroup in 2.Fi22"],
["2x(3^(1+6).3)b.2.S4","normalizer of a radical 3-subgroup in 2.Fi22"],
["2x(3^2.QD16)","origin: Ostermann, tests: 1.o.r., pow[2,3]\nSylow 3 normalizer in sporadic Higman Sims group HS"],
["2x(3x2.U4(2)):2","10th maximal subgroup of 2^2.O8+(2)"],
["2x(3xU4(2)):2","10th maximal subgroup of 2.O8+(2)"],
["2x11:10","Sylow 11 normalizer in HN"],
["2x13:6","Sylow 13 normalizer in 2.Fi22"],
["2x2.A9","7th maximal subgroup of 2^2.O8+(2)"],
["2x2.F4(2)","3rd maximal subgroup of 2^2.2E6(2)"],
["2x2.Fi22","subquotient of 2.BM9, needed in the construction of 2^2.Fi22.2"],
["2x2.S6(2)","1st maximal subgroup of 2^2.O8+(2)"],
["2x2F4(2)'","maximal subgroup of 2.Fi22"],
["2x2^3:L3(2)","6th maximal subgroup of 2.M22,\nmaximal subgroup of M22.2"],
["2x2^3:L3(2)x2","5th maximal subgroup of 2.M22.2"],
["2x3.Fi22","7th maximal subgroup of (2^2x3).2E6(2)"],
["2x3.Fi22N3","Sylow 3 normalizer in 6.Fi22"],
["2x3.O7(3)","2nd maximal subgroup of 6.Fi22"],
["2x3^2.2.S4","6th maximal subgroup of 2.M12"],
["2x3^2:2A4","8th maximal subgroup of 2.A9"],
["2x3^4:(2xA6)","2nd maximal subgroup of Isoclinic(2.U4(3).2_1) = SO(-1,6,3)"],
["2x3^4:A6","1st maximal subgroup of 2.U4(3)"],
["2x3^5.3^(1+2).2.S4","normalizer of a radical 3-subgroup in 2.Fi22"],
["2x3^5.3^3.(2xS4)","normalizer of a radical 3-subgroup in 2.Fi22"],
["2x3^5:(3^2:SD16)","Sylow 3 normalizer in 2.Suz"],
["2x3^5:M11","5th maximal subgroup of 2.Suz"],
["2x3^5:U4(2):2","normalizer of a radical 3-subgroup in 2.Fi22"],
["2x3^6.M11","5th maximal subgroup of 6.Suz"],
["2x3_1.U4(3).2_2","4th maximal subgroup of 6.U6(2)"],
["2x47:23","30th maximal subgroup of 2.B"],
["2x5^2:4S5","10th maximal subgroup of 2.Ru"],
["2x6.Fi22","7th maximal subgroup of (2^2x3).2E6(2)"],
["2x6x11:5","Sylow 11 normalizer in 6.Fi22"],
["2x7:6","Sylow 7 normalizer in O7(3)"],
["2x7^2:(3x2A4)","Sylow 7 normalizer in 2.Co1"],
["2xA5","origin: CAS library, tests: 1.o.r., pow[2,3,5]"],
["2xA6","3rd maximal subgroup of 2.L3(4)"],
["2xA7","3rd and 4th maximal subgroup of 2.M22"],
["2xA8","8th maximal subgroup of 2.Ru"],
["2xA9","7th maximal subgroup of 2.O8+(2)"],
["2xBN5","Sylow 5 normalizer in 2.B"],
["2xCo1N3","Sylow 3 normalizer in 2.Co1"],
["2xCo1N5","Sylow 5 normalizer in 2.Co1"],
["2xF4(2)","3rd maximal subgroup of 2.2E6(2)"],
["2xFi22","subquotient group of BM9, needed in the construction of 2^2.Fi22.2"],
["2xFi22.2","factor group of BM9, needed in the construction of 2^2.Fi22.2"],
["2xFi22N3","Sylow 3 normalizer in 2.Fi22"],
["2xFi22N5","Sylow 5 normalizer in 2.Fi22"],
["2xFi23","3rd maximal subgroup of 2.B"],
["2xL2(11)","8th maximal subgroup of 2.M22"],
["2xL2(11).2","2nd maximal subgroup of 2.M12.2 (preimage of novelty L2(11).2 < M12.2),\n7th maximal subgroup of 2.M22.2"],
["2xL3(2)","6th maximal subgroup of 2.L3(4)"],
["2xM11","1st maximal subgroup of 2.M12,\n8th (and 9th, see 2.HSM9) maximal subgroup of 2.HS,\n9th maximal subgroup of McL.2"],
["2xM12N3","Sylow 3 normalizer in 2.M12"],
["2xM22","11th maximal subgroup of 2.U6(2)"],
["2xO7(3)","2nd maximal subgroup of 2.Fi22"],
["2xS3x2.U4(3).2_2","intermediate table, needed to construct 2.(S3x2.U4(3).2_2).2"],
["2xS3x7:6","Sylow 7 normalizer in 2.Fi22"],
["2xS3xS6(2)","3A normalizer in 2.F4(2)"],
["2xS3xU4(3).(2^2)_{122}","intermediate table, needed to construct 2.(S3x2.U4(3).2_2).2"],
["2xS3xU4(3).2_2","intermediate table, needed to construct 2.(S3x2.U4(3).2_2).2"],
["2xS5","origin: CAS library, tests: 1.o.r., pow[2,3,5]"],
["2xS6(2)","Weyl group of type E7"],
["2xTh","5th maximal subgroup of 2.B"],
["2xU3(3)","1st maximal subgroup of 2.J2"],
["2xU3(3).2","7th maximal subgroup of S6(3)"],
["2xU3(5).2","5th maximal subgroup of 2.Ru"],
["2xU4(3).2_2","4th maximal subgroup of 2.U6(2)"],
["2xU5(2)","3rd maximal subgroup of 2.Suz,\n1st maximal subgroup of 2.U6(2)"],
["2xU5(2).2","4th maximal subgroup of 2.Suz.2"],
["2xa6.2^2","origin: CAS library,\n11th maximal subgroup of HS,\ntests: 1.o.r., pow[2,3,5]"],
["2xm12","origin: CAS library,\nmaximal subgroup of Co3,\nRestricted characters decompose properly.\ntests: 1.o.r., pow[2,3,5,11]"],
["3.(2x2^(1+8)):(U4(2):2x2)","maximal subgroup of 3.Fi22.2"],
["3.(3^(1+2)+x3^2):2S4","origin: Dixon's Algorithm"],
["3.(3^(3+3):L3(3))","origin: Dixon's Algorithm"],
["3.(3xM10):2","origin: Dixon's Algorithm"],
["3.(A4x2(A4xA4).2).2","origin: Dixon's Algorithm"],
["3.(A4x3):2","5th maximal subgroup of 3.A7"],
["3.2E6(2)","computed by Frank L\"ubeck in August 2005 using a combination of\nDeligne-Lusztig theory, the known table of 2E6(2), character theoretic\nmethods, and some combinatorics"],
["3.2E6(2).2","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["3.2E6(2)M4","4th maximal subgroup of 3.2E6(2),\ndiffers from 3.2E6(2)M3 = 3xF4(2) only by fusion map"],
["3.2E6(2)M5","5th maximal subgroup of 3.2E6(2),\ndiffers from 3.2E6(2)M3 = 3xF4(2) only by fusion map"],
["3.2E6(2)M8","8th maximal subgroup of 3.2E6(2),\ndiffers from 3.2E6(2)M7 = 3.Fi22 only by fusion map"],
["3.2E6(2)M9","9th maximal subgroup of 3.2E6(2),\ndiffers from 3.2E6(2)M7 = 3.Fi22 only by fusion map"],
["3.2^(1+12).3U4(3).2","9th maximal subgroup of 3.F3+,\nconstructed in January 2004 by Thomas Breuer from the tables of the\nfactor groups modulo the central subgroups of orders 2 and 3,\ntests: 1.o.r., pow[2,3,5,7]"],
["3.2^(1+4)+:3^2.2","origin: Dixon's Algorithm"],
["3.2^(2+4):(3x3):2","origin: constructed by Thomas Breuer 1996/09/17 using the tables of\n2^(2+4):(3x3):2, 2^4:a7, and 3.2^4:a7,\ntable of the intersection of (nonconjugate) maximal subgroups\n3.2^4:A7 and 3.2^4:A7 in 3.McL"],
["3.2^(2+4):(S3xS3)","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["3.2^4:a7","9th maximal subgroup of 3.McL,\ntable constructed 1996/09/10 by Thomas Breuer using the tables of McL,\n3.McL, and 2^4:a7"],
["3.3^(1+4):2S5","origin: computed from factor group 3^(1+4):2S5 and 3.McL,\nmaximal subgroup of 3.Mcl,\ncharacters are sorted w.r. to normal series given by 3.3.3^4.2.A5.2,\n3rd power map determined only up to matrix automorphism (41,42),\ntests: 1.o.r., pow[2,3,5]"],
["3.3^(1+4):4S5","maximal subgroup of 3.McL.2,\ntests: 1.o.r., pow[2,3,5]"],
["3.3^(1+6):2^(3+4):3^2:2","origin: Dixon's Algorithm"],
["3.3^(2+4):2(A4x2^2).2","11th maximal subgroup of 3.Suz"],
["3.3^(2+4):2(S4xD8)","12th maximal subgroup of 3.Suz.2"],
["3.3^4.3^2.Q8","origin: constructed 1996/09/09 by T. Breuer using the tables of\n3^4.3^2.Q8, 3^(2+4):2S5, McL, and 3.McL"],
["3.3^5.U4(2)","derived subgroup of the 9A centralizer in the Monster,\nconstructed by Simon Norton, July 1997"],
["3.3^5:(3^2:SD16)","origin: Dixon's Algorithm"],
["3.3^5:U4(2):2","origin: Dixon's Algorithm"],
["3.A6","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["3.A6.(2x4)","11th maximal subgroup of 2.Ru"],
["3.A6.2^2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["3.A6.2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["3.A6.2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["3.A6.2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["3.A6M2","2nd maximal subgroup of 3.A6,\ndiffers from 3.A6M1 = 3xA5 only by fusion map"],
["3.A6M5","5th maximal subgroup of 3.A6,\ndiffers from 3.A6M4 = 3xSymm(4) only by fusion map"],
["3.A7","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3.A7.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3.F3+","origin: ATLAS of finite groups, tests: 1.o.r."],
["3.F3+.2","origin: ATLAS of finite groups, tests: 1.o.r."],
["3.F3+.2N5","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["3.F3+.2N7","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["3.F3+N5","origin: Dixon's Algorithm"],
["3.Fi22","origin: ATLAS of finite groups, tests: 1.o.r."],
["3.Fi22.2","origin: ATLAS of finite groups, tests: 1.o.r."],
["3.Fi22M3","3rd maximal subgroup of 3.Fi22,\ndiffers from 3.Fi22M2 only by fusion map"],
["3.Fi22M5","5th maximal subgroup of 3.Fi22,\ncomputed in March 2000 by Thomas Breuer using character theoretic methods\nfrom the known tables of Fi22, 3.Fi22, and Fi22M5"],
["3.G2(3)","origin: ATLAS of finite groups, tests: 1.o.r."],
["3.G2(3).2","origin: ATLAS of finite groups, tests: 1.o.r."],
["3.G2(3)M2","2nd maximal subgroup of 3.G2(3),\ndiffers from 3.G2(3)M1 = 3xU3(3).2 only by fusion map"],
["3.G2(3)M4","4th maximal subgroup of 3.G2(3),\ndiffers from 3.G2(3)M3 = 3.(3^(1+2)+x3^2):2S4 only by fusion map"],
["3.G2(3)M6","6th maximal subgroup of 3.G2(3),\ndiffers from 3.G2(3)M5 = 3xL3(3).2 only by fusion map"],
["3.J3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,17,19]"],
["3.J3.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,17,19]"],
["3.L3(4)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3.L3(4).2^2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3.L3(4).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3.L3(4).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3.L3(4).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3.L3(4).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3.L3(4).3.2_2","origin: ATLAS of Finite Groups"],
["3.L3(4).3.2_3","constructed using `CharacterTableOfTypeGS3'"],
["3.L3(4).6","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3.L3(4)M4","4th maximal subgroup of 3.L3(4),\ndiffers from 3.A6 = 3.L3(4)M3 only by fusion map"],
["3.L3(4)M5","5th maximal subgroup of 3.L3(4),\ndiffers from 3.A6 = 3.L3(4)M3 only by fusion map"],
["3.L3(4)M7","7th maximal subgroup of 3.L3(4),\ndiffers from 3xL3(2) = 3.L3(4)M6 only by fusion map"],
["3.L3(4)M8","8th maximal subgroup of 3.L3(4),\ndiffers from 3xL3(2) = 3.L3(4)M6 only by fusion map"],
["3.L3(7)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,19],\nconstructions: SL(3,7)"],
["3.L3(7).2","origin: ATLAS of finite groups"],
["3.L3(7).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,19]"],
["3.L3(7).S3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,19]"],
["3.L3(7)M2","2nd maximal subgroup of 3.L3(7),\ndiffers from 3.L3(7)M1 = 3x7^2:2.L2(7).2 only by fusion map"],
["3.L3(7)M4","4th maximal subgroup of 3.L3(7),\ndiffers from 3.L3(7)M3 = 3xL2(7).2 only by fusion map"],
["3.L3(7)M5","5th maximal subgroup of 3.L3(7),\ndiffers from 3.L3(7)M3 = 3xL2(7).2 only by fusion map"],
["3.M22","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["3.M22.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["3.M22M2","2nd maximal subgroup of 3.M22,\nconstructed by Stefan Irnich using GAP"],
["3.McL","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]\n3rd power map determined only up to table automorphism (35,36)"],
["3.McL.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["3.McL.2N3","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["3.McL.2N5","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["3.McLM10","10th maximal subgroup of 3.McL,\ndiffers from 3.McLM9 = 3.2^4:a7 only by fusion map"],
["3.McLM3","3rd maximal subgroup of 3.McL,\ndiffers from 3.McLM2 only by fusion map"],
["3.O7(3)","origin: ATLAS of finite groups, tests: 1.o.r."],
["3.O7(3).2","origin: ATLAS of finite groups, tests: 1.o.r."],
["3.O7(3)M5","5th maximal subgroup of 3.O7(3),\ndiffers from 3.O7(3)M4 = 3.G2(3) only by fusion map"],
["3.O7(3)M9","origin: Dixon's Algorithm"],
["3.ON","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19,31]"],
["3.ON.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19,31]"],
["3.ON.2M4","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["3.ON.2N3","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["3.ON.2N7","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["3.ONM5","constructed by T. Breuer (1995/08/15) using the tables of ON, 3.ON, ONM5,\nstructure is 3.(3^2:4xA6).2,\n5th maximal subgroup of 3.ON,\ntable is sorted w.r. to normal series given by 3.3^2.2.2.A6.2,\ntests: 1.o.r., pow[2,3,5]"],
["3.ONM6","6th maximal subgroup of 3.ON, type 3^{1+4}_+:2^{1+4}_-D_{10}\nconstructed by T. Breuer (1995/08/13) using the tables of ON, 3.ON, ONM6,\ntable is sorted according to (unique) chief series 3.3^4.2.2^4.5.2,\n(of course should be stored as projective table of ONM6 but this table is\nsorted in a too ugly way)\ntests: 1.OR, pow[2,3,5], fusion in 3.ON"],
["3.Suz","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"],
["3.Suz.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"],
["3.U3(11)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11,37],\nconstructions: SU(3,11)"],
["3.U3(11).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11,37]"],
["3.U3(11).3","origin: ATLAS of finite groups"],
["3.U3(11).S3","origin: ATLAS of finite groups"],
["3.U3(5)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: SU(3,5)"],
["3.U3(5).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3.U3(5).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3.U3(5).S3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3.U3(5)M2","2nd maximal subgroup of 3.U3(5),\ndiffers from 3.U3(5)M1 = 3.A7 only by fusion map"],
["3.U3(5)M3","3rd maximal subgroup of 3.U3(5),\ndiffers from 3.U3(5)M1 = 3.A7 only by fusion map"],
["3.U3(5)M6","6th maximal subgroup of 3.U3(5),\ndiffers from 3.U3(5)M5 = 3.A6.2_3 only by fusion map"],
["3.U3(5)M7","7th maximal subgroup of 3.U3(5),\ndiffers from 3.U3(5)M5 = 3.A6.2_3 only by fusion map"],
["3.U3(8)","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: SU(3,8)"],
["3.U3(8).2","origin: ATLAS of finite groups, tests: 1.o.r."],
["3.U3(8).3_1","origin: ATLAS of finite groups, tests: 1.o.r."],
["3.U3(8).3_2","origin: ATLAS of finite groups, tests: 1.o.r."],
["3.U3(8).6","origin: ATLAS of finite groups, tests: 1.o.r., tests: 1.o.r."],
["3.U3(8).S3","origin: ATLAS of finite groups"],
["3.U6(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["3.U6(2).2","origin: ATLAS of finite groups"],
["3.U6(2).3","origin: ATLAS of finite groups"],
["3.U6(2)M10","10th maximal subgroup of 3.U6(2),\ndiffers from 3.U6(2)M8 = 3xS6(2) only by fusion map"],
["3.U6(2)M12","12th maximal subgroup of 3.U6(2),\ndiffers from 3.U6(2)M11 = 3.M22 only by fusion map"],
["3.U6(2)M13","13th maximal subgroup of 3.U6(2),\ndiffers from 3.U6(2)M11 = 3.M22 only by fusion map"],
["3.U6(2)M3","3rd maximal subgroup of 3.U6(2),\nconstructed in March 2000 by Thomas Breuer using char. theor. methods\nfrom the known tables of 3.U6(2) and 2^9.L3(4)"],
["3.U6(2)M5","5th maximal subgroup of 3.U6(2),\ndiffers from 3.U6(2)M4 = 3_1.U4(3).2_2 only by fusion map"],
["3.U6(2)M6","6th maximal subgroup of 3.U6(2),\ndiffers from 3.U6(2)M4 = 3_1.U4(3).2_2 only by fusion map"],
["3.U6(2)M9","9th maximal subgroup of 3.U6(2),\ndiffers from 3.U6(2)M8 = 3xS6(2) only by fusion map"],
["3.s7x2","origin: CAS library,\ntests: 1.o.r., pow[2,3,5,7]"],
["31:10","31 normalizer in J4"],
["31:15","15th maximal subgroup of Th"],
["31:30","8th maximal subgroup of ON.2,\nconstructions: AGL(1,31)"],
["31:6","31 normalizer in L3(5).2, G2(5), Ly"],
["37:12","origin: CAS library,\nmaximal subgroup of J4,\nTest: OR1, JAMES,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3,37]"],
["37:18","9th maximal subgroup of Ly"],
["3D4(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["3D4(2).3","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(3D4(2))"],
["3D4(3)","computed using Magma V2.23-9     Mon Oct  1 2018 10:41:55 on schedir\n[Seed = 2806849869]\nTotal time: 30.539 seconds, Total memory usage: 115.25MB"],
["3D4(4)","computed by Eamonn O'Brien using Magma, April 2014"],
["3^(1+10):(2xU5(2):2)","7th maximal subgroup of Fi24"],
["3^(1+10):U5(2):2","table computed with CliffordTable( U5(2).2 ->\n                                   3^10:U5(2).2  -> 3^1+10:U5(2).2 )"],
["3^(1+10)_+:(2x2^(1+6)_-:3^(1+2)_+:2S4)","origin: Dixon's Algorithm,\nsolvable subgroup of maximal order in Fi24'.2"],
["3^(1+10)_+:2^(1+6)_-:3^(1+2)_+:2S4","origin: Dixon's Algorithm,\nsolvable subgroup of maximal order in Fi24'"],
["3^(1+12).(2xU5(2).2)","subgroup of the 3B normalizer in M,\nhas been used in the construction of the character table of this group"],
["3^(1+12).2.Suz.2","Maximal subgroup of M,\nComputed by R. W. Barraclough"],
["3^(1+12):6.Suz.2","Computed by R. W. Barraclough"],
["3^(1+2)+.2S4","origin: Dixon's Algorithm"],
["3^(1+2)+:2A4","subgroup of U4(2), table computed from a representation of this group"],
["3^(1+2)+:2S4","origin: Dixon's Algorithm"],
["3^(1+2):8","origin: Ostermann, tests: 1.o.r., pow[2,3]\nSylow 3 normalizer in sporadic Janko group J2"],
["3^(1+2):8:4","origin: Dixon's Algorithm,\nSylow 3 normalizer in 2.G2(4)"],
["3^(1+2):D8","origin: Ostermann, tests: 1.o.r., pow[2,3]\nSylow 3 normalizer in sporadic Mathieu group M24,\nSylow 3 normalizer in sporadic Held group He,\n5th maximal subgroup (novelty) in M12.2"],
["3^(1+2):SD16","origin: Ostermann, tests: 1.o.r., pow[2,3]\nSylow 3 normalizer in sporadic Rudvalis group Ru,"],
["3^(1+2)_+.(2S4x3)","origin: Dixon's Algorithm"],
["3^(1+2)_+:Q8","origin: Dixon's Algorithm"],
["3^(1+4)+.2^(1+4)-.S3","origin: Dixon's Algorithm"],
["3^(1+4)+.4S4","origin: Dixon's Algorithm"],
["3^(1+4).2U4(2)","origin: Dixon's Algorithm,\n1st maximal subgroup of S6(3),\ncentralizer of 3C element in Co1"],
["3^(1+4).2U4(2).2","origin: Dixon's Algorithm,\n13th maximal subgroup of Co1,\n1st maximal subgroup of S6(3).2"],
["3^(1+4).2^(1+1+2+2).S3","15th maximal subgroup of U6(2)"],
["3^(1+4):2S5","origin: CAS library,\nmaximal subgroup (normalizer of 3A element) in McL,\ntable sorted w.r. to normal series 3.3^4.2.A5.2,\ntests: 1.o.r., pow[2,3,5]"],
["3^(1+4):4A5","origin: constructed from tables HNC3B, 4A5, and permutation character,\n14th maximal subgroup of HN,\n3B normalizer,\ntests: 1.o.r., pow[2,3,5]"],
["3^(1+4):4S4","origin: Dixon's Algorithm,\nsolvable subgroup of maximal order in McL.2"],
["3^(1+4):4S5","origin: Dixon's algorithm,\nmaximal subgroup of McL.2, normalizer of 3A element,\nthe table is sorted w.r. to normal series 3.3^4.2.(S5x2),\ntests: 1.o.r., pow[2,3,5]"],
["3^(1+4)_+.2S4","origin: Dixon's Algorithm,\n3A normalizer in U4(3)"],
["3^(1+4)_+:(S3xQD16)","Sylow 3 normalizer in the sporadic simple Conway group Co2,\norigin: Dixon's Algorithm"],
["3^(1+6):2^(3+4):3^2:2","origin: Dixon's Algorithm,\nmaximal subgroup of Fi22,\ntable sorted w.r. to normal series 3.3^6.2^3.2^4.3^2.2,\ntests: 1.o.r., pow[2,3]"],
["3^(1+6)_+:2^(3+4):(S3xS3)","origin: Dixon's Algorithm,\nmaximal subgroup of Fi22.2,\ntable sorted w.r. to normal series 3.3^6.2^3.2^4.3^2.2.2,\ntests: 1.o.r., pow[2,3]"],
["3^(1+8).2^(1+6).3^(1+2).2S4","origin: Dixon's Algorithm,\nmaximal subgroup of Fi23,\ncharacters and classes are sorted w.r. to normal series given by\n3.3^8.2.2^6.3.3^2.2.2^2.3.2,\ntests: 1.o.r., pow[2,3]"],
["3^(1+8).2^(1+6).U4(2).2","13th maximal subgroup in B,\n3B normalizer in B,\ncomputed in April 2003 using a degree 19683 perm. repr."],
["3^(2+4):2(S4xD8)","12th maximal subgroup of Suz.2,\norigin: Dixon's Algorithm"],
["3^(2+4):2A5.D8","7th maximal subgroup of Ly,\norigin: computed from tables of subgroup 3.3^(1+4):4S5, Sylow 2 subgroup,\n        and supergroup Ly\ntable is sorted w.r. to normal series given by 3^2.3^4.2.A5.D8,\ntests: 1.o.r., pow[2,3,5]"],
["3^(2+4):80","origin: Dixon's Algorithm"],
["3^(2+5+10).(M11x2S4)","14th maximal subgroup of M,\ncomputed in September 2023 by Tim Burness, using Magma"],
["3^(3+2+6+6):(L3(3)xSD16)","15th maximal subgroup of M,\ncomputed in September 2023 by Tim Burness, using Magma"],
["3^(3+3):L3(3)","origin: Dixon's Algorithm"],
["3^(3+4):(2.S4)^2","origin: Dixon's Algorithm"],
["3^(3+4):2(S4xA4)","3rd maximal subgroup of S6(3),\norigin: Dixon's Algorithm"],
["3^(3+4):2(S4xS4)","origin: Dixon's Algorithm,\n15th maximal subgroup of Co1,\ntable is sorted w.r. to normal series 3^3.3^4.2.2^2.3.2.2^2.3.2"],
["3^(3+6):(L3(3)xD8)","maximal subgroup (novelty) in O8+(3).D8,\nnormalizer of a 3^3 subgroup in B,\ncomputed in March 2003 using the degree 3360 perm. repr. of O8+(3).S4"],
["3^(3+6):26","origin: Dixon's Algorithm"],
["3^1+4:2^1+4.s5","origin: CAS library,\nmaximal subgroup of Co2,\nSource: Table named 'gg' from Birmingham.\nTest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3,5]"],
["3^1+4:4s6","origin: CAS library,\nmaximal subgroup of Co3,\nComputed using CAYLEY\n[to get 4s6 and inertia factor groups]. Complement classes are, if not\nunique, the first of the classes that belong to the corresponding\nclass of the factor group.\nTest: OR1, JAMES, JAMES,n=3,\nrestricted characters from c3 and induced \ncharacters from the complement decompose properly.\ntests: 1.o.r., pow[2,3,5]"],
["3^12.6.Suz.2","Computed by R. W. Barraclough"],
["3^2+4:2(2^2xa4)2","origin: Dixon algorithm,\n11th maximal subgroup of Suz,\ntests: 1.o.r., pow[2,3]"],
["3^2.(3^(1+4)_+.2S4)","6th maximal subgroup of 3^2.U4(3), contributed by G. Hiss,\norigin: Dixon's Algorithm"],
["3^2.(3^4:A6)","1st maximal subgroup of 3^2.U4(3), contributed by G. Hiss,\norigin: Dixon's Algorithm"],
["3^2.(3x3^(1+2)+):2^2","Sylow 3 normalizer in G2(3)"],
["3^2.(3x3^(1+2)+):D8","origin: Dixon's Algorithm"],
["3^2.2.S4","origin: CAS library, tests: 1.o.r., pow[2,3],\nconstructions: AGL(2,3)"],
["3^2.3^(1+2):8","origin: CAS library,\nSylow 3 normalizer in sporadic Janko group J3,\nmaximal subgroup of J3,\ntests: 1.o.r., pow[2,3]"],
["3^2.3^(1+2):8.2","origin: computed using GAP and tables of J3, J3.2, J3M7,\n7th maximal subgroup of J3.2,\ntests: 1.o.r., pow[2,3]"],
["3^2.3^3.3^6.(S4x2S4)","origin: Dixon's Algorithm,\n17th maximal subgroup of B"],
["3^2.3^4.3^8.(A5x2A4).2","origin: Computed by A. Hulpke, using Dixon's Algorithm"],
["3^2.3^4.3^8.(S5x2S4)","origin: Dixon's Algorithm,\n12th maximal subgroup of Fi24"],
["3^2.U4(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3^2.U4(3).(2^2)_{133}","3rd maximal subgroup of 3.Suz.2"],
["3^2.U4(3).2_3'","2nd maximal subgroup of 3.Suz,\ntable constructed with GAP from the tables of 3.Suz and SuzM2,\ntests: 1.o.r., pow[2,3,5,7]"],
["3^2.U4(3).D8","origin: ATLAS of finite groups,\ntable was constructed by Dixon's algorithm,\ntests: 1.o.r., pow[2,3,5,7]"],
["3^2:2A4","8th maximal subgroup of A9"],
["3^2:2A4x3","maximal subgroup of 3D4(2).3"],
["3^2:8","3rd maximal subgroup of 2.A6"],
["3^2:Q8","origin: Ostermann, tests: 1.o.r., pow[2,3]\nSylow 3 normalizer in sporadic Mathieu group M22"],
["3^2:Q8.2","origin: Ostermann, tests: 1.o.r., pow[2,3]\nSylow 3 normalizer in sporadic Mathieu group M11,\nmaximal subgroup of M11,\nSylow 3 normalizer in sporadic Mathieu group M23,\nSylow 3 normalizer in M22.2"],
["3^3.(3x3^(1+2)+):2^2","origin: Dixon's Algorithm"],
["3^3.3^(1+2):8","origin: Dixon's Algorithm"],
["3^3.3^(1+2):8.2","origin: Dixon's Algorithm"],
["3^3.S4","origin: Dixon's Algorithm\nsubgroup of U5(2).2"],
["3^3.[3^10].(L3(3)x2^2)","11th maximal subgroup of Fi24"],
["3^3.[3^10].GL3(3)","origin: computed by Thomas Breuer in December 2000,\nusing a combination of Dixon's Algorithm and other techniques"],
["3^3:A4","origin: Dixon's Algorithm,\nnormal subgroup of index 2 in U4(2)M4"],
["3^3:L3(3)","origin: Dixon's Algorithm"],
["3^3:S4`","origin: Dixon's Algorithm"],
["3^4.(3xSL(2,3)).2","origin: Dixon's Algorithm"],
["3^4.2U4(2)","factor group in central extension S6(3)M1"],
["3^4.2U4(2).2","table of factor group of S6(3).2M1 resp. Co1M13"],
["3^4.3^2.Q8","origin: Dixon's Algorithm,\ntable of an intersection of maximal subgroups 3^{1+4}:4S_5 and 3^4:M_{10}\nof the sporadic simple McLaughlin group McL"],
["3^4.3^2:4","origin: Dixon's Algorithm"],
["3^4.A6.D8","origin: Dixon's Algorithm"],
["3^4:(2xA5)","origin: Dixon's Algorithm\nsubgroup of U5(2).2"],
["3^4:(2xA6)","origin: Dixon's Algorithm"],
["3^4:(3^2:Q8)","origin: Ostermann, tests: 1.o.r., pow[2,3]\nSylow 3 normalizer in sporadic McLaughlin group McL,"],
["3^4:(M10x2)","5th maximal subgroup of McL.2,\norigin: Dixon's Algorithm"],
["3^4:2(A4xA4).2","origin: Dixon's Algorithm"],
["3^4:2(A4xA4).4","origin: computed by Klaus Lux using Dixon's Algorithm,\n13th maximal subgroup of HN,\ntable is sorted w.r. to normal series 3^4.2.2^4.3^2.2.2,\ntests: 1.o.r., pow[2,3],"],
["3^4:2(S4xS4).2","12th maximal subgroup of HN.2,\norigin: Dixon's Algorithm"],
["3^4:2^(1+4).(5:4)","Sylow 3 normalizer in ON.2,\n5th maximal subgroup of ON.2,\n,origin: Dixon's Algorithm"],
["3^4:2^(1+4)D10","origin: Ostermann, tests: 1.o.r., pow[2,3,5]\nSylow 3 normalizer in sporadic O'Nan group ON,\nmaximal subgroup of ON"],
["3^4:2^3.S4","origin: Dixon's Algorithm"],
["3^4:2^3.S4(a)","14th maximal subgroup of O8+(2),\norigin: Dixon's Algorithm"],
["3^4:3^2:D8","origin: Dixon's Algorithm"],
["3^4:40","origin: Dixon's Algorithm"],
["3^4:A6","origin: computed using the tables of U4(3), U4(3).2_3,\n3^4:M10 and A6; maximal subgroup of U4(3)"],
["3^4:GL2(9)","origin: Dixon's Algorithm,\nconstructions: AGL(2,9)"],
["3^4:S5","origin: Dixon's Algorithm,\n4th maximal subgroup of U5(2)"],
["3^4:S6","origin: Dixon's Algorithm"],
["3^4:m10","origin: CAS library,\n maximal subgroup of mcl\n  structure:= 3^4:m10\n  1st &&nbsp;2nd orthogonality relations are satisfied\n  symmetric squares decompose properly\n  created 30/01/1985\ntests: 1.o.r., pow[2,3,5]"],
["3^5.3^(1+2).2.S4","origin: Dixon's Algorithm"],
["3^5.3^3.(2xS4)","origin: Dixon's Algorithm"],
["3^5.U4(2)","nonsplit extension of 3^5 with U4(2),\ncentral quotient of the derived subgroup of the 9A centralizer\nin the Monster,\nconstructed by Simon Norton, July 1997"],
["3^5:(2xU4(2).2)","10th maximal subgroup of Fi22.2,\norigin: Dixon's Algorithm"],
["3^5:(2xm11)","origin: CAS library,\nmaximal subgroup of Co3,\nTest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3,5,11]"],
["3^5:(3^2:SD16)","origin: Ostermann, tests: 1.o.r., pow[2,3]\nSylow 3 normalizer in sporadic Suzuki group Suz,"],
["3^5:(M10x2)","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["3^5:(M11x2)","6th maximal subgroup of Suz.2,\norigin: Dixon's Algorithm"],
["3^5:2S6","origin: contructed in GAP using table of 3^4:2A6, and perm. char.,\n8th maximal subgroup of Th,\n3C normalizer,\ntable is sorted w.r. to normal series given by 3.3^4.2.A6.2,\ntests: 1.o.r., pow[2,3,5]"],
["3^5:M10","6th maximal subgroup of 3.McL,\nconstructed 1996/09/09 by Thomas Breuer using the tables of 3^4.m10, McL,\nand 3.McL"],
["3^5:M11","maximal subgroup of Suz,\ntests: 1.o.r., pow[2,3,5,11]"],
["3^5:U4(2)","table computed with CliffordTable( U4(2) -> 3^5:U4(2) ),\n3rd power map determined by class fusion into O7(3)"],
["3^6.L4(3).D8","maximal subgroup in O8+(3).D8,\nnormalizer of a 3^6 subgroup in B,\ncomputed in March 2003 using the degree 3360 perm. repr. of O8+(3).S4"],
["3^6.M11","5th maximal subgroup of 3.Suz,\ntable constructed in GAP using tables of SuzM5 and 3.Suz,\ntests: 1.o.r., pow[2,3,5,11]"],
["3^6:(L4(3)x2)","constructed using Dixon's Algorithm plus character theoretic methods"],
["3^6:(M11x2)","6th maximal subgroup of 3.Suz.2"],
["3^6:2M12","origin: Dixon's Algorithm,\n11th maximal subgroup of Co1,\ntable is sorted w.r. to normal series 3^6.2.M12,\ntests: 1.o.r., pow[2,3,5,11]"],
["3^6:2U4(3).2_1","origin: Dixon's Algorithm,\nstabilizer of an isotropic point in O8-(3)"],
["3^6:L3(3)","2nd maximal subgroup of S6(3),\norigin: Dixon's Algorithm"],
["3^6:L4(3)","origin: Dixon's Algorithm,\nmaximal subgroup of O8+(3),\ntable is sorted w.r. to normal series 3^6.L4(3),\ntests: 1.o.r., pow[2,3,5,13]"],
["3^6:L4(3):2_2","origin: Dixon's Algorithm"],
["3^7.O7(3)","origin: constructed by Alexander Hulpke,\n5th maximal subgroup of F3+"],
["3^7.O7(3):2","non-split extension of 3^7 by O7(3).2,\norigin: computed by Faryad Ali using Clifford matrices,\nmaximal subgroup of F3+.2,\ntests: 1.o.r., pow[2,3,5,7,13]"],
["3^7:O7(3)","table computed with CliffordTable( O7(3) -> 3^7:O7(3) )"],
["3^8.O8-(3).2_3","11th maximal subgroup of M,\ncomputed in September 2023 by Tim Burness, using Magma"],
["3_1.U4(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3_1.U4(3).(2^2)_{122}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["3_1.U4(3).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3_1.U4(3).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3_1.U4(3).2_2'","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]\n"],
["3_2.U4(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]\n3rd power map determined only up to matrix automorphisms (40,41), (42,43)"],
["3_2.U4(3).(2^2)_{133}","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3_2.U4(3).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3_2.U4(3).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,5,7]\n3rd power map determined only up to table automorphism (33,34)"],
["3_2.U4(3).2_3'","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["3x(2x2^(1+8)):U4(2):2","7th maximal subgroup of 3.Fi22"],
["3x(2x2^(1+8)_+).2.2^4.(S3xS3)","normalizer of a radical 2-subgroup in 3.Fi22"],
["3x(2xL3(3)).2","14th maximal subgroup of 6.Suz"],
["3x(3xA6):2_2","6th maximal subgroup in 3.J3"],
["3x(A4x11:5).2","Sylow 11 normalizer in 3.F3+"],
["3x(D10xA9).2","defect normalizer in 3.F3+"],
["3x11:5","Sylow 11 normalizer in 3.M22, 3.McL"],
["3x13:6","Sylow 13 normalizer in 3.Fi22 and 3.G2(3)"],
["3x17:16","Sylow 17 normalizer in 3.F3+"],
["3x2(A4xA4).2^2","normalizer of a radical 2-subgroup in 3.McL"],
["3x2.(2xL2(11))","8th maximal subgroup of 12.M22"],
["3x2.2^(4+8):(S3xA5)","7th maximal subgroup of 6.U6(2)"],
["3x2.A5","1st maximal subgroup of 6.A6"],
["3x2.A8","8th maximal subgroup of 3.McL"],
["3x2.F4(2)","4th maximal subgroup of 6.2E6(2)"],
["3x2.Fi22.2","subgroup of 2.BM9, needed in its construction"],
["3x2.Fi22N2","normalizer of a radical 2-subgroup in 6.Fi22"],
["3x2.G2(4)","1st maximal subgroup of 6.Suz"],
["3x2.J2.2","6th maximal subgroup of 6.Suz"],
["3x2.J2.2N5","Sylow 5 normalizer in 6.Suz"],
["3x2.L2(25)","16th maximal subgroup of 6.Suz"],
["3x2.L3(2)","2nd and 3rd maximal subgroup of 6.A7"],
["3x2.M22M5","5th maximal subgroup of 6.M22"],
["3x2.SuzM4","4th maximal subgroup of 6.Suz"],
["3x2.SuzM7","7th maximal subgroup of 6.Suz,\nstructure 3x(2.2^4.2^6):3A6"],
["3x2.SuzM9","9th maximal subgroup of 6.Suz"],
["3x2.Symm(4)","4th maximal subgroup of 6.A6"],
["3x23:11","Sylow 23 normalizer in 3.F3+"],
["3x29:14","Sylow 29 normalizer in 3.F3+"],
["3x2F4(2)'","9th maximal subgroup of 3.Fi22"],
["3x2^(1+4)_-:A5","8th maximal subgroup of 3.J3"],
["3x2^(1+6)_-.U4(2)","4th maximal subgroup of 3.Suz"],
["3x2^(1+8)_+:U4(2)","2nd maximal subgroup of 3.U6(2)"],
["3x2^(2+4):(3xS3)","9th maximal subgroup of 3.J3"],
["3x2^(2+8):(A5xS3)","9th maximal subgroup of 3.Suz"],
["3x2^(4+6).3A6","7th maximal subgroup of 3.Suz"],
["3x2^(5+8):(2xS4)","normalizer of a radical 2-subgroup in 3.Fi22"],
["3x2^(5+8):(S3xD8)","normalizer of a radical 2-subgroup in 3.Fi22"],
["3x2^(5+8):(S3xS4)","normalizer of a radical 2-subgroup in 3.Fi22"],
["3x2^10.2^2.2^2.S4","normalizer of a radical 2-subgroup in 3.Fi22"],
["3x2^10.2^3.L3(2)","normalizer of a radical 2-subgroup in 3.Fi22"],
["3x2^10.2^3.S4","normalizer of a radical 2-subgroup in 3.Fi22"],
["3x2^10.2^4.S5","normalizer of a radical 2-subgroup in 3.Fi22"],
["3x2^3:L3(2)","6th maximal subgroup of 3.M22"],
["3x2^4:(3xA5)","4th maximal subgroup of 3.J3"],
["3x2^4:A5","1st and 2nd maximal subgroup of 3.L3(4)"],
["3x2^4:s5","5th maximal subgroup of 3.M22"],
["3x2^5.A5","1st and 2nd maximal subgroup of 6.L3(4)"],
["3x2^6.2^5.S6","normalizer of a radical 2-subgroup in 3.Fi22"],
["3x2^6:S6(2)","6th maximal subgroup of 3.Fi22"],
["3x4.M22M5","5th maximal subgroup of 12.M22"],
["3x4.M22M6","6th maximal subgroup of 12.M22"],
["3x4.M22N2","Sylow 2 normalizer in 12.M22"],
["3x4^2:D12","normalizer of a radical 2-subgroup in 3.G2(3)"],
["3x4^3.L3(2)","9th maximal subgroup of 3.ON"],
["3x4_1.2^4:A5","1st and 2nd maximal subgroup of 12_1.L3(4), contributed by G. Hiss"],
["3x4_2.2^4:A5","1st and 2nd maximal subgroup of 12_2.L3(4), contributed by G. Hiss"],
["3x5:4xS5","normalizer of a radical 5-subgroup in 3.Fi22"],
["3x5^(1+2):3:8","12th maximal subgroup of 3.McL"],
["3x5^2:(4xS3)","Sylow 5 normalizer in 3.Suz"],
["3x7:6","Sylow 7-normalizer in 3.G2(3)"],
["3x7^(1+2):(D8x3)","Sylow 7-normalizer in 3.ON"],
["3xA10.2","12th maximal subgroup of 3.Fi22"],
["3xA5","1st maximal subgroup of 3.A6"],
["3xA5.2","4th maximal subgroup of 3.A7"],
["3xF3+N7","Sylow 7 normalizer in 3.F3+"],
["3xF4(2)","3rd maximal subgroup of 3.2E6(2)"],
["3xFi22N2","normalizer of a radical 2-subgroup in 3.Fi22"],
["3xFi22N5","Sylow 5 normalizer in 3.Fi22"],
["3xFi23","1st maximal subgroup of 3.F3+"],
["3xG2(4)","1st maximal subgroup of 3.Suz"],
["3xIsoclinic(2.A5.2)","4th maximal subgroup of 6.A7"],
["3xIsoclinic(2.M12.2)","10th maximal subgroup of 6.Suz"],
["3xJ1","3rd maximal subgroup of 3.ON"],
["3xJ2.2","6th maximal subgroup of 3.Suz"],
["3xJ3N2","Sylow 2 normalizer in 3.J3"],
["3xL2(11)","8th maximal subgroup of 3.M22"],
["3xL2(16).2","1st maximal subgroup of 3.J3"],
["3xL2(17)","5th maximal subgroup of 3.J3"],
["3xL2(19)","2nd maximal subgroup of 3.J3"],
["3xL2(25)","16th maximal subgroup of 3.Suz"],
["3xL2(31)","7th maximal subgroup of 3.ON"],
["3xL3(2)","2nd and 3rd maximal subgroup of 3.A7"],
["3xL3(3).2","14th and 15th maximal subgroup of 3.Suz,\n(fusions differ by an autom. of the subgroup,\nso the same fusion is stored for both maxes)"],
["3xL3(4).2_2","7th maximal subgroup of 3.McL"],
["3xL3(7).2","1st maximal subgroup of 3.ON"],
["3xM11","11th maximal subgroup of 3.McL"],
["3xM12","14th maximal subgroup of 3.Fi22"],
["3xM12.2","10th maximal subgroup of 3.Suz"],
["3xM12N2","Sylow 2-normalizer in 3.G2(3)"],
["3xM22C2A","normalizer of a radical 2-subgroup in 3.McL"],
["3xMcLN2","Sylow 2 normalizer in 3.McL"],
["3xO8+(2):S3","4th maximal subgroup of 3.Fi22"],
["3xONM11","11th maximal subgroup of 3.ON,\ndiffers from 3.ONM10 only by fusion map"],
["3xONM2","2nd maximal subgroup of 3.ON,\ndiffers from 3.ONM1 only by fusion map"],
["3xONM8","8th maximal subgroup of 3.ON,\ndiffers from 3.ONM7 only by fusion map"],
["3xONN2","Sylow 2 normalizer in 3.ON"],
["3xS3x7:6","Sylow 7 normalizer in 3.Fi22"],
["3xS3xU4(2)","14th maximal subgroup of 3.U6(2)"],
["3xSymm(4)","4th maximal subgroup of 3.A6"],
["3xU5(2)","3rd maximal subgroup of 3.Suz,\n1st maximal subgroup of 3.U6(2)"],
["4(A4xA4).4","origin: Dixon's Algorithm"],
["4.2^4","stabilizer of chain (2A < [2^8]) in HS,\nstabilizer of chain (2A < Sylow2) in HS,\norigin: Dixon's Algorithm"],
["4.2^4.S5","origin: CAS library, tests: 1.o.r., pow[2,3,5]"],
["4.2^4:(2xS3)","origin: Dixon's Algorithm,\nnormalizer of 4.2^4:2 in HS,\ntable is sorted w.r.t. normal series 2.2.2^2.2^2.3.2.2"],
["4.2^4:S4","origin: Dixon's Algorithm,\nnormalizer of 4.2^4:2^2 in HS, of structure 4.2^4:S4,\ntable is sorted w.r.t. normal series 2.2.2^2.2^2.2^2.3.2"],
["4.3^(1+4)_+.2S4","6th maximal subgroup of 4.U4(3), contributed by G. Hiss"],
["4.A6.2_3","origin: ATLAS of finite groups"],
["4.HS.2","extension of the central product of C4 and 2.HS by an automorphism,\nmaximal subgroup of HN.2,\n"],
["4.L2(25).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"],
["4.L2(49).2_3","origin: ATLAS of finite groups"],
["4.L2(81).2_3","origin: ATLAS of finite groups"],
["4.L2(81).4_2","constructed using `PossibleCharacterTablesOfTypeMGA',\nsubgroup of GammaL(2,81)"],
["4.L4(5)","computed by Thomas Breuer in December 2005,\nusing the character tables of the factor groups, Dixon's algorithm,\nand character theoretic methods"],
["4.M22","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["4.M22.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["4.M22M2","2nd maximal subgroup of 4.M22,\nconstructed by Stefan Irnich using GAP"],
["4.M22M5","5th maximal subgroup of 4.M22,\nconstructed by Stefan Irnich using GAP"],
["4.M22M6","6th maximal subgroup of 4.M22"],
["4.M22N2","origin: Dixon's Algorithm"],
["4.U4(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: SU(4,3)"],
["4.U4(3).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["4.U4(3).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["4.U4(3).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["4.U4(3).4","origin: ATLAS of finite groups, test: 1.o.r., pow[2,3,5,7],\nconstructions: GU(4,3)"],
["4.s4","origin: CAS library,\n test:= 1. o.r., sym 2 decompose correctly \ntests: 1.o.r., pow[2,3]"],
["41:4","2nd maximal subgroup of Sz(32)"],
["41:40","46th maximal subgroup of M,\nconstructions: AGL(1,41)"],
["43:14","origin: CAS library,\nmaximal subgroup of J4,\nTest: 1.OR, JAMES,\nand resticted characters decompose properly.\ntests: 1.o.r., pow[2,7,43]"],
["47:23","30th maximal subgroup of B"],
["4^2.L3(4)","constructed using `PossibleCharacterTablesOfTypeV4G'"],
["4^2:D12","origin: CAS library, tests: 1.o.r., pow[2,3]"],
["4^2:D12.2","origin: Dixon's Algorithm,\n8th maximal subgroup of M12.2,\ntable is sorted w.r. to normal series\n2^2<4^2<4^2.2<4^2.S3<4^2.D12<4^2.D12.2"],
["4^2:s3","origin: CAS library,\nmaximal subgroup of U3(3),\n test:= 1. o.r., sym 2 decompose correctly \ntests: 1.o.r., pow[2,3]"],
["4^3.(L3(2)x2)","origin: Dixon's Algorithm,\n6th maximal subgroup of ON.2"],
["4^3.D8","origin: Ostermann, tests: 1.o.r., pow[2]\nSylow 2 normalizer in sporadic O'Nan group ON,"],
["4^3.L3(2)","origin: Dixon's Algorithm,\n9th maximal subgroup of ON,\ntable is sorted w.r. to normal series given by 2^3.2^3.L3(2),\ntests: 1.o.r., pow[2,3,7]"],
["4^3:(L3(2)x2)","6th maximal subgroup of 2.HS,\norigin: Dixon's Algorithm"],
["4^3:S4","origin: Dixon's Algorithm,\nnormalizer of 4^3:2^2 in HS,\ntable is sorted w.r.t. normal series 2^2.2.2^3.2^2.3.2"],
["4^3:psl(3,2)","origin: CAS library,\n7th maximal subgroup of HS,\ntests: 1.o.r., pow[2,3,7]"],
["4_1.2^4:A5","1st and 2nd maximal subgroup of 4_1.L3(4), contributed by G. Hiss"],
["4_1.L3(4)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["4_1.L3(4).(2^2)_{1*2*3*}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_1.L3(4).(2^2)_{1*2*3}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_1.L3(4).(2^2)_{1*23*}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_1.L3(4).(2^2)_{1*23}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_1.L3(4).(2^2)_{12*3*}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_1.L3(4).(2^2)_{12*3}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_1.L3(4).(2^2)_{123*}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_1.L3(4).(2^2)_{123}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_1.L3(4).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["4_1.L3(4).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["4_1.L3(4).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["4_2.2^4:A5","1st and 2nd maximal subgroup of 4_2.L3(4), contributed by G. Hiss"],
["4_2.L3(4)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["4_2.L3(4).(2^2)_{1*2*3*}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_2.L3(4).(2^2)_{1*2*3}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_2.L3(4).(2^2)_{1*23*}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_2.L3(4).(2^2)_{1*23}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_2.L3(4).(2^2)_{12*3*}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_2.L3(4).(2^2)_{12*3}","constructed using `PossibleCharacterTablesOfTypeMGA',\n3rd maximal subgroup of ON.2"],
["4_2.L3(4).(2^2)_{123*}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_2.L3(4).(2^2)_{123}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["4_2.L3(4).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["4_2.L3(4).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["4_2.L3(4).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]\n2nd power map determined by fusion into 4.U4(3).2_3"],
["4x11:5","Sylow 11 normalizer in 4.M22"],
["4x7:3","Sylow 7 normalizer in 4.M22"],
["59:29","45th maximal subgroup of M"],
["5:4","2nd maximal subgroup of A5.2,\nconstructions: AGL(1,5)"],
["5:4x2.A5","12th maximal subgroup of 2.HS,\n15th maximal subgroup of 2.Ru,\nstructure 5:4x2.A5"],
["5:4x2^2","normalizer of chain (2B < 2B^2) in HS, contained in HSM12\n"],
["5:4xA4","normalizer of 2B^2 in HS, contained in HSM12\n"],
["5:4xHS.2","15th maximal subgroup of B"],
["5:4xS4","Sylow 5 normalizer in O7(3)"],
["5:4xS5","10th maximal subgroup of HS.2,\nstructure 5:4xS5"],
["5:4xS6","5A normalizer in F4(2)"],
["5:4xU3(5).2N2","defect normalizer of a 2-block of defect 5 in HN.2"],
["5:4xU3(5):2","6th maximal subgroup of HN.2"],
["5:4xa5","origin: CAS library,\nmaximal subgroup of Ru,\nsource: received from S.Mattarei\ntest: 1.OR, JAMES, JAMES,n=5,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3,5]"],
["5^(1+2)+:24","origin: Dixon's Algorithm"],
["5^(1+2)+:4A5","origin: Dixon's Algorithm"],
["5^(1+2)+:8","origin: Dixon's Algorithm"],
["5^(1+2):(24:2)","origin: Ostermann, tests: 1.o.r., pow[2,3,5]\nSylow 5 normalizer in sporadic Conway group Co3,\n10th maximal subgroup of McL.2"],
["5^(1+2):(4x4):4","origin: Dixon's Algorithm"],
["5^(1+2):(8.2)","origin: Dixon's algorithm,\nmaximal subgroup of U3(5).2,\nSylow 5 normalizer in sporadic Higman Sims group HS,\nSylow 5 normalizer in U3(5).2,\ntable is sorted w.r. to normal series 5.5^2.8.2,\n2nd power map determined only up to matrix automorphisms,\ntests: 1.o.r., pow[2,5]"],
["5^(1+2):3:8","origin: Ostermann, tests: 1.o.r., pow[2,3,5]\nSylow 5 normalizer in sporadic McLaughlin group McL,\nmaximal subgroup of McL"],
["5^(1+2):4S4","origin: Ostermann, tests: 1.o.r., pow[2,3,5],\nSylow 5 normalizer in sporadic Conway group Co2,\n9th maximal subgroup of Th"],
["5^(1+2):8:4","origin: Dixon's Algorithm"],
["5^(1+2):GL2(5)","origin: Dixon's Algorithm,\n19th maximal subgroup of Co1,\n5C normalizer in Co1,\ntable is sorted w.r. to normal series 5.5^2.2.2.A5.2,\ntests: 1.o.r., pow[2,3,5]"],
["5^(1+4).2^(1+4).A5.4","21st maximal subgroup of B,\norigin: Dixon's Algorithm"],
["5^(1+4):2^(1+4).5.4","origin: CAS library,\nnames:=group4; 5**[1+4].2**(1+4).5.4\n order: 2,000,000 = 2^7.5^6\n number of classes: 53\n source: koichiro harada\n         on the simple group f of order\n         2^14.3^6.5^6.7.11.19\n         proceedings of the conference\n         on finite groups\n         park city, utah (1975)\n test: 1. o.r. satisfied\n comments: - \ntests: 1.o.r., pow[2,5]"],
["5^(1+4):4.3^2:D8","origin: Dixon's Algorithm,\nsolvable subgroup of maximal order in Ly"],
["5^(1+4):4S6","5th maximal subgroup of Ly,\norigin: computed using permutation characters, tables of LyN2, LyN5,\nG2(5)M1, and 2.(2xA6),\ncharacters are sorted w.r. to normal series given by 5.5^4.2.2.A6.2,\ntests: 1.o.r., pow[2,3,5]"],
["5^(1+4):GL(2,5)","origin: computed from factor group GL(2,5), subgroup LyN5,\n        and supergroup G2(5);\nmaximal subgroup of G2(5),\ntests: 1.o.r., pow[2,3,5]"],
["5^(1+4)_+:(4Y2^(1+4)_-.5.4)","7th maximal subgroup of HN.2,\norigin: Dixon's Algorithm"],
["5^(1+6):2.J2.4","16th maximal subgroup of M,\nconstructed using Dixon's algorithm and character theoretic methods"],
["5^(2+2+4):(S3xGL2(5))","22nd maximal subgroup of M"],
["5^(3+3).(2xL3(5))","19th maximal subgroup of M"],
["5^1+2:(2^5)","origin: CAS library,\nmaximal subgroup of Ru,\nsource: received from S.Mattarei\ntest: 1.OR, JAMES, JAMES,n=5,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,5]"],
["5^2.5.5^2.4A5","origin: constructed by Alexander Hulpke,\n10th maximal subgroup of HN,\ntable is sorted w.r. to normal series 5^2.5.5^2.2.2.A5,\ntests: 1.o.r., pow[2,3,5]"],
["5^2.5.5^2.4S5","11th maximal subgroup of HN.2,\n2nd maximal subgroup of G2(5),\norigin: Dixon's Algorithm"],
["5^2:(4xS3)","origin: Ostermann, tests: 1.o.r., pow[2,3,5]\nSylow 5 normalizer in sporadic Suzuki group Suz,\n8th maximal subgroup (and Sylow 5 normalizer) in J2:2,"],
["5^2:2A5","origin: Dixon's Algorithm,\n21st maximal subgroup of Co1,\ntable is sorted w.r. to normal series 5^2.2.A5"],
["5^2:4A4","origin: Ostermann, tests: 1.o.r., pow[2,3,5]\nSylow 5 normalizer in sporadic Held group He,\n8th maximal subgroup and Sylow 5 normalizer in 2F4(2)',\nmaximal subgroup of He"],
["5^2:4S4xS5","23rd maximal subgroup of B"],
["5^2:4s5","origin: CAS library,\nmaximal subgroup of Ru,\nsource: received from S.Mattarei\ntest: 1.OR, JAMES, JAMES,n=3, JAMES,n=5,\nand restricted characters decompose properly.\nconstructions: AGL(2,5),\ntests: 1.o.r., pow[2,3,5]"],
["5^2:D12","origin: CAS library,\nSylow 5 normalizer in sporadic Janko group J2,\n test:= 1. o.r., sym 2 decompose correctly \ntests: 1.o.r., pow[2,3,5]"],
["5^2:S3","origin: Dixon's Algorithm"],
["5^3.psl(3,5)","origin: CAS library,\nmaximal subgroup of Ly,\ntest : 1.OR satisfied, JAMES, JAMES,n=5,\nand restricted characters decompose correctly\ntests: 1.o.r., pow[2,3,5,31]"],
["5^3:(2xA5).2","origin: Dixon's Algorithm"],
["5^3:(4x(2xA5).2)","origin: Dixon's Algorithm"],
["5^3:(4xS5)","origin: Dixon's Algorithm,\n20th maximal subgroup of Co1,\ntable is sorted w.r. to normal series 5^3.2.2.A5.2,\ntests: 1.o.r., pow[2,3,5]"],
["5^3:62","origin: Dixon's Algorithm"],
["5^4:(3x2.L2(25)).2","28th maximal subgroup of M"],
["6.(3^(1+4).[2^7.3])","origin: Dixon's Algorithm"],
["6.(A4x3).2","origin: Dixon's Algorithm,\n5th maximal subgroup of 6.A7, structure is (3^2xQ8).S3"],
["6.2E6(2)","constructed using `CharacterTableOfCommonCentralExtension'"],
["6.2E6(2).2","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["6.2E6(2)M5","5th maximal subgroup of 6.2E6(2)"],
["6.2E6(2)M9","9th maximal subgroup of 6.2E6(2)"],
["6.A6","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["6.A6.2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["6.A6.2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["6.A6M2","2nd maximal subgroup of 6.A6,\ndiffers from 6.A6M1 = 3x2.A5 only by fusion map"],
["6.A6M3","origin: Dixon's Algorithm"],
["6.A6M5","5th maximal subgroup of 6.A6,\ndiffers from 6.A6M4 = 3x2.Symm(4) only by fusion map"],
["6.A6N2","Sylow 2 normalizer in 6.A6 and 6.A7,\norigin: Dixon's Algorithm"],
["6.A7","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["6.A7.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["6.Fi22","origin: ATLAS of finite groups, tests: 1.o.r."],
["6.Fi22.2","origin: ATLAS of finite groups, tests: 1.o.r."],
["6.Fi22M3","3rd maximal subgroup of 6.Fi22"],
["6.Fi22M5","5th maximal subgroup of 6.Fi22,\nconstructed in March 2000 by Thomas Breuer, using the known tables of\n3.Fi22M5, 2.Fi22M5, and 6.Fi22"],
["6.L3(4)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["6.L3(4).(2^2)_{1*2*3*}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["6.L3(4).(2^2)_{1*2*3}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["6.L3(4).(2^2)_{1*23*}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["6.L3(4).(2^2)_{1*23}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["6.L3(4).(2^2)_{12*3*}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["6.L3(4).(2^2)_{12*3}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["6.L3(4).(2^2)_{123*}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["6.L3(4).(2^2)_{123}","constructed using `PossibleCharacterTablesOfTypeMGA'"],
["6.L3(4).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["6.L3(4).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["6.L3(4).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["6.L3(4)M7","7th maximal subgroup of 6.L3(4),\ndiffers from 6xL3(2) = 6.L3(4)M6 only by fusion map"],
["6.L3(4)M8","8th maximal subgroup of 6.L3(4),\ndiffers from 6xL3(2) = 6.L3(4)M6 only by fusion map"],
["6.M22","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["6.M22.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["6.M22M2","2nd maximal subgroup of 6.M22,\nconstructed by Stefan Irnich using GAP"],
["6.M22M7","subdirect product of 3.A6.2_3 and C4,\n7th maximal subgroup of 6.M22"],
["6.O7(3)","origin: ATLAS of finite groups, tests: 1.o.r."],
["6.O7(3).2","origin: ATLAS of finite groups"],
["6.O7(3)M11","11th maximal subgroup of 6.O7(3),\ndiffers from 6.O7(3)M10 = 3xIsoclinic(2.A9.2) only by fusion map"],
["6.O7(3)M5","5th maximal subgroup of 6.O7(3),\ndiffers from 6.O7(3)M4 = 2x3.G2(3) only by fusion map"],
["6.O7(3)M8","8th maximal subgroup of 6.O7(3),\ndiffers from 6.O7(3)M7 = 3x2.S6(2) only by fusion map"],
["6.Suz","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"],
["6.Suz.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"],
["6.SuzM11","11th maximal subgroup of 6.Suz,\norigin: Dixon's Algorithm"],
["6.SuzM8","8th maximal subgroup of 6.Suz,\nstructure (SL(2,3) Y 6.L3(4)).2,\norigin: Dixon's Algorithm"],
["6.U6(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["6.U6(2).2","origin: ATLAS of finite groups"],
["6.U6(2)M10","10th maximal subgroup of 6.U6(2),\ndiffers from 6.U6(2)M9 = 6xS6(2) only by fusion map"],
["6.U6(2)M13","13th maximal subgroup of 6.U6(2),\ndiffers from 6.U6(2)M12 = 6.M22 only by fusion map"],
["6.U6(2)M3","3rd maximal subgroup of 6.U6(2),\nintersection of a 6.U6(2) and a (2^10x3).M22 in 3.Fi22,\nstructure 2^10:3.L3(4),\nconstructed in March 2000 by Thomas Breuer using char. theor. methods\nfrom the known tables of 6.U6(2), 2.U6(2)M3, and 3.U6(2)M3"],
["6.U6(2)M6","6th maximal subgroup of 6.U6(2),\ndiffers from 6.U6(2)M5 = 6_1.U4(3).2_2 only by fusion map"],
["6.U6(2)M9","9th maximal subgroup of 6.U6(2),\ndiffers from 6.U6(2)M8 = 6xS6(2) only by fusion map"],
["67:22","8th maximal subgroup of Ly"],
["6^2:D12","origin: Dixon's Algorithm"],
["6^2:S3","origin: Dixon's Algorithm"],
["6_1.U4(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["6_1.U4(3).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["6_1.U4(3).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["6_1.U4(3).2_2'","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["6_2.U4(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]\n3rd power map determined only up to matrix automorphisms (80,82)(81,83)\nand (76,78)(77,79)"],
["6_2.U4(3).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["6_2.U4(3).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]\n3rd power map determined only up to table automorphism (59,61)(60,62)"],
["6_2.U4(3).2_3'","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["6x11:5","Sylow 11 normalizer in 3.Fi22"],
["6x13:6","Sylow 13 normalizer in 6.Fi22"],
["6x2.F4(2)","3rd maximal subgroup of (2^2x3).2E6(2)"],
["6x2^3:L3(2)","6th maximal subgroup of 6.M22"],
["6x5:4xS5","normalizer of a radical 5-subgroup in 6.Fi22"],
["6x7:3","Sylow 7 normalizer in 3.McL"],
["6xF4(2)","3rd maximal subgroup of 6.2E6(2)"],
["6xFi22N5","Sylow 5 normalizer in 6.Fi22"],
["6xL2(11)","8th maximal subgroup of 6.M22"],
["6xL3(2)","6th maximal subgroup of 6.L3(4)"],
["6xO8+(2):S3","4th maximal subgroup of 6.Fi22"],
["6xS3x7:6","Sylow 7 normalizer in 6.Fi22"],
["6xU5(2)","maximal subgroup of 6.Suz"],
["7:12","origin: Dixon's Algorithm"],
["7:3xpsl(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]"],
["7:6","origin: CAS library,\nmaximal subgroup of J1,\ntest: 1.OR, JAMES, JAMES, n=3,\nand restricted characters decompose properly,\nconstructions: AGL(1,7),\ntests: 1.o.r., pow[2,3,7]"],
["7:6xA7","19th maximal subgroup of F3+"],
["7:6xL3(2)","11-th maximal subgroup of He.2"],
["7:6xS7","19th maximal subgroup of Fi24"],
["7^(1+2).Sp(2,7)","origin: Dixon's Algorithm\n7A centralizer in Sp(4,7)"],
["7^(1+2):(D8x3)","origin: Ostermann, tests: 1.o.r., pow[2,3,7]\nSylow 7 normalizer in sporadic O'Nan group ON,"],
["7^(1+2):(S3x3)","origin: Ostermann, tests: 1.o.r., pow[2,3,7]\nSylow 7 normalizer in sporadic Held group He,"],
["7^(1+2):(S3x6)","origin: Dixon's Algorithm\n(group taken from a perm. repr. of He.2),\nSylow 7 normalizer in He.2 and Fi24',"],
["7^(1+2):48","origin: Dixon's Algorithm"],
["7^(1+2)_+:(3xD16)","7th maximal subgroup of ON.2,\norigin: Dixon's Algorithm"],
["7^(1+2)_+:(6xS3).2","20th maximal subgroup of Fi24,\norigin: Dixon's Algorithm"],
["7^(1+4):(3x2.S7)","24th maximal subgroup of M,\nconstructed in August 2004 by Thomas Breuer,\nusing a combination of Dixon's algorithm and character theoretic methods"],
["7^(2+1+2):GL2(7)","29th maximal subgroup of M"],
["7^1+4.2A7","7B centralizer in the Monster group,\nconstructed using Dixon's algorithm, from a permutation representation"],
["7^2:(3x2A4)","origin: Ostermann, tests: 1.o.r., pow[2,3,7],\nSylow 7 normalizer in sporadic Conway group Co1 and in F4(2)"],
["7^2:(3x2S4)","origin: Dixon's Algorithm,\n11th maximal subgroup of Th,\ntable is sorted w.r. to normal series 7^2.3.2.2^2.3.2,\ntests: 1.o.r., pow[2,3,5,7]"],
["7^2:2.L2(7).2","origin: constructed using Dixon's algorithm & table of L3(7),\n1st and 2nd maximal subgroup of L3(7),\ntests: 1.o.r., pow[2,3,7]"],
["7^2:24","origin: Dixon's Algorithm"],
["7^2:2A4","origin: Dixon's Algorithm"],
["7^2:2psl(2,7)","origin: CAS library,\nmaximal subgroup of He and M,\ntest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly.\ntests: 1.o.r., pow[2,3,7]"],
["7^2:S3","origin: Dixon's Algorithm"],
["8^2:S3","origin: Dixon's Algorithm"],
["9.U3(8).3_3","origin: ATLAS of finite groups,constructed using `PossibleCharacterTablesOfTypeMGA'"],
["9:6","origin: Dixon's Algorithm,\n3rd maximal subgroup of L2(8).3"],
["A10","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["A10.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: Aut(A10)"],
["A11","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["A11.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11],\nconstructions: Aut(A11)"],
["A11Syl2","origin: cayley, tests: 1.o.r.\ntable of sylow 2 subgroup of the alternating group A11,"],
["A12","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["A12.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11],\nconstructions: Aut(A12)"],
["A13","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"],
["A13.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13],\nconstructions: Aut(A13)"],
["A14","origin: CAS library,\n    names:=     a14\n    order:     2^10.3^5.5^2.7^2.11.13 = 43589145600\n    number of classes: 72\n    source:    stockhofe [aachen] from table of s14 (kerber,bayreuth)\n    comments:  alternating group\n    test:      orth, min\ntests: 1.o.r., pow[2,3,5,7,11,13]"],
["A14.2","origin: CAS library,\n    names:=     s14\n    order:     2^11.3^5.5^2.7^2.11.13 = 87178291200\n    number of classes: 135\n    source:    kerber [bayreuth]\n    comments:  symmetric group\n    test:      orth, min\ntests: 1.o.r., pow[2,3,5,7,11,13],\nconstructions: Aut(A14)"],
["A15","origin: CAS library,\n    names:=     a15\n    order:     2^10.3^6.5^3.7^2.11.13 = 653837184000\n    number of classes: 94\n    source:    stockhofe [aachen] from table of s15 (kerber,bayreuth)\n    comments:  alternating group\n    test:      orth, min\ntests: 1.o.r., pow[2,3,5,7,11,13]"],
["A15.2","origin: CAS library,\n    names:=     s15\n    order:     2^11.3^6.5^3.7^2.11.13 = 1307674368000\n    number of classes: 176\n    source:    kerber [bayreuth]\n    comments:  symmetric group\n    test:      orth, min\ntests: 1.o.r., pow[2,3,5,7,11,13],\nconstructions: Aut(A15)"],
["A16","origin: CAS library,\n    names:=     a16\n    order:     2^14.3^6.5^3.7^2.11.13 = 10461394944000\n    number of classes: 123\n    source:    stockhofe [aachen] from table of s16 (kerber,bayreuth)\n    comments:  alternating group\n    test:      orth, min\ntests: 1.o.r., pow[2,3,5,7,11,13]"],
["A16.2","origin: CAS library,\n    names:=     s16\n    order:     2^15.3^6.5^3.7^2.11.13 = 20922789888000\n    number of classes: 231\n    source:    kerber [bayreuth]\n    comments:  symmetric group\n    test:      orth, min\ntests: 1.o.r., pow[2,3,5,7,11,13],\nconstructions: Aut(A16)"],
["A17","origin: computed from generic table of alternating groups (reordered)"],
["A17.2","origin: computed from generic table of symmetric groups (reordered),\nconstructions: Aut(A17)"],
["A18","computed using generic character table for alternating groups"],
["A18.2","origin: computed from generic table of symmetric groups (reordered),\nconstructions: Aut(A18)"],
["A19","computed using generic character table for alternating groups"],
["A19.2","origin: computed from generic table of symmetric groups (reordered),\nconstructions: Aut(A19)"],
["A4xC4","stabilizer of chain ([4] < [256]) in HS"],
["A4xS3","origin: CAS library, tests: 1.o.r., pow[2,3]"],
["A5","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["A5.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5],\nconstructions: Aut(A5)"],
["A5.2xM22.2","18th maximal subgroup of B"],
["A5xA5","7th maximal subgroup of G2(4)"],
["A6","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["A6.2^2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5],\nconstructions: Aut(A6), PGammaL(2,9)"],
["A6.2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["A6.2_1M3","3rd maximal subgroup of A6.2_1,\ndiffers from A6.2_1M2 only by fusion map"],
["A6.2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5],\nconstructions: PGL(2,9), PGU(2,9)"],
["A6.2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["A6.D8","origin: CAYLEY\nmaximal subgroup of 2.M12, (normalizer of A6),\ntests: 1.o.r., pow[2,3,5]"],
["A6M2","2nd maximal subgroup of A6,\ndiffers from A6M1 only by fusion map"],
["A6M5","5th maximal subgroup of A6,\ndiffers from A6M4 only by fusion map"],
["A6xL2(8):3","20th maximal subgroup of F3+"],
["A7","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["A7.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: Aut(A7)"],
["A8","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["A8.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: Aut(A8)"],
["A8.2N2","origin: CAS library,\nnames:=s61; s6[1]\n order: 2^7 = 128\n number of classes: 20\n source:dye, r.h.\n        the classes and characters of\n        certain maximal and other subgroups\n        of o 2n+2(2)\n        ann.mat.pura appl.(4) 107\n        (1975), 13-47\n comments:table blown up using cas-system \nSylow 2 subgroup in S8,\ntests: 1.o.r., pow[2]"],
["A9","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["A9.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: Aut(A9)"],
["A9M5","5th maximal subgroup of A9,\ndiffers from A9M4 = L2(8).3 only by fusion map"],
["A9xS3","16th maximal subgroup of Co1"],
["B","origin: ATLAS of finite groups, tests: 1.o.r."],
["BN7","Sylow 7 normalizer in the sporadic simple group B,\nstructure (2^2x7^2:(3x2A4)).2,\norigin: Dixon's Algorithm,\nconstructed by Thomas Breuer using the Atlas' structure information"],
["C9Y3.3^5.U4(2)","9A centralizer in the sporadic simple Monster group M,\ncentral product of a cyclic group of order 9 with 3.3^5.U4(2),\nconstructed by Simon Norton, July 1997"],
["Co1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13,23]"],
["Co1N3","origin: Ostermann, tests: 1.o.r., pow[2,3]\nSylow 3 normalizer in sporadic Conway group Co1,"],
["Co1N5","origin: Dixon's Algorithm,\nthe table is equivalent to that given in Ostermann's book"],
["Co2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,23]"],
["Co2N2","origin: Dixon's Algorithm"],
["Co2N7","structure is (7:3xD8).2,\norigin: Dixon's Algorithm"],
["Co3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,23]"],
["Co3N2","origin: Ostermann, tests: 1.o.r., pow[2]\nSylow 2 normalizer in sporadic Conway group Co3,"],
["Co3N3","origin: Ostermann, tests: 1.o.r., pow[2,3],\nSylow 3 normalizer in sporadic Conway group Co3,\nsolvable subgroup of maximal order in Co3"],
["D10xA5","normalizer of a defect 5-subgroup of type 5CD in G2(4)"],
["D120","origin: CAS library,\nnames:d60\norder: 2^3.3.5 = 120\nnumber of classes: 33\nsource:generated by dixon-algorithm\naachen [1980]\ntest: 1. o.r., sym 2 decompose correctly\ncomments:generators: a,b\nrelations: a^60 = b^2 = (ab)^2 = 1 \ntests: 1.o.r., pow[2,3,5]"],
["D20","5th maximal subgroup of L2(11).2"],
["D24","3rd maximal subgroup of L2(11).2"],
["D62","3rd maximal subgroup of L2(32),\n4th maximal subgroup of Sz(32)"],
["D6xD10","origin: CAS library,\n test:= 1. o.r.,sym 2, 3 and restricted characters of j1 decompose  \n    correctly \ntests: 1.o.r., pow[2,3,5]"],
["D8x2F4(2)'.2","normalizer of a defect group of type D8 in B"],
["D8xL4(3).2_2","maximal subgroup of O8-(3).2_1"],
["D8xS6(2)","normalizer of a type D8 defect group in Fi23"],
["D8xU3(3).2","normalizer of a defect group of type D8 in Co1"],
["D8xV4","normalizer of a chain (2B < Syl2) in HS"],
["E6(2)","origin: originally computed by B. Fischer,\ncorrected in 2016 by W. Unger, after computation of the table with Magma\n(power maps and irrationalities on classes of element order 91),\ntests: 1.o.r"],
["F3+","origin: ATLAS of finite groups, tests: 1.o.r."],
["F3+.2","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(F3+)"],
["F3+M14","14th maximal subgroup of F3+,\ndiffers from F3+M13 only by fusion map"],
["F3+M7","7th maximal subgroup of F3+,\nnon-split extension 2^11.M_24,\norigin: constructed from table of the split extension (J4M1)\nby changing 2nd power map and representative orders"],
["F3+N5","Sylow 5 normalizer in the sporadic simple group F3+,\nstructure (A4x5^2:4A4).2,\norigin: Dixon's Algorithm,\nconstructed independently by A. Hulpke (directly from the group F3+)\nand Thomas Breuer (using the Atlas' structure information)"],
["F4(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["F4(2).2","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(F4(2))"],
["F4(2).2M8","origin: Dixon's Algorithm"],
["F4(2)M10","differs from 3D4(2).3 only by fusion into F4(2)"],
["F4(2)M13","origin: Dixon's Algorithm"],
["F4(2)M2","2nd maximal subgroup of F4(2),\ndiffers from F4(2)M1 only by fusion map"],
["F4(2)M4","4th maximal subgroup of F4(2),\ndiffers from F4(2)M3 only by fusion map"],
["F4(2)M6","6th maximal subgroup of F4(2),\ndiffers from F4(2)M5 only by fusion map"],
["F4(2)M8","differs from O8+(2).3.2 only by fusion into F4(2)"],
["F4(2)N7B","differs from (7:3xL2(7)):2 only by fusion map to F4(2)"],
["F4(3)","computed by Eamonn O'Brien using Magma, May/June 2024"],
["Fi22","origin: ATLAS of finite groups, tests: 1.o.r."],
["Fi22.2","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(Fi22)"],
["Fi22.2M4","4th maximal subgroup of Fi22.2, normalizer of a 2^10 subgroup,\nsorted w.r.t. normal series 2^10 < 2^10:M22 < 2^10:M22:2,\norigin: Dixon's Algorithm"],
["Fi22M3","3rd maximal subgroup of Fi22,\ndiffers from Fi22M2 only by fusion map"],
["Fi22N3","origin: Ostermann\nSylow 3 normalizer in sporadic Fischer group Fi22,\n3rd power map computed from the group"],
["Fi22N5","origin: Ostermann, tests: 1.o.r., pow[2,3,5]\nSylow 5 normalizer in sporadic Fischer group Fi22,"],
["Fi23","origin: ATLAS of finite groups, tests: 1.o.r."],
["Fi23M8","origin: Dixon's Algorithm,\n8th maximal subgroup of Fi23,\ntable is sorted w.r. to normal series 3^3.3^7.2.L3(3),\ntests: 1.o.r."],
["Fi23N3","origin: Dixon's Algorithm,\nSylow 3 normalizer in Fi23 (computed from a representation of this group)\nand in B (see [Wil98])"],
["G2(3)","origin: ATLAS of finite groups, tests: 1.o.r."],
["G2(3).2","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(G2(3))"],
["G2(3).2N2","Sylow 2 normalizer in G2(3).2"],
["G2(3)M2","2nd maximal subgroup of G2(3),\ndiffers from G2(3)M1 only by fusion map"],
["G2(3)M4","4th maximal subgroup of G2(3),\ndiffers from G2(3)M3 only by fusion map"],
["G2(3)M6","6th maximal subgroup of G2(3),\ndiffers from G2(3)M5 only by fusion map"],
["G2(4)","origin: ATLAS of finite groups, tests: 1.o.r."],
["G2(4).2","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(G2(4))"],
["G2(4)N2","origin: Dixon's Algorithm"],
["G2(5)","origin: ATLAS of finite groups, tests: 1.o.r."],
["G2(7)","computed using Magma V2.27-3     Tue Jun  4 2024 12:41:42 on schedir\n[Seed = 2017523455]\nTotal time: 5.650 seconds, Total memory usage: 64.12MB"],
["HN","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19]"],
["HN.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19],\nconstructions: Aut(HN)"],
["HN.2M13","13th maximal subgroup of HN.2, structure 3^(1+4)_+:4S5\norigin: Dixon's Algorithm"],
["HN.2N3","origin: Dixon's Algorithm"],
["HNM12","12th maximal subgroup of HN,\ndiffers from HNM11 only by fusion map"],
["HNN2","origin: Dixon's Algorithm,\nSylow 2 normalizer in the sporadic simple Harada-Norton group HN"],
["HNN3","origin: Dixon's Algorithm"],
["HNN5","origin: Dixon's Algorithm"],
["HS","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["HS.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11],\nconstructions: Aut(HS)"],
["HS.2N5","origin: Dixon's algorithm,\nmaximal subgroup of HS.2,\nSylow 5 normalizer in HS.2,\ntable is sorted w.r. to normal series 5.5^2.8.2.2,\ntests: 1.o.r., pow[2,5]"],
["HSM3","3rd maximal subgroup of HS,\ndiffers from HSM2 only by fusion map"],
["HSM9","9th maximal subgroup of HS,\ndiffers from HSM8 only by fusion map"],
["HSN2","origin: Ostermann, tests: 1.o.r., pow[2]\nSylow 2 normalizer in sporadic Higman Sims group HS"],
["He","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,17]"],
["He.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,17],\nconstructions: Aut(He)"],
["Isoclinic((3^2x2).U4(3).2_3')","2nd maximal subgroup of 6.Suz,\nisoclinic group of the (3^2x2).U4(3).2_3' given in the ATLAS"],
["Isoclinic(12.M22.2)","isoclinic group of the 12.M22.2 given in the ATLAS"],
["Isoclinic(12_1.L3(4).2_1)","isoclinic group of the 12_1.L3(4).2_1 given in the ATLAS"],
["Isoclinic(12_1.L3(4).2_2)","isoclinic group of the 12_1.L3(4).2_2 given in the ATLAS"],
["Isoclinic(12_1.U4(3).2_2')","isoclinic group of the 12_1.U4(3).2_2' given in the ATLAS"],
["Isoclinic(12_1.U4(3).2_2)","isoclinic group of the 12_1.U4(3).2_2 given in the ATLAS"],
["Isoclinic(12_2.L3(4).2_1)","isoclinic group of the 12_2.L3(4).2_1 given in the ATLAS"],
["Isoclinic(12_2.L3(4).2_3)","isoclinic group of the 12_2.L3(4).2_3 given in the ATLAS"],
["Isoclinic(12_2.U4(3).2_3')","isoclinic group of the 12_2.U4(3).2_3' given in the ATLAS"],
["Isoclinic(12_2.U4(3).2_3)","isoclinic group of the 12_2.U4(3).2_3 given in the ATLAS"],
["Isoclinic(2.A10.2)","isoclinic group of the 2.A10.2 given in the ATLAS"],
["Isoclinic(2.A11.2)","isoclinic group of the 2.A11.2 given in the ATLAS"],
["Isoclinic(2.A12.2)","isoclinic group of the 2.A12.2 given in the ATLAS"],
["Isoclinic(2.A13.2)","isoclinic group of the 2.A13.2 given in the ATLAS"],
["Isoclinic(2.A5.2)","isoclinic group of the 2.A5.2 given in the ATLAS"],
["Isoclinic(2.A6.2_2)","isoclinic group of the 2.A6.2_2 given in the ATLAS"],
["Isoclinic(2.A6x2)","central product of 2.A6 with a cyclic group of order 4,\nsubgroup of 4.A6.2_3"],
["Isoclinic(2.A7.2)","isoclinic group of the 2.A7.2 given in the ATLAS"],
["Isoclinic(2.A8.2)","7th maximal subgroup of McL.2,\nisoclinic group of the 2.A8.2 given in the ATLAS"],
["Isoclinic(2.A9.2)","isoclinic group of the 2.A9.2 given in the ATLAS"],
["Isoclinic(2.F4(2).2)","isoclinic group of the 2.F4(2).2 given in the ATLAS"],
["Isoclinic(2.Fi22.2)","isoclinic group of the 2.Fi22.2 given in the ATLAS"],
["Isoclinic(2.G2(4).2)","isoclinic group of the 2.G2(4).2 given in the ATLAS"],
["Isoclinic(2.HS.2)","isoclinic group of the 2.HS.2 given in the ATLAS"],
["Isoclinic(2.J2.2)","isoclinic group of the 2.J2.2 given in the ATLAS"],
["Isoclinic(2.L2(11).2)","isoclinic group of the 2.L2(11).2 given in the ATLAS"],
["Isoclinic(2.L2(13).2)","isoclinic group of the 2.L2(13).2 given in the ATLAS"],
["Isoclinic(2.L2(17).2)","isoclinic group of the 2.L2(17).2 given in the ATLAS"],
["Isoclinic(2.L2(19).2)","isoclinic group of the 2.L2(19).2 given in the ATLAS"],
["Isoclinic(2.L2(23).2)","isoclinic group of the 2.L2(23).2 given in the ATLAS"],
["Isoclinic(2.L2(25).2_1)","isoclinic group of the 2.L2(25).2_1 given in the ATLAS"],
["Isoclinic(2.L2(25)x2)","central product of 2.L2(25) with a cyclic group of order 4,\nsubgroup of 4.L2(25).2_3"],
["Isoclinic(2.L2(27).2)","isoclinic group of the 2.L2(27).2 given in the ATLAS"],
["Isoclinic(2.L2(27).6)","isoclinic group of the 2.L2(27).6 given in the ATLAS"],
["Isoclinic(2.L2(29).2)","isoclinic group of the 2.L2(29).2 given in the ATLAS"],
["Isoclinic(2.L2(31).2)","isoclinic group of the 2.L2(31).2 given in the ATLAS"],
["Isoclinic(2.L2(49).2_1)","isoclinic group of the 2.L2(49).2_1 given in the ATLAS"],
["Isoclinic(2.L2(49)x2)","central product of 2.L2(49) with a cyclic group of order 4,\nsubgroup of 4.L2(49).2_3"],
["Isoclinic(2.L2(81).2_2)","isoclinic group of the 2.L2(81).2_2 given in the ATLAS"],
["Isoclinic(2.L2(81)x2)","central product of 2.L2(81) with a cyclic group of order 4,\nsubgroup of 4.L2(81).2_3, 4.L2(81).4_2"],
["Isoclinic(2.L3(2).2)","isoclinic group of the 2.L3(2).2 given in the ATLAS"],
["Isoclinic(2.L3(4).2_1)","4th maximal subgroup of 2.HS"],
["Isoclinic(2.L4(3).2_1)","isoclinic group of the 2.L4(3).2_1 given in the ATLAS"],
["Isoclinic(2.L4(3).2_2)","isoclinic group of the 2.L4(3).2_2 given in the ATLAS"],
["Isoclinic(2.L4(3).2_3)","isoclinic group of the 2.L4(3).2_3 given in the ATLAS"],
["Isoclinic(2.M12.2)","isoclinic group of the 2.M12.2 given in the ATLAS"],
["Isoclinic(2.M22.2)","isoclinic group of the 2.M22.2 given in the ATLAS"],
["Isoclinic(2.O7(3).2)","isoclinic group of the 2.O7(3).2 given in the ATLAS"],
["Isoclinic(2.O8+(2).2)","isoclinic group of the 2.O8+(2).2 given in the ATLAS"],
["Isoclinic(2.S4(5).2)","isoclinic group of the 2.S4(5).2 given in the ATLAS"],
["Isoclinic(2.S6(3).2)","isoclinic group of the 2.S6(3).2 given in the ATLAS"],
["Isoclinic(2.Suz.2)","isoclinic group of the 2.Suz.2 given in the ATLAS"],
["Isoclinic(2.U4(2).2)","isoclinic group of the 2.U4(2).2 given in the ATLAS"],
["Isoclinic(2.U6(2).2)","isoclinic group of the 2.U6(2).2 given in the ATLAS"],
["Isoclinic(2x2.F4(2).2)","central product of C4 and 2.F4(2).2"],
["Isoclinic(2x3^(1+2)_+:Q8)","9th maximal subgroup of 6.L3(4)"],
["Isoclinic(2x3^2:Q8)","9th maximal subgroup of 2.L3(4)"],
["Isoclinic(3.A6.2_3x2)","subdirect product of 3.A6.2_3 with a cyclic group of order 4,\nfactor group of 12.A6.2_3"],
["Isoclinic(3.L3(4).3,1)","1st isoclinic group of the 3.L3(4).3 given in the ATLAS"],
["Isoclinic(3.L3(4).3,2)","2nd isoclinic group of the 3.L3(4).3 given in the ATLAS"],
["Isoclinic(3.L3(4).6,1)","1st isoclinic group of the 3.L3(4).6 given in the ATLAS"],
["Isoclinic(3.L3(4).6,2)","2nd isoclinic group of the 3.L3(4).6 given in the ATLAS"],
["Isoclinic(3.L3(7).3,1)","1st isoclinic group of the 3.L3(7).3 given in the ATLAS"],
["Isoclinic(3.L3(7).3,2)","2nd isoclinic group of the 3.L3(7).3 given in the ATLAS"],
["Isoclinic(3.U3(11).3,1)","1st isoclinic group of the 3.U3(11).3 given in the ATLAS"],
["Isoclinic(3.U3(11).3,2)","2nd isoclinic group of the 3.U3(11).3 given in the ATLAS"],
["Isoclinic(3.U3(5).3,1)","1st isoclinic group of the 3.U3(5).3 given in the ATLAS"],
["Isoclinic(3.U3(5).3,2)","2nd isoclinic group of the 3.U3(5).3 given in the ATLAS"],
["Isoclinic(3.U3(8).3_2,1)","1st isoclinic group of the 3.U3(8).3_2 given in the ATLAS"],
["Isoclinic(3.U3(8).3_2,2)","2nd isoclinic group of the 3.U3(8).3_2 given in the ATLAS"],
["Isoclinic(3.U3(8)x3)","central product of 3.U3(8).2_3 with a cyclic group of order 9,\nsubgroup of 9.U3(8).3_3"],
["Isoclinic(3.U6(2).3,1)","1st isoclinic group of the 3.U6(2).3 given in the ATLAS"],
["Isoclinic(3.U6(2).3,2)","2nd isoclinic group of the 3.U6(2).3 given in the ATLAS"],
["Isoclinic(4.M22.2)","isoclinic group of the 4.M22.2 given in the ATLAS"],
["Isoclinic(4.U4(3).2_2)","isoclinic group of the 4.U4(3).2_2 given in the ATLAS"],
["Isoclinic(4.U4(3).2_3)","isoclinic group of the 4.U4(3).2_3 given in the ATLAS"],
["Isoclinic(6.A6.2_2)","isoclinic group of the 6.A6.2_2 given in the ATLAS"],
["Isoclinic(6.A6x2)","central product of 6.A6 with a cyclic group of order 4,\nsubgroup of 12.A6.2_3"],
["Isoclinic(6.A7.2)","isoclinic group of the 6.A7.2 given in the ATLAS"],
["Isoclinic(6.Fi22.2)","isoclinic group of the 6.Fi22.2 given in the ATLAS"],
["Isoclinic(6.M22.2)","isoclinic group of the 6.M22.2 given in the ATLAS"],
["Isoclinic(6.O7(3).2)","isoclinic group of the 6.O7(3).2 given in the ATLAS"],
["Isoclinic(6.Suz.2)","isoclinic group of the 6.Suz.2 given in the ATLAS"],
["Isoclinic(6.U6(2).2)","isoclinic group of the 6.U6(2).2 given in the ATLAS"],
["Isoclinic(6_1.U4(3).2_1)","isoclinic group of the 6_1.U4(3).2_1 given in the ATLAS"],
["Isoclinic(6_1.U4(3).2_2')","isoclinic group of the 6_1.U4(3).2_2' given in the ATLAS"],
["Isoclinic(6_1.U4(3).2_2)","isoclinic group of the 6_1.U4(3).2_2 given in the ATLAS"],
["Isoclinic(6_2.U4(3).2_1)","isoclinic group of the 6_2.U4(3).2_1 given in the ATLAS"],
["Isoclinic(6_2.U4(3).2_3')","2nd maximal subgroup of 2.Suz,\nisoclinic group of the 6_2.U4(3).2_3' given in the ATLAS"],
["Isoclinic(6_2.U4(3).2_3)","isoclinic group of the 6_2.U4(3).2_3 given in the ATLAS"],
["Isoclinic(L2(13).2x2)","subdirect product of L2(13).2 and C4,\n13th maximal subgroup of 2.Ru"],
["Isoclinic(L2(25).2_3x2)","subdirect product of L2(25).2_3 with a cyclic group of order 4,\nfactor group of 4.L2(25).2_3"],
["Isoclinic(L2(49).2_3x2)","subdirect product of L2(49).2_3 with a cyclic group of order 4,\nfactor group of 4.L2(49).2_3"],
["Isoclinic(L2(81).2_3x2)","subdirect product of L2(81).2_3 with a cyclic group of order 4,\nfactor group of 4.L2(81).2_3"],
["Isoclinic(S8x2)","subdirect product of S8 and C4,\n5th maximal subgroup of 2.HS"],
["Isoclinic(U3(5).2x2)","subdirect product of U3(5).2 and C4,\n2nd (and 3rd, see 2.HSM3) maximal subgroup of 2.HS"],
["Isoclinic(U3(8).3_3x3)","subdirect product of U3(8).3_3 with a cyclic group of order 9,\nfactor group of 9.U3(8).3_3"],
["J1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19]"],
["J1x2","2nd maximal subgroup of ON.2"],
["J2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["J2.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: Aut(J2)"],
["J2.2x2","7th maximal subgroup of Suz.2"],
["J2N2","origin: Ostermann, tests: 1.o.r., pow[2,3]\nSylow 2 normalizer in sporadic Janko group J2"],
["J3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,17,19]"],
["J3.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,17,19],\nconstructions: Aut(J3)"],
["J3M3","3rd maximal subgroup of J3,\ndiffers from J3M2 only by fusion map"],
["J3N2","origin: Ostermann, tests: 1.o.r., pow[2,3]\nSylow 2 normalizer in sporadic Janko group J3"],
["J4","origin: ATLAS of finite groups, tests: 1.o.r.,\npow[2,3,5,7,11,23,29,31,37,43]"],
["J4M4","origin: CAS library,2nd power map determined by fusion into J4,\nmaximal subgroup of J4,\ntests: 1.o.r., pow[2,3,5,7]"],
["L2(11)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11]"],
["L2(11).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11],\nconstructions: Aut(L2(11))"],
["L2(121)M3","3rd maximal subgroup of L2(121),\ndiffers from L2(121)M2 only by fusion map"],
["L2(13)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13]"],
["L2(13).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13],\nconstructions: Aut(L2(13))"],
["L2(16)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,17]"],
["L2(16).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,17]"],
["L2(16).4","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,17],\nconstructions: Aut(L2(16)), PGammaL(2,16), SigmaL(2,16), PSigmaL(2,16)"],
["L2(17)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,17]"],
["L2(17).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,17],\nconstructions: Aut(L2(17))"],
["L2(17)x2","5th maximal subgroup of J3.2"],
["L2(19)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,19]"],
["L2(19).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,19],\nconstructions: Aut(L2(19))"],
["L2(23)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,11,23]"],
["L2(23).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,11,23],\nconstructions: Aut(L2(23))"],
["L2(25)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"],
["L2(25).(2x4)","7th maximal subgroup of 2.Ru"],
["L2(25).2^2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\nconstructions: Aut(L2(25)), PGammaL(2,25)"],
["L2(25).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\nconstructions: PGL(2,25)"],
["L2(25).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\nconstructions: PSigmaL(2,25)"],
["L2(25).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"],
["L2(25)M3","3rd maximal subgroup of L2(25),\ndiffers from L2(25)M2 = A5.2 only by fusion map"],
["L2(27)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13]"],
["L2(27).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13],\nconstructions: PGL(2,27)"],
["L2(27).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13],\nconstructions: PSigmaL(2,27)"],
["L2(27).6","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,13],\nconstructions: Aut(L2(27)), PGammaL(2,27)"],
["L2(29)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,29]"],
["L2(29).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,29],\nconstructions: Aut(L2(29))"],
["L2(31)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,31]"],
["L2(31).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,31],\nconstructions: Aut(L2(31))"],
["L2(32)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,11,31]"],
["L2(32).5","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11,31],\nconstructions: Aut(L2(32)), PGammaL(2,32), SigmaL(2,32), PSigmaL(2,32)"],
["L2(49)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["L2(49).2^2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: Aut(L2(49)), PGammaL(2,49)"],
["L2(49).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: PGL(2,49)"],
["L2(49).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: PSigmaL(2,49)"],
["L2(49).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["L2(64).6","origin: Dixon's Algorithm,\nconstructions: Aut(L2(64)), PGammaL(2,64)"],
["L2(8)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7]"],
["L2(8).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7],\nconstructions: Aut(L2(8))"],
["L2(8):3x2","4th maximal subgroup of 2.A9"],
["L2(81)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,41]"],
["L2(81).(2x4)","constructed using `PossibleCharacterTablesOfTypeGV4',\nconstructions: Aut(L2(81)), PGammaL(2,81)"],
["L2(81).2^2","constructed using `PossibleCharacterTablesOfTypeGV4'"],
["L2(81).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,41],\nconstructions: PSL(2,81) extended by a field automorphism of order 2"],
["L2(81).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,41],\nconstructions: PGL(2,81)"],
["L2(81).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,41]"],
["L2(81).4_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,41],\nconstructions: PSigmaL(2,81)"],
["L2(81).4_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,41]\n2nd power map determined only up to matrix automorphism (19,20)"],
["L3(11)","origin: program of B. Hemkemeier and U. J\"urgens for the construction\nof GL(n,q) character tables"],
["L3(2)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7]"],
["L3(2).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7],\nconstructions: Aut(L3(2))"],
["L3(2).2x2","8th maximal subgroup of J2.2"],
["L3(2)wr2","8th maximal subgroup of L6(2)"],
["L3(2)xS3","normalizer of a radical 3-subgroup in M24 and He,\n"],
["L3(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,13]"],
["L3(3).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,13],\nconstructions: Aut(L3(3))"],
["L3(3)xD8","factor group of a maximal subgroup 3^(3+6):(L3(3)xD8) of O8+(3).D8"],
["L3(4)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["L3(4).2^2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["L3(4).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["L3(4).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["L3(4).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["L3(4).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["L3(4).3.2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["L3(4).3.2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["L3(4).6","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["L3(4).D12","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: Aut(L3(4))"],
["L3(4)M4","4th maximal subgroup of L3(4),\ndiffers from L3(4)M3 only by fusion map"],
["L3(4)M5","5th maximal subgroup of L3(4),\ndiffers from L3(4)M3 only by fusion map"],
["L3(4)M7","7th maximal subgroup of L3(4),\ndiffers from L3(4)M6 only by fusion map"],
["L3(4)M8","8th maximal subgroup of L3(4),\ndiffers from L3(4)M6 only by fusion map"],
["L3(4)Syl2","origin: CAS library,\nSylow 2 subgroup of M21 = L3(4)\ntests: 1.o.r., pow[2],\n2nd power map determined only up to matrix automorphisms,"],
["L3(5)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,31]"],
["L3(5).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,31],\nconstructions: Aut(L3(5))"],
["L3(7)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,19]"],
["L3(7).2","origin: ATLAS of finite groups,\n2nd power map determined only up to matrix automorphism (9,10)"],
["L3(7).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,19],\nconstructions: PGL(3,7)"],
["L3(7).S3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,19],\nconstructions: Aut(L3(7))"],
["L3(7)M2","2nd maximal subgroup of L3(7),\ndiffers from L3(7)M1 = 7^2:2.L2(7).2 only by fusion map"],
["L3(7)M4","4th maximal subgroup of L3(7),\ndiffers from L3(7)M3 = L3(2).2 only by fusion map"],
["L3(7)M5","5th maximal subgroup of L3(7),\ndiffers from L3(7)M3 = L3(2).2 only by fusion map"],
["L3(8)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,73]"],
["L3(8).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,73],\nconstructions: SL(3,8) extended by transpose-inverse"],
["L3(8).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,73],\nconstructions: PGammaL(3,8), SigmaL(3,8), PSigmaL(3,8)"],
["L3(8).6","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,73],\nconstructions: Aut(L3(8)), SigmaL(3,8) extended by transpose-inverse"],
["L3(9)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]"],
["L3(9).2^2","constructed using `PossibleCharacterTablesOfTypeGV4',\nconstructions: Aut(L3(9)), SigmaL(3,9) extended by transpose-inverse"],
["L3(9).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13],\nconstructions: SL(3,9) extended by transpose-inverse"],
["L3(9).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13],\nconstructions: PGammaL(3,9), SigmaL(3,9), PSigmaL(3,9)"],
["L3(9).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]"],
["L4(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"],
["L4(3).2^2","origin: CAS library,\ntests: 1.o.r., pow[2,3,5,13],\nconstructions: Aut(L4(3)), PGL(4,3) extended by transpose-inverse"],
["L4(3).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\nconstructions: PGL(4,3)"],
["L4(3).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\nconstructions: PSL(4,3) extended by transpose-inverse, PGO(+1,6,3)"],
["L4(3).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"],
["L4(3)M4","4th maximal subgroup of L4(3),\ndiffers from L4(3)M3 only by fusion map"],
["L4(4)","origin: constructed by T. Breuer using the perm. repr. on 85 points\nand the table of the subgroup 3.L3(4).3"],
["L4(4).2^2","constructed using `PossibleCharacterTablesOfTypeGV4',\nconstructions: Aut(L4(4)), PSigmaL(4,4) extended by transpose-inverse"],
["L4(4).2_1","origin: constructed by T. Breuer using the perm. repr. on 85 points\nand the table of the subgroup L4(4),\nconstructions: PSigmaL(4,4)"],
["L4(4).2_2","origin: constructed by T. Breuer using the perm. repr. on 170 points\nand the table of the subgroup L4(4),\nconstructions: PSL(4,4) extended by transpose-inverse"],
["L4(4).2_3","origin: constructed by T. Breuer using the perm. repr. on 170 points\nand the table of the subgroup L4(4),\nL4(4).2_3 is the simple group L4(4) extended by the product of,\nthe Frobenius automorphism and ``transpose inverse''"],
["L4(5)","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, Jun. 03rd, 2003"],
["L4(9)","origin: constructed by Thomas Breuer, February 2001"],
["L5(2)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,31]"],
["L5(2).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,31],\nconstructions: Aut(L5(2))"],
["L5(3)","origin/source :{M.R. Darafsheh,M. Rajabi Tarkhorani,\nThe Character table of The group $SL_{5}(3)$} ,to appear;\ntests: 1.o.r., pow[2,3,5,11,13]."],
["L5(3).2","origin/source : M.R. Darafsheh,\ntable of the automorphism group of SL_5(3),\ntests: 1.o.r., pow[2,3,5,11,13],\nconstructions: Aut(L5(3))"],
["L6(2)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,31]"],
["L6(2).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,31],\nconstructions: Aut(L6(2))"],
["L7(2)","origin: CAS library,\ntests: 1.o.r., pow[2,3,5,7,31]"],
["L7(2).2","origin/source : M.R. Darafsheh,\ntable of the automorphism group of GL_7(2),\ntests: 1.o.r., pow[2,3,5,7,31,127], sym[2,3,5,7],\nconstructions: Aut(L7(2))"],
["L8(2)","origin: program of B. Hemkemeier and U. J\"urgens for the construction\nof GL(n,q) character tables,\nindependently computed by M. R. Darafsheh, M. Khademi, K. Azizi,\nand M. H. Jafari"],
["Ly","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,31,37,67]"],
["LyM6","maximal subgroup of Ly,\nof structure 3^5:(2xM11),\norigin: table constructed from tables of subgroup 3^5:M11,\n        factor group 2xM11, and supergroup Ly;\ntests: 1.o.r., pow[2,3,5,11]"],
["LyN2","origin: constructed from the Sylow 2 subgroup of A11 by K.Lux,\n(Note: The table in Ostermann's paper is fishy!)\ntests: 1.o.r.\nSylow 2 normalizer in sporadic Lyons group Ly,\nSylow 2 normalizer in McL.2,\nSylow 2 subgroup of 2.A11,"],
["LyN3","origin: Ostermann,\nSylow 3 normalizer in sporadic Lyons group Ly,\ntests: 1.o.r., pow[2,3]"],
["LyN5","origin: Ostermann,\nSylow 5 normalizer in sporadic Lyons group Ly,\ntests: 1.o.r., pow[2,5]"],
["M","origin: ATLAS of finite groups, tests: 1.o.r."],
["M11","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11]"],
["M11N2","origin: Ostermann, tests: 1.o.r., pow[2]\nSylow 2 normalizer in sporadic Mathieu group M11"],
["M11xA6.2^2","30th maximal subgroup of M"],
["M11xS3","maximal subgroup of 3.McL.2"],
["M12","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11]"],
["M12.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11],\nconstructions: Aut(M12)"],
["M12.2M3","3rd maximal subgroup of M12.2,\ndiffers from M12.2M2 only by fusion map"],
["M12.2x2","11th maximal subgroup of Suz.2"],
["M12C4","structure is 4^2:2"],
["M12M2","2nd maximal subgroup of M12,\ndiffers from M12M1 only by fusion map"],
["M12M4","4th maximal subgroup of M12,\ndiffers from M12M3 only by fusion map"],
["M12M7","7th maximal subgroup of M12,\ndiffers from M12M6 only by fusion map"],
["M12N2","origin: Ostermann, tests: 1.o.r., pow[2]\nSylow 2 normalizer in sporadic Mathieu group M12"],
["M12N3","origin: Ostermann, tests: 1.o.r., pow[2,3]\nSylow 3 normalizer in sporadic Mathieu group M12"],
["M22","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["M22.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11],\nconstructions: Aut(M22)"],
["M22.2M3","origin: Dixon's Algorithm,\n3rd maximal subgroup of M22.2, of structure 2^4.S6,\ntable is sorted w.r. to normal series 2^4.A_6.2,"],
["M22.2M4","origin: Dixon's Algorithm,\n4th maximal subgroup of M22.2,\ntable is sorted w.r. to normal series 2^4<2^4.A5<2^4.S5<2^4.(S5x2)"],
["M22C2A","origin: CAS library,\ncentralizer of an involution in the sporadic simple Mathieu group M22,\ncomputed using CAYLEY,\ntests: 1.o.r., pow[2,3],\n2nd power map determined only up to matrix automorphisms,"],
["M23","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,23]"],
["M23C2A","involution centralizer in sporadic Mathieu group M23,\norigin: CAYLEY, tests: 1.o.r., pow[2,3,7]"],
["M24","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,23]"],
["M24C2A","origin: CAS library (name was s2m24),\ntests: 1.o.r., pow[2,3,7]"],
["M24C2B","origin: CAS library,\ntests: 1.o.r., pow[2,3,5],\n2nd power map determined only up to matrix automorphisms,"],
["M24N2","origin: Ostermann, tests: 1.o.r., pow[2]\nSylow 2 normalizer in sporadic Mathieu group M24\nSylow 2 normalizer in sporadic Held group He"],
["M8.S4","9th maximal subgroup of M12,\norigin: CAS library, tests: 1.o.r., pow[2,3]"],
["MN5","Sylow 5 normalizer in the Monster group M,\nstructure: 5^(1+6):(4x5^2:(4xS3)),\norigin: computed from a permutation representation of the maximal\nsubgroup of type 5^(1+6).2.J2.4 in M using Dixon's Algorithm"],
["McL","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"],
["McL.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11],\nconstructions: Aut(McL)"],
["McL.2N3","origin: Dixon's Algorithm"],
["McLM10","10th maximal subgroup of McL,\ndiffers from McLM9 = 2^4:a7 only by fusion map"],
["McLM3","3rd maximal subgroup of McL,\ndiffers from McLM2 only by fusion map"],
["McLN2","origin: Ostermann, tests: 1.o.r., pow[2],\n2nd power map determined only up to matrix automorphisms,\nSylow 2 normalizer in sporadic McLaughlin group McL,\nSylow 2 subgroup of 2.A8,"],
["NDG(12.M22,3^2)","origin: Dixon's Algorithm"],
["NDG(2.Co1,3^3)","origin: Dixon's Algorithm"],
["NDG(2.Co1,5^2)","origin: Dixon's Algorithm"],
["NDG(2.HS,Q8)","normalizer in 2.HS of a 2-defect group of the type Q8"],
["NDG(2.HS,Q8).2","origin: Dixon's Algorithm"],
["NDG(3.ON,D8)","origin: Dixon's Algorithm"],
["NDG(Co1,5^2)","origin: Dixon's Algorithm"],
["NDG(HN,3^2)","origin: Dixon's Algorithm"],
["NDG(HN.2,3^2)","origin: Dixon's Algorithm"],
["NDG(He.2,3^2)","normalizer of a 3-block in He.2,\norigin: Dixon's Algorithm"],
["NDG(J4,3^2)","origin: Dixon's Algorithm"],
["NDG(ON,D8)","origin: Dixon's Algorithm"],
["NDG(ON,D8).2","origin: Dixon's Algorithm"],
["NRS(M22,[2^6])","origin: Dixon's Algorithm"],
["NRS(M24,2^(2+2+4)a)","normalizer of a radical 2-subgroup in M24,\nisomorphic with 2^(2+2+4).(S3xS3)"],
["NRS(M24,2^(4+4))","normalizer of a radical 2-subgroup in M24,\nhad been called NRS(M24,2^(2+2+4)b) in an earlier version\nbut this does not fit to the structure,\norigin: Dixon's Algorithm"],
["NRS(M24,[2^9]a)","normalizer of a radical 2-subgroup in M24 and He,\nisomorphic with [2^9].S3a"],
["NRS(M24,[2^9]b)","normalizer of a radical 2-subgroup in M24,\nisomorphic with [2^9].S3b"],
["NRS(O8+(2),2^(3+3+3)_a)","normalizer of a radical 2-subgroup in O8+(2)"],
["NRS(O8+(2),2^(3+3+3)_b)","normalizer of a radical 2-subgroup in O8+(2)"],
["O10+(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["O10+(2).2","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(O10+(2))"],
["O10+(3)","computed using Magma V2.23-9     Fri Sep  7 2018 13:29:59 on schedir\n[Seed = 114244632]\nTotal time: 2488.960 seconds, Total memory usage: 669.47MB"],
["O10-(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["O10-(2).2","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(O10-(2))"],
["O10-(3)","computed by Eamonn O'Brien using Magma, November 2007"],
["O12+(2)","computed using Magma V2.23-9     Tue Sep  4 2018 16:30:32 on schedir\n[Seed = 4079370222]\nTotal time: 88.750 seconds, Total memory usage: 160.03MB"],
["O12+(2).2"," name: o+12[2].2,\nsource/origin: J.S.Frame [1986] with technical support from Aachen,\nconstructions: Aut(O12+(2))"],
["O12+(3)","computed by Eamonn O'Brien using Magma, February 2014"],
["O12-(2)","computed using Magma V2.23-9     Tue Sep  4 2018 15:08:42 on schedir\n[Seed = 1184079492]\nTotal time: 59.070 seconds, Total memory usage: 160.03MB"],
["O12-(2).2","origin: CAS libary\nname:o12-[2]:2,\nsource/origin: J.S. Frame, H.Pahlings 1987,\nconstructions: Aut(O12-(2))"],
["O12-(3)","computed by Eamonn O'Brien using Magma, February 2014"],
["O7(3)","origin: ATLAS of finite groups, tests: 1.o.r."],
["O7(3).2","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(O7(3))"],
["O7(3).2x2","3rd maximal subgroup of O8-(3).2_1"],
["O7(3)M11","11th maximal subgroup of O7(3),\ndiffers from O7(3)M10 = A9.2 only by fusion map"],
["O7(3)M5","5th maximal subgroup of O7(3),\ndiffers from O7(3)M4 = G2(3) only by fusion map"],
["O7(3)M8","8th maximal subgroup of O7(3),\ndiffers from O7(3)M7 = S6(2) only by fusion map"],
["O7(3)N3A","origin: Dixon's Algorithm"],
["O7(5)","origin: Dixon's algorithm plus character theoretic methods,\nThomas Breuer, October 2003"],
["O7(5).2","origin: Dixon's algorithm plus character theoretic methods,\nThomas Breuer, September 2003,\nconstructions: Aut(O7(5))"],
["O8+(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["O8+(2).2","origin: ATLAS of finite groups, tests: 1.o.r."],
["O8+(2).3","origin: ATLAS of finite groups, tests: 1.o.r."],
["O8+(2).3.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: Aut(O8+(2))"],
["O8+(2):S3x2","4th maximal subgroup of 2.Fi22,\n3rd maximal subgroup of Fi22.2"],
["O8+(2)M11","11th maximal subgroup of O8+(2),\ndiffers from O8+(2)M10 = (3xU4(2)):2 only by fusion map"],
["O8+(2)M12","12th maximal subgroup of O8+(2),\ndiffers from O8+(2)M10 = (3xU4(2)):2 only by fusion map"],
["O8+(2)M16","16th maximal subgroup of O8+(2),\ndiffers from O8+(2)M15 = (A5xA5):2^2 only by fusion map"],
["O8+(2)M17","17th maximal subgroup of O8+(2),\ndiffers from O8+(2)M15 = (A5xA5):2^2 only by fusion map"],
["O8+(2)M2","2nd maximal subgroup of O8+(2),\ndiffers from O8+(2)M1 = S6(2) only by fusion map"],
["O8+(2)M3","3rd maximal subgroup of O8+(2),\ndiffers from O8+(2)M1 = S6(2) only by fusion map"],
["O8+(2)M5","5th maximal subgroup of O8+(2),\ndiffers from O8+(2)M4 = 2^6:A8 only by fusion map"],
["O8+(2)M6","6th maximal subgroup of O8+(2),\ndiffers from O8+(2)M4 = 2^6:A8 only by fusion map"],
["O8+(2)M8","8th maximal subgroup of O8+(2),\ndiffers from O8+(2)M7 = A9 only by fusion map"],
["O8+(2)M9","9th maximal subgroup of O8+(2),\ndiffers from O8+(2)M7 = A9 only by fusion map"],
["O8+(2)N2","origin: Dixon's Algorithm"],
["O8+(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]"],
["O8+(3).(2^2)_{111}","table of the normal subgroup O8+(3).V4 in O8+(3).S4,\nconstructed by T. Breuer using the tables of O8+(3), O8+(3).2_1"],
["O8+(3).(2^2)_{122}","constructed using `PossibleCharacterTablesOfTypeGV4',\nconstructions: PGO(+1,8,3)"],
["O8+(3).2_1","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: PSO(+1,8,3)"],
["O8+(3).2_1'","differs from O8+(3).2_1 only by fusion into O8+(3).(2^2)_{111}"],
["O8+(3).2_1''","differs from O8+(3).2_1 only by fusion into O8+(3).(2^2)_{111}"],
["O8+(3).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]"],
["O8+(3).2_2'","differs from O8+(3).2_2 only by fusion into O8+(3).2^2"],
["O8+(3).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]"],
["O8+(3).3.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]"],
["O8+(3).4","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13],\n2nd power map determined only up to matrix automorphism (141,143)(142,144)"],
["O8+(3).A4","origin: constructed by T. Breuer using the tables of O8+(3), O8+(3).3,\nO8+(3).(2^2)_{111},\ntests: 1.o.r., pow[2,3,5,7,13,]"],
["O8+(3).D8","constructed (by accident) in April 2003 using Dixon's algorithm and\ncharacter theoretic methods"],
["O8+(3).S4","origin: constructed by T. Breuer using the tables of O8+(3), O8+(3).A4,\nO8+(3).2_2, O8+(3).4, B\ntests: 1.o.r., pow[2,3,5,7,13,],\nconstructions: Aut(O8+(3))"],
["O8+(3)M11","11th maximal subgroup of O8+(3),\ndiffers from O8+(2) only by fusion map"],
["O8+(3)M12","12th maximal subgroup of O8+(3),\ndiffers from O8+(2) only by fusion map"],
["O8+(3)M13","13th maximal subgroup of O8+(3),\ndiffers from O8+(2) only by fusion map"],
["O8+(3)M14","origin: Dixon's Algorithm,\n14th maximal subgroup of O8+(3)"],
["O8+(3)M16","16th maximal subgroup of O8+(3),\ndiffers from O8+(3)M15 only by fusion map"],
["O8+(3)M17","17th maximal subgroup of O8+(3),\ndiffers from O8+(3)M15 only by fusion map"],
["O8+(3)M19","19th maximal subgroup of O8+(3),\ndiffers from (A4xU4(2)):2 only by fusion map"],
["O8+(3)M2","2nd maximal subgroup of O8+(3),\ndiffers from O7(3) only by fusion map"],
["O8+(3)M20","20th maximal subgroup of O8+(3),\ndiffers from (A4xU4(2)):2 only by fusion map"],
["O8+(3)M21","21st maximal subgroup of O8+(3),\ndiffers from (A4xU4(2)):2 only by fusion map"],
["O8+(3)M22","22nd maximal subgroup of O8+(3),\ndiffers from (A4xU4(2)):2 only by fusion map"],
["O8+(3)M23","23rd maximal subgroup of O8+(3),\ndiffers from (A4xU4(2)):2 only by fusion map"],
["O8+(3)M25","25th maximal subgroup of O8+(3),\ndiffers from (A6xA6):2^2 only by fusion map"],
["O8+(3)M26","26th maximal subgroup of O8+(3),\ndiffers from (A6xA6):2^2 only by fusion map"],
["O8+(3)M27","27th maximal subgroup of O8+(3),\nstructure 2.((A4 wr 2^2):2),\ncentralizer of a 2D element in O8+(3),\norigin: Dixon's Algorithm"],
["O8+(3)M3","3rd maximal subgroup of O8+(3),\ndiffers from O7(3) only by fusion map"],
["O8+(3)M4","4th maximal subgroup of O8+(3),\ndiffers from O7(3) only by fusion map"],
["O8+(3)M5","5th maximal subgroup of O8+(3),\ndiffers from O7(3) only by fusion map"],
["O8+(3)M6","6th maximal subgroup of O8+(3),\ndiffers from O7(3) only by fusion map"],
["O8+(3)M8","8th maximal subgroup of O8+(3),\ndiffers from 3^6:L4(3) only by fusion map"],
["O8+(3)M9","9th maximal subgroup of O8+(3),\ndiffers from 3^6:L4(3) only by fusion map"],
["O8+(7)","computed by Eamonn O'Brien using Magma, December 2011"],
["O8-(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["O8-(2).2","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(O8-(2))"],
["O8-(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13,41]"],
["O8-(3).2^2","constructed using `PossibleCharacterTablesOfTypeGV4',\nconstructions: Aut(O8-(3))"],
["O8-(3).2_1","computed by T. Breuer in October 2002\nusing Dixon's algorithm and character theoretic methods\norigin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13,41],\nconstructions: PGO(-1,8,3)"],
["O8-(3).2_1M4","4th maximal subgroup of O8-(3).2_1,\ndiffers from O8-(3).2_1M3 only by fusion map"],
["O8-(3).2_2","computed by Thomas Breuer in July 2007,\nusing the group and character theoretic methods"],
["O8-(3).2_3","computed by Thomas Breuer in July 2007,\nusing the group and character theoretic methods"],
["O8-(3)M3","3rd maximal subgroup of O8-(3),\ndiffers from O8-(3)M2 only by fusion map"],
["O8-(3)M8","8th maximal subgroup of O8-(3),\ndiffers from O8-(3)M7 only by fusion map"],
["O9(3)","origin: Dixon's algorithm plus character theoretic methods,\nThomas Breuer, September 2003"],
["ON","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19,31]"],
["ON.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19,31],\nconstructions: Aut(ON)"],
["ON.2N2","origin: Dixon's Algorithm"],
["ONM11","11th maximal subgroup of ON,\ndiffers from ONM10 only by fusion map"],
["ONM2","2nd maximal subgroup of ON,\ndiffers from ONM1 only by fusion map"],
["ONM5","origin: constructed as subdirect product of 3^2:Q8 and M10,\nstructure is (3^2:4xA6).2,\n5th maximal subgroup of ON,\ntable is sorted w.r. to normal series given by 3^2.2.2.A6.2,\ntests: 1.o.r., pow[2,3,5]"],
["ONM8","8th maximal subgroup of ON,\ndiffers from ONM7 only by fusion map"],
["P1/G1/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^4.A5"],
["P1/G1/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^4.A5"],
["P1/G1/L1/V1/ext4","origin: Hanrath library,\nstructure is 4^4.A5"],
["P1/G1/L1/V1/ext5","origin: Hanrath library,\nstructure is 5^4.A5"],
["P1/G1/L1/V1/ext6","origin: Hanrath library,\nstructure is 6^4.A5"],
["P1/G1/L1/V2/ext3","origin: Hanrath library,\nstructure is 3^4.A5"],
["P1/G1/L1/V2/ext6","origin: Hanrath library,\nstructure is 6^4.A5"],
["P1/G2/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^5.A5"],
["P1/G2/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^5.A5"],
["P1/G2/L1/V1/ext4","origin: Hanrath library,\nstructure is 4^5.A5"],
["P1/G2/L1/V2/ext2","origin: Hanrath library,\nstructure is 2^5.A5"],
["P1/G2/L1/V2/ext4","origin: Hanrath library,\nstructure is 4^5.A5"],
["P1/G2/L2/V2/ext2","origin: Hanrath library,\nstructure is 2^5.A5"],
["P1/G2/L2/V2/ext4","origin: Hanrath library,\nstructure is 4^5.A5"],
["P1/G3/L2/V1/ext2","origin: Hanrath library,\nstructure is 2^6.A5"],
["P1/G3/L2/V1/ext3","origin: Hanrath library,\nstructure is 3^6.A5"],
["P11/G1/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^6.L3(2)"],
["P11/G1/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^6.L3(2)"],
["P11/G1/L1/V1/ext4","origin: Hanrath library,\nstructure is 4^6.L3(2)"],
["P11/G1/L1/V2/ext2","origin: Hanrath library,\nstructure is 2^6.L3(2)"],
["P11/G1/L1/V2/ext4","origin: Hanrath library,\nstructure is 4^6.L3(2)"],
["P11/G1/L1/V3/ext2","origin: Hanrath library,\nstructure is 2^6.L3(2)"],
["P11/G1/L1/V3/ext4","origin: Hanrath library,\nstructure is 4^6.L3(2)"],
["P11/G2/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^6.L3(2)"],
["P11/G2/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^6.L3(2)"],
["P11/G2/L1/V2/ext2","origin: Hanrath library,\nstructure is 2^6.L3(2)"],
["P11/G3/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^7.L3(2)"],
["P11/G3/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^7.L3(2)"],
["P11/G3/L1/V2/ext3","origin: Hanrath library,\nstructure is 3^7.L3(2)"],
["P11/G3/L3/V1/ext2","origin: Hanrath library,\nstructure is 2^7.L3(2)"],
["P11/G3/L3/V2/ext3","origin: Hanrath library,\nstructure is 3^7.L3(2)"],
["P11/G3/L4/V2/ext2","origin: Hanrath library,\nstructure is 2^7.L3(2)"],
["P11/G3/L4/V2/ext3","origin: Hanrath library,\nstructure is 3^7.L3(2)"],
["P11/G3/L4/V3/ext2","origin: Hanrath library,\nstructure is 2^7.L3(2)"],
["P11/G4/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^8.L3(2)"],
["P11/G4/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^8.L3(2)"],
["P12/G1/L2/V1/ext2","origin: Hanrath library,\nstructure is 2^8.2.L3(2),\ncharacters sorted with permutation (59,60).\nThe table on the microfiche is incorrect:\nA comparison with the table computed from the group showed that\nin the 12 irreducible characters 72,73,75,76,78,79,81,82,84,85,87,88\n(of degree 56), the values on the classes 51..64 had to be replaced\nby their complex conjugates;\nthe structure constant for 12, 25, 51 was not integral."],
["P12/G1/L2/V1/ext3","origin: Hanrath library,\nstructure is 3^8.2.L3(2)"],
["P13/G1/L2/V1/ext2","origin: Hanrath library,\nstructure is 2^7.2^3:sl(3,2),\ncharacters sorted with permutation (45,47,49,46)(48,51,52,50)"],
["P13/G1/L2/V1/ext3","origin: Hanrath library,\nstructure is 3^7.2^3:sl(3,2),\ncharacters sorted with permutation (82,83)(95,97)(100,102)"],
["P13/G1/L6/V1/ext2","origin: Hanrath library,\nstructure is 2^7.2^3:sl(3,2),\ncharacters sorted with permutation (45,46)(50,51)"],
["P1L62","origin: CAS library,\ntests: 1.o.r., pow[2,3,5,7,31]"],
["P1L82","origin: CAS library,\nconstructions: AGL(7,2)"],
["P2/G1/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^8.2.A5"],
["P2/G1/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^8.2.A5"],
["P2/G2/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^8.2.A5"],
["P2/G2/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^8.2.A5"],
["P2/G2/L1/V2/ext2","origin: Hanrath library,\nstructure is 2^8.2.A5"],
["P21/G1/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^5.A6"],
["P21/G1/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^5.A6"],
["P21/G1/L1/V1/ext4","origin: Hanrath library,\nstructure is 4^5.A6"],
["P21/G1/L3/V2/ext3","origin: Hanrath library,\nstructure is 3^5.A6"],
["P21/G2/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^9.A6"],
["P21/G2/L1/V2/ext2","origin: Hanrath library,\nstructure is 2^9.A6"],
["P21/G2/L1/V3/ext2","origin: Hanrath library,\nstructure is 2^9.A6"],
["P21/G2/L2/V1/ext2","origin: Hanrath library,\nstructure is 2^9.A6"],
["P21/G2/L2/V2/ext2","origin: Hanrath library,\nstructure is 2^9.A6"],
["P21/G2/L2/V3/ext2","origin: Hanrath library,\nstructure is 2^9.A6"],
["P21/G2/L5/V2/ext2","origin: Hanrath library,\nstructure is 2^9.A6"],
["P21/G3/L2/V1/ext2","origin: Hanrath library,\nstructure is 2^10.A6"],
["P21/G3/L5/V1/ext2","origin: Hanrath library,\nstructure is 2^10.A6"],
["P27/G1/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^6.A7,\ncharacters sorted with permutation (19,21,22,23)"],
["P27/G1/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^6.A7,\ncharacters sorted with permutation (26,28,29,30)(33,35,36,37)(64,65)(69,70)"],
["P27/G1/L1/V1/ext4","origin: Hanrath library,\nstructure is 4^6.A7,\ncharacters sorted with permutation (33,35,36,37)(40,42,43,44)\n(47,49,50,51)(97,98)(102,103)(107,108)(112,113)(117,118)(122,123)"],
["P2L62","origin: CAS library,\ntests: 1.o.r., pow[2,3,5,7]"],
["P2L82","origin: CAS library"],
["P31/G1/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^7.A8,\ncharacters sorted with permutation (26,29)(27,28)(30,31,32,33,34)(36,37)\n(39,40,42,41)(44,45)(46,49,48,47)(54,55)(56,57)"],
["P31/G1/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^7.A8,\ncharacters sorted with permutation (35,38)(36,37)(39,40,41,42,43)(46,49)\n(47,48)(50,51,52,53,54)(58,59)(60,61)(70,71)(72,73)(80,81)\n(102,104,105,106)(109,111,112,113)(120,121)(129,130)\n(134,137,139,135,138,140,136)(146,148,147)"],
["P3L62","origin: CAS library,\ntests: 1.o.r., pow[2,3,7]"],
["P41/G1/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^7.L2(8),\ncharacters sorted with permutation (12,14,15,13)(19,20)"],
["P41/G1/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^7.L2(8),\ncharacters sorted with permutation (11,13)(12,16,15,14)"],
["P41/G1/L1/V2/ext2","origin: Hanrath library,\nstructure is 2^7.L2(8),\ncharacters sorted with permutation (12,14,15,13)(19,20)"],
["P41/G1/L1/V3/ext3","origin: Hanrath library,\nstructure is 3^7.L2(8),\ncharacters sorted with permutation (11,13)(12,16,15,14)"],
["P41/G1/L1/V4/ext2","origin: computed from PerfectGroup(64512,4),\nstructure is 2^7.L2(8).\nNOTE: The table 2.4.7 in the microfiche of [HP89] is not correct,\nthe 2A Clifford matrix and the table head had to be changed."],
["P41/G1/L1/V4/ext3","origin: Hanrath library,\nstructure is 3^7.L2(8),\ncharacters sorted with permutation (11,13)(12,16,15,14)"],
["P41/G2/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^8.L2(8),\ncharacters sorted with permutation (21,22)"],
["P41/G2/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^8.L2(8),\ncharacters sorted with permutation (29,30)(34,35)(37,39)(38,42,41,40)"],
["P43/G1/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^10.L2(11),\ncharacters sorted with permutation (2,6,4,3)"],
["P43/G2/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^10.L2(11),\ncharacters sorted with permutation (2,6,4,3)"],
["P43/G3/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^10.L2(11),\ncharacters sorted with permutation (2,6,4,3)"],
["P43/G3/L1/V2/ext2","origin: Hanrath library,\nstructure is 2^10.L2(11),\ncharacters sorted with permutation (2,6,4,3)"],
["P48/G1/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^10.M11,\ncharacters sorted with permutation (13,15)(14,16,17,18)(20,21)(23,24)\n(30,31,32,33,34)(39,42)(49,50)"],
["P48/G1/L1/V2/ext2","origin: Hanrath library,\nstructure is 2^10.M11,\ncharacters sorted with permutation (13,15)(14,16,17,18)(20,21)(23,24)\n(30,31,32,33,34)(39,42)(49,50)"],
["P49/G1/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^7.U3(3),\ncharacters sorted with permutation (16,19,21,20,18)(23,25)(24,26)\n(37,39,42,41,38)"],
["P49/G1/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^7.U3(3),\ncharacters sorted with permutation (16,17)(19,20,25,22)(21,23,24,26)\n(32,35,36)(40,41)(45,46)(49,50)(52,53)"],
["P49/G1/L1/V2/ext3","origin: Hanrath library,\nstructure is 3^7.U3(3),\ncharacters sorted with permutation (16,17)(19,20,25,22)(21,23,24,26)\n(32,35,36)(40,41)(45,46)"],
["P50/G1/L1/V1/ext2","origin: Hanrath library,\nstructure is 2^6.U4(2),\ncharacters sorted with permutation (35,38)(36,37)(39,40,41,42,43),\n(table is equal to that of 2^6:U4(2) = O8-(2)M1)"],
["P50/G1/L1/V1/ext3","origin: Hanrath library,\nstructure is 3^6.U4(2),\ncharacters sorted with permutation (46,47)(56,59)(57,60,58,61)(62,63)\n(66,70,67)(68,72,69)(71,73)(74,78,79,76,75)(81,85)(82,88,87)(83,86)\n(92,94,95,96)(99,101,102,103)"],
["P50/G1/L1/V1/ext4","origin: Hanrath library,\nstructure is 4^6.U4(2),\ncharacters sorted with permutation (59,62)(60,61)(63,64,65,66,67)\n(77,79,80,81)(84,86,87,88)(92,95)(98,99)\n(111,116,119,118,114,112,115,117,113)(122,123)(125,126,127)"],
["QD16.2","auxiliary table for the construction of (QD16x2F4(2)').2,\norigin: Dixon's Algorithm"],
["R(27)","origin: ATLAS of finite groups, tests: 1.o.r."],
["R(27).3","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(R(27))"],
["Ru","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13,29]"],
["RuN2","origin: Ostermann\nSylow 2 normalizer in sporadic Rudvalis group Ru,\n2nd power map is not determined by the characters,"],
["S10(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["S12(2)","computed by Christoph Koehler using the group and char. theor. methods"],
["S3","constructions: AGL(1,3)"],
["S3wrS4","10th maximal subgroup of S12"],
["S3x13:6","Sylow 13 normalizer in Fi23"],
["S3x2.A5","3B-normalizer in 2.G2(4)"],
["S3x2.U4(3).2_2","8th maximal subgroup of 2.Fi22"],
["S3x3_1.U4(3).2_2","8th maximal subgroup of 3.Fi22"],
["S3x6_1.U4(3).2_2","normalizer of a 3-defect group of order 9 in 6.Fi22"],
["S3xA5","3B-normalizer in G2(4)"],
["S3xFi22.2","9th maximal subgroup of B"],
["S3xJ2.2","7th maximal subgroup of 3.Suz.2"],
["S3xM12.2","11th maximal subgroup of 3.Suz.2"],
["S3xO7(3)","5th maximal subgroup of Fi23"],
["S3xO8+(3):S3","4th maximal subgroup of Fi24"],
["S3xS6","7th maximal subgroup of S6(2)"],
["S3xS6(2)","6th maximal subgroup of S8(2)"],
["S3xTh","9th maximal subgroup of M"],
["S3xU4(2)","14th maximal subgroup of U6(2)"],
["S3xU4(3)","origin: in the CAS library with the names u4q3.s3 and f22u3,\ntest: 1.o.r.,sym2 decompose correctly\ntests: 1.o.r., pow[2,3,5,7]"],
["S3xU4(3).(2^2)_{122}","7th maximal subgroup of Fi22.2"],
["S3xU4(3).2_2","8th maximal subgroup of Fi22"],
["S4(4)","origin: ATLAS of finite groups, tests: 1.o.r."],
["S4(4).2","origin: ATLAS of finite groups, tests: 1.o.r."],
["S4(4).2M3","3rd maximal subgroup of S4(4).2"],
["S4(4).2M5","5th maximal subgroup of S4(4).2,\ndiffers from S4(4).2M4 = L2(16).4 only by fusion map"],
["S4(4).2M7","7th maximal subgroup of S4(4).2"],
["S4(4).4","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(S4(4))"],
["S4(4)M2","2nd maximal subgroup of S4(4)"],
["S4(4)M4","4th maximal subgroup of S4(4),\ndiffers from S4(4)M3 = L2(16).2 only by fusion map"],
["S4(4)M6","6th maximal subgroup of S4(4),\ndiffers from S4(4)M5 only by fusion map"],
["S4(5)","origin: ATLAS of finite groups, tests: 1.o.r."],
["S4(5).2","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(S4(5)), SO(5,5)"],
["S4(7)","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, Jan. 09th, 2001"],
["S4(7).2","origin: Dixon's Algorithm,\nconstructions: Aut(S4(7))"],
["S4(8)","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, Jul. 10th, 2003"],
["S4(8).3","computed using Magma V2.28-15    Thu Jan 16 2025 09:46:52 on schedir\n[Seed = 3859373309]\nTotal time: 0.890 seconds, Total memory usage: 32.09MB"],
["S4(9)","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, Aug. 23rd, 2004"],
["S4(9).2^2","constructed using `PossibleCharacterTablesOfTypeGV4',\nambiguity resolved using that the action on the classes of element order\n80 of S4(9).2_2 is given by the power map *3,\nconstructions: Aut(S4(9))"],
["S4(9).2_1","PGammaS4(9), i.e, the simple group extended by the field automorphism,\norigin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, Aug. 23rd, 2004"],
["S4(9).2_2","the simple group extended by the diagonal automorphism,\norigin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, Aug. 23rd, 2004"],
["S4(9).2_3","the simple group extended by the product of diag. and field automorphism,\norigin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, Aug. 24th, 2004"],
["S4wrS3","8th maximal subgroup of S12"],
["S4x2F4(2)'.2","16th maximal subgroup of B"],
["S4x2^2","normalizer of chain (2A < 4.2^4.2) in HS"],
["S4x5^2:4S4","Sylow 5 normalizer in F3+.2"],
["S4xL3(2).2","10-th maximal subgroup of He.2"],
["S4xO8+(2):S3","13th maximal subgroup of Fi24"],
["S4xS3","9th maximal subgroup of M12.2"],
["S4xS6(2)","12th maximal subgroup of Fi23"],
["S4xU4(2).2","7th maximal subgroup of O8-(3)"],
["S5xS9","17th maximal subgroup of Fi24"],
["S6(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["S6(2)N2","origin: Dixon's Algorithm"],
["S6(3)","origin: ATLAS of finite groups, tests: 1.o.r."],
["S6(3).2","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(S6(3))"],
["S6(4)","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, Dec. 27th, 2000"],
["S6(4).2","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, May 21st, 2005,\nconstructions: Aut(S6(4))"],
["S6(5)","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, Dec. 27th, 2000,\nnot yet sorted compatibly w.r.t. the outer involution!"],
["S6xL2(8):3","18th maximal subgroup of Fi24"],
["S8(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["S8(2)M3","origin: Dixon's Algorithm,\n3rd maximal subgroup of S8(2),\n2A centralizer in S8(2),\nsorted w.r.t. normal series 2 < 2^7 < 2^7:S6(2)"],
["S8(3)","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, Oct. 06th, 2003"],
["Suz","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"],
["Suz.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13],\nconstructions: Aut(Suz)"],
["SuzN2","origin: Ostermann\nSylow 2 normalizer in sporadic Suzuki group Suz,\nused the group for determining the 2nd power map"],
["Symm(4)","symmetric group on 4 points"],
["Sz(32)","origin: ATLAS of finite groups, tests: 1.o.r."],
["Sz(32).5","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(Sz(32))"],
["Sz(8)","origin: ATLAS of finite groups, tests: 1.o.r."],
["Sz(8).3","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(Sz(8))"],
["Th","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13,19,31]"],
["ThM7","origin: constructed by Alexander Hulpke,\n7th maximal subgroup of Th,\n3B^2 normalizer in Th,\ntable is sorted w.r. to normal series 3^2.3^3.3^2.3^2.2.2^2.3.2,\ntests: 1.o.r., pow[2,3]"],
["ThN2","origin: Ostermann\nSylow 2 normalizer in sporadic Thompson group Th,\npower map computed from the group"],
["ThN3","Sylow 3 normalizer in Th,\norigin: Dixon's Algorithm"],
["ThN3B","origin: constructed by Alexander Hulpke,\n6th maximal subgroup of Th,\n3B normalizer in Th,\ntable is sorted w.r. to normal series 3.3^2.3.3^2.3.3^2.2.2^2.3.2,\ntests: 1.o.r., pow[2,3]"],
["U3(11)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11,37]"],
["U3(11).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11,37]"],
["U3(11).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11,37],\nconstructions: PGU(3,11)"],
["U3(11).S3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11,37],\nconstructions: Aut(U3(11))"],
["U3(11)M4","4th maximal subgroup of U3(11),\ndiffers from U3(11)M3 = L2(11).2 only by fusion map"],
["U3(11)M5","5th maximal subgroup of U3(11),\ndiffers from U3(11)M3 = L2(11).2 only by fusion map"],
["U3(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7]"],
["U3(3).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7],\nconstructions: Aut(U3(3))"],
["U3(4)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"],
["U3(4).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"],
["U3(4).4","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\nconstructions: Aut(U3(4))"],
["U3(5)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["U3(5).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["U3(5).2N2","origin: Dixon's Algorithm"],
["U3(5).3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: PGU(3,5)"],
["U3(5).3.2","origin: ATLAS of finite groups,\nmaximal subgroup of Co3,\ntests: 1.o.r., pow[2,3,5,7],\nconstructions: Aut(U3(5))"],
["U3(5)M2","2nd maximal subgroup of U3(5),\ndiffers from U3(5)M1 = A7 only by fusion map"],
["U3(5)M3","3rd maximal subgroup of U3(5),\ndiffers from U3(5)M1 = A7 only by fusion map"],
["U3(5)M6","6th maximal subgroup of U3(5),\ndiffers from U3(5)M5 = A6.2_3 only by fusion map"],
["U3(5)M7","7th maximal subgroup of U3(5),\ndiffers from U3(5)M5 = A6.2_3 only by fusion map"],
["U3(7)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,43]"],
["U3(7).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,43],\nconstructions: Aut(U3(7))"],
["U3(8)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,19]"],
["U3(8).(S3x3)","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(U3(8))"],
["U3(8).2","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: PSU(3,8) extended by transpose-inverse"],
["U3(8).3^2","origin: Dixon's Algorithm,\nconstructions: PGammaU(3,8)"],
["U3(8).3_1","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: PSigmaU(3,8)"],
["U3(8).3_2","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: PGU(3,8)"],
["U3(8).3_3","origin: ATLAS of finite groups, tests: 1.o.r."],
["U3(8).6","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: PSigmaU(3,8) extended by transpose-inverse"],
["U3(8).S3","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: PGU(3,8) extended by transpose-inverse"],
["U3(8)M4","4th maximal subgroup of U3(8),\ndiffers from U3(8)M3 only by fusion map"],
["U3(8)M5","5th maximal subgroup of U3(8),\ndiffers from U3(8)M3 only by fusion map"],
["U3(9)","origin: ATLAS of finite groups, tests: 1.o.r."],
["U3(9).2","origin: ATLAS of finite groups, tests: 1.o.r."],
["U3(9).4","origin: ATLAS of finite groups, tests: 1.o.r.,\nconstructions: Aut(U3(9))"],
["U4(2)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"],
["U4(2).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5],\nconstructions: Aut(U4(2)), GO(-1,6,2), PGO(-1,6,2), SO(-1,6,2), PSO(-1,6,2)"],
["U4(3)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["U4(3).(2^2)_{122}","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["U4(3).(2^2)_{133}","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\ncomputed from the tables of U4(3), U4(3).2_1, U4(3).2_3, U4(3).2_3'"],
["U4(3).(2^2)_{133}M6","6th maximal subgroup of U4(3).(2^2)_{133},\ndiffers from U4(3).(2^2)_{133}M5 only by fusion map"],
["U4(3).2_1","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: PSO(-1,6,3)"],
["U4(3).2_1M10","10th maximal subgroup of U4(3).2_1,\ndiffers from U4(3).2_1M9 only by fusion map"],
["U4(3).2_1M4","4th maximal subgroup of U4(3).2_1,\ndiffers from U4(3).2_1M3 only by fusion map"],
["U4(3).2_2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: PSU(4,3) extended by transpose-inverse"],
["U4(3).2_3","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"],
["U4(3).4","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: PGU(4,3)"],
["U4(3).D8","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\nconstructions: Aut(U4(3)), PGU(4,3) extended by transpose-inverse"],
["U4(3)M12","12th maximal subgroup of U4(3),\ndiffers from A7=U4(3)M10 only by fusion map"],
["U4(3)M3","3rd maximal subgroup of U4(3),\ndiffers from U4(2)=U4(3)M2 only by fusion map"],
["U4(3)M9","9th maximal subgroup of U4(3),\ndiffers from 2^4:a6=U4(3)M8 only by fusion map"],
["U4(4)","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, Sep. 04th, 1999"],
["U4(4).4","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, Sep. 29th, 2004,\nconstructions: Aut(U4(4))"],
["U4(5)","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, Jul. 09th, 2003"],
["U4(5).2^2","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, July 2007;\nlater constructed using `PossibleCharacterTablesOfTypeGV4',\nconstructions: Aut(U4(5)), PGU(4,5) extended by transpose-inverse"],
["U4(5).2_1","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, August 2005,\nconstructions: PSigmaU(4,5), PSU(4,5) extended by transpose-inverse"],
["U4(5).2_2","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, August 2005,\nconstructions: PGU(4,5)"],
["U4(5).2_3","origin: computed using Dixon's algorithm and character theoretic methods,\nThomas Breuer, August 2005"],
["U5(2)","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11]"],
["U5(2).2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11],\nconstructions: Aut(U5(2))"],
["U5(3)","origin: computed using character theoretic methods,\nThomas Breuer, May 3rd, 2009"],
["U5(4)","origin: computed using character theoretic methods,\nThomas Breuer, Apr. 10th, 2005"],
["U5(4).2","origin: computed using character theoretic methods,\nThomas Breuer, Apr. 10th, 2005"],
["U6(2)","origin: ATLAS of finite groups, tests: 1.o.r."],
["U6(2).2","origin: ATLAS of finite groups, tests: 1.o.r."],
["U6(2).3","origin: ATLAS of finite groups, tests: 1.o.r."],
["U6(2).3.2","origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11],\nconstructions: Aut(U6(2))"],
["U6(2)M10","10th maximal subgroup of U6(2),\ndiffers from U6(2)M8 = S6(2) only by fusion map"],
["U6(2)M12","12th maximal subgroup of U6(2),\ndiffers from U6(2)M11 = M22 only by fusion map"],
["U6(2)M13","13th maximal subgroup of U6(2),\ndiffers from U6(2)M11 = M22 only by fusion map"],
["U6(2)M5","5th maximal subgroup of U6(2),\ndiffers from U6(2)M4 = U4(3).2_2 only by fusion map"],
["U6(2)M6","6th maximal subgroup of U6(2),\ndiffers from U6(2)M4 = U4(3).2_2 only by fusion map"],
["U6(2)M9","9th maximal subgroup of U6(2),\ndiffers from U6(2)M8 = S6(2) only by fusion map"],
["U6(4)","computed by Eamonn O'Brien in 2007, using MAGMA"],
["U7(2)","computed by Frank L\"ubeck in April 2007, using MAGMA"],
["U72CT","origin: CAS library,\ntests: 1.o.r., pow[2,3,5,11]"],
["[2^20]:(S3xL3(2))","5th maximal subgroup of F4(2),\nconstructed as a factor of the table of 2.F4(2)M5"],
["[2^20]:A6.2^2","computed using Magma V2.27-3, Jun 21 2024 10:59:12 on schedir\n[Seed = 3976194619]\nTotal time: 32.579 seconds, Total memory usage: 64.12MB"],
["[2^22]:(S3xS3):2","computed using Magma V2.27-3, Aug 13 2024 14:19:27 on schedir\n[Seed = 2793118306]\nTotal time: 14.679 seconds, Total memory usage: 64.12MB"],
["[2^30].L5(2)","8th maximal subgroup of B,\nsorted w.r.t. normal series 2^5 < 2^10 < 2^20 < [2^30] < [2^30].L5(2),\ncomputed by Eamonn O'Brien using Magma, March 2007"],
["[2^35].(S5xL3(2))","10th maximal subgroup of B,\ncomputed by Eamonn O'Brien using Magma, March 2007"],
["[2^9].S3a","normalizer of a radical 2-subgroup in M24 and He,\norigin: Dixon's Algorithm"],
["[2^9].S3b","normalizer of a radical 2-subgroup in M24 and He,\norigin: Dixon's Algorithm"],
["[7^6]:(6x6)","origin: Dixon's Algorithm"],
["a4","origin: CAS library,\n    names:=     a4; psl[2,3]\n                    a1(3)     (lie-not.)\n    order:     2^2.3 = 12\n    number of classes: 4\n    source:    generated by dixon-algorithm aachen (1982)\n    comments:  alternating group, catalogue nr.12.5\n    test:      orth, min, sym(3)\nconstructions: AGL(1,4),\ntests: 1.o.r., pow[2,3]"],
["a4xa5","origin: CAS library,\nmaximal subgroup of j2,\ntest: 1. o.r., sym 2 decompose correctly \ntests: 1.o.r., pow[2,3,5]"],
["a4xs5","origin: CAS library,\nmaximal subgroup of Co3,\ntest: restricted characters decompose properly,\ntests: 1.o.r., pow[2,3,5]"],
["a5wc2","origin: CAS library,\ntests: 1.o.r., pow[2,3,5]"],
["a5xd10","origin: CAS library,\nmaximal subgroup of J2,\nnormalizer of a defect 5-subgroup of type 5AB in G2(4),\ntest: 1.OR, JAMES, JAMES,n=3,\nand restricted characters decompose properly,\ntests: 1.o.r., pow[2,3,5]"],
["affine","origin: CAS library,\ntests: 1.o.r., pow[2,3,5]"],
["b33141","origin: CAS library,\nnames:b33141\norder: 2^6.3^2 = 576\nnumber of classes: 23\nsource:generated by dixon-algorithm\naachen  [1981],\nbrown, h. / buelow, r. / neubueser, j.\nwondratschek, h. / zassenhaus, h.\ncrystallographic groups of\nfour dimensional space\ncomments:isomorphism type 576.1\nq-classes: 33/14\ngenerators:\na:  1  0  0  0    b:  -1 -1 -1  2    c:  1  0  0  0\n0 -1  0  0         0  0  1  0        0 -1  0  0\n0  0 -1  0         0 -1  0  0        0  0  1  0\n0 -1 -1  1        -1 -1  0  1        1  0  1 -1\n\nd:  0  0 -1  0    e:   0 -1  0  1    f:  0  1  0 -1\n1  1  1 -2        -1  0  0  1        0  0 -1 -1\n-1  0  0  0         1  1  1 -1        1  0  0 -1\n0  0  0 -1         0  0  1  0        1  1  0 -1 \n\ntest: 1. o.r., sym 2, 3 decompose correctly\ntests: 1.o.r., pow[2,3]"],
["bd10","origin: CAS library,\nnames:=bd10\n order: 2^2.5 = 20\n number of classes: 8\n source: generated by dixon-algorithm\n         aachen [1984]\n comments:generators: a,b,c\n relations: a^2=b^2=c^5=a*b*c \n test: 1. o.r., sym 2 decompose correctly \ntests: 1.o.r., pow[2,5]"],
["bd6","origin: CAS library,\nnames:=bd6\n order: 2^2.3 = 12\n number of classes: 6\n source:generated by dixon-algorithm\n        aachen [1984]\n test: 1. o.r., sym 2, 3 decompose correctly\n comments:generators: a,b,c\n          relations: a^2=b^2=c^3=a*b*c \ntests: 1.o.r., pow[2,3]"],
["bd8","origin: CAS library,\nnames:=bd8\n order: 2^4 = 16\n number of classes: 7\n source: generated by dixon-algorithm\n         aachen [1984]\n test: 1. o.r., sym 2 decompose correctly\n comments:generators: a,b,c\n          relations: a^2=b^2=c^4=a*b*c \ntests: 1.o.r., pow[2]"],
["c2aj4","origin: CAS library,\npower maps corrected (using GAP): 93->52, 94->51; T. Breuer, 07.06.90\ntests: 1.o.r., pow[2,3,5,7,11]"],
["c3d2","origin: CAS library,\ntests: 1.o.r., pow[2,3,7]"],
["esp43t","origin: CAS library,\ntests: 1.o.r., pow[2,3,5]"],
["f22s2","Sylow 2-subgroup and Sylow 2 normalizer in Fi22,\norigin: CAS library,\ntests: 1.o.r., pow[2],\n2nd power map determined only up to matrix automorphisms,"],
["frob","origin: CAS library,\nconstructions: AGL(1,29),\ntests: 1.o.r., pow[2,7,29]"],
["g61","origin: CAS library,\nnames;g61\norder: 2^4.3.5^4.13 = 390,000\nnumber of classes: 61\nsource:generated by cayley-algorithms\nand cas-system\naachen [1979]\ntest: 1. o.r., sym 2 decompose correctly\ncomments:frobenius-group \ntests: 1.o.r., pow[2,3,5,13]"],
["g61s1","origin: CAS library,\nnames:=g61s1\n order: 2^4.3.13 = 624\n number of classes: 60\n source:generated by cayley-algorithms\n       and cas-system\n       aachen [1979]\n comments:factorgroup of index 625 in g61 \ntests: 1.o.r., pow[2,3,13]"],
["g72x16","origin: CAS library,\n test:= 1. o.r., sym 2 decompose correctly  \ntests: 1.o.r., pow[2,3]"],
["ghh","origin: CAS library,\ntests: 1.o.r., pow[2,3,5]"],
["gl25","origin: CAS library,\nnames:=gl25\n order: 2^5.3.5 = 480\n number of classes: 24\n source:generated by cas-algorithms\n        aachen [1981]\n comments: - \ntests: 1.o.r., pow[2,3,5]"],
["group2","origin: CAS library,\nnames:group2\norder: 2^9 = 512\nnumber of classes: 41\nsource;generated by cas-algorithms\naachen [1980]\ntest: 1. o.r. satisfied\ncomments:p-group \ntests: 1.o.r., pow[2]"],
["group3","origin: CAS library,\nnames:=group3\n order:3^2.7 = 63\n number of classes:15\n source:generated by dixon-algorithm\n        aachen  [1981]\n test: 1. o.r. satisfied\n comments:-\ntests: 1.o.r., pow[3,7]"],
["group5","origin: CAS library,\ntests: 1.o.r., pow[2,3,7]"],
["group6","origin: CAS library,\nnames:=group6\n order: 2^5.3 = 96\n number of classes: 13\n source:generated by dixon-algorithm\n        aachen [1982]\n comments:generators:a,b\n          relations: (a*b)^2=(a^3*b^2)^2=(a^2*b^3)^2=(a^-1*b^2)^2=1 \ntests: 1.o.r., pow[2,3]"],
["gs4","origin: CAS library,\ntests: 1.o.r., pow[2,3]"],
["h4","origin: CAS library,\nnames:=h4\n       order: 2^6.3^2.5^2 = 14,400\n       number of classes: 34\n       source:grove, l.c.\n             the characters of the\n             hecatonicosahedroidal group\n             j.reine angew. math. 265\n             [1974],160-169\n       comments: -\ntests: 1.o.r., pow[2,3,5]"],
["hed3","origin: CAS library,\ntests: 1.o.r., pow[2,3]"],
["hess","origin: CAS library,\nnames:=hess\n order: 2^3.3^4 = 648\n number of classes: 24\n source:generated by dixon-algorithm\n       aachen [1980]\n comments:matrix group over gf(19) with size 3 and\n         generators:\n         1  0  0    0  0  1    14 14 14    16  0  0\n         0  7  0    1  0  0    14  3  2     0 16  0\n         0  0 11    0  1  0    14  2  3     0  0 17 \ntests: 1.o.r., pow[2,3]"],
["hsd2","origin: CAS library,\ntests: 1.o.r., pow[2,3,5]"],
["j2nd2","origin: CAS library,\ntests: 1.o.r., pow[2,3,5]"],
["j3m4","origin: CAS library,\n4th maximal subgroup of J3,\ntable is sorted w.r. to normal series 2^4.3.A5,\nconstructions: AGL(2,4),\ntests: 1.o.r., pow[2,3,5]"],
["j3m6","origin: CAS library,\nmaximal subgroup of j3, (3 x a6):2 \ntests: 1.o.r., pow[2,3,5]"],
["m12d2","origin: CAS library,\ntests: 1.o.r., pow[2,3]"],
["mo61","origin: CAS library,\nnames:=mo61; m6[1]\n order: 2^7.3^2 = 1,152\n number of classes: 20\n source:dye, r.h.\n        the classes and characters of\n        certain maximal and other subgroups\n        of o 2n+2(2)\n        ann.mat.pura appl.(4) 107\n        (1975), 13-47\n comments:semidirect product of an elementary\n          abelian group of order 2^4 and o4,\n          table blown up using cas-system\ntests: 1.o.r., pow[2,3]"],
["mo62","origin: CAS library,\nnames:=mo62; m6[2]\n order: 2^7.3.5 = 1,920\n number of classes: 18\n source:dye, r.h.\n        the classes and characters of\n        certain maximal and other subgroups\n        of o 2n+2(2)\n        ann.mat.pura appl.(4) 107\n        (1975), 13-47\n comments:semidirect product of an elementary\n          abelian group of order 2^4 and o4,\n          table blown up using cas-system \ntests: 1.o.r., pow[2,3,5]"],
["mo62p","origin: CAS library,\nnames:=mo62p; m6[2]+\n order: 2^6.3.5 = 960\n number of classes: 12\n source:dye, r.h.\n        the classes and characters of\n        certain maximal and other subgroups\n        of o 2n+2(2)\n        ann.mat.pura appl.(4) 107\n        (1975), 13-47\n comments:semidirect product of an elementary\n          abelian group of order 2^4 and o4+,\n          table blown up using cas-system \ntests: 1.o.r., pow[2,3,5]"],
["mo81","origin: CAS library,\nnames:=mo81; m8[1]\n order: 2^13.3^2.5.7 = 2,580,480\n number of classes: 64\n source:dye, r.h.\n        the classes and characters of\n        certain maximal and other subgroups\n        of o 2n+2(2)\n        ann.mat.pura appl.(4) 107\n        (1975), 13-47\n comments:semidirect product of an elementary\n          abelian group of order 2^6 and o6,\n          table blown up using cas-system\ntests: 1.o.r., pow[2,3,5,7]"],
["mx1j4","origin: CAS library,\ntests: 1.o.r., pow[2,3,5,7,11,23]"],
["ons1","origin: CAS library,\nnames:=ons1\n order: 2^9.3.7 = 10,752\n number of classes: 18\n source:o'nan, m.e.\n       some evidence for the existence\n       of a new finite simple group\n       proc. london math. soc. [3] 32\n       (1976),421-479\n comments:subgroup of index 42,858,585 in on \ntests: 1.o.r., pow[2,3,7]"],
["pap","origin: CAS library,\nnames:=pap\n order: 2^2.3^3 = 108\n number of classes: 11\n source:norman, j.f.\n       the group characters for a group of\n       order 108 associated with a pappus\n       theorem of projective geometry,\n       [romanian summary]\n       an. univ. timisoara ser. sti.mat.11\n       (1973),115-122\n       generated by dixon algorithm\n       aachen (1980)\n comments:degree:4\n         generators:a,b,c,d\n         relations: a^2=b^2=c^2=d^3=1\n                    (ac)^3=(acd)^3=(bd)^2=1\n                    (ad)^2=(da)^2\n                    [ab]=[bc]=[cd]=1 \ntests: 1.o.r., pow[2,3]"],
["s2wrs2","origin: CAS library,\nnames:=s2wrs2; d8\n     order: 2^3 = 8\n     number of classes: 5\n     source:saenger, f.\n            einige charakterentafeln von symmetrien\n            symmetrischer gruppen\n            mitt.math.sem.giessen\n            heft 98 [1973], 21-38\n     comments:wreath-product of s2 with s2\n     test: orth.1, minus   \ntests: 1.o.r., pow[2]"],
["s2wrs3","origin: CAS library,\nnames:=s2wrs3\n      order: 2^4.3 = 48\n      number of classes: 10\n      source:saenger, f.\n             einige charakterentafeln von symmetrien\n             symmetrischer gruppen\n             mitt.math.sem. giessen\n             heft 98 [1973], 21 - 38\n      comments:wreath-product of s2 with s3\n      test: orth.1, minus, sym(3)   \ntests: 1.o.r., pow[2,3]"],
["s2wrs4","origin: CAS library,\nnames:=s2wrs4\n    order: 2^7.3 = 384\n    number of classes: 20\n    source:saenger, f.\n           einige charakterentafeln von symmetrien\n           symmetrischer gruppen\n           mitt.math.sem. giessen\n           heft 98 [1973], 21 - 38\n    comments:wreath-product of s2 with s4\n    test: orth.1, minus, sym(3)   \ntests: 1.o.r., pow[2,3]"],
["s2wrs5","origin: CAS library,\nnames:=s2wrs5\n         order: 2^8.3.5 = 3,840\n         number of classes: 36\n         source:saenger, f.\n                einige charakterentafeln von symmetrien\n                symmetrischer gruppen\n                mitt.math.sem. giessen\n                heft 98 [1973], 21 -38\n         comments:wreath-product of s2 with s5\n         test: orth.1, minus, sym(3)   \ntests: 1.o.r., pow[2,3,5]"],
["s3wrs2","origin: CAS library,\nnames:=s3wrs2, o4p2\n    order: 2^3.3^2 = 72\n    number of classes: 9\n    source:saenger, f.\n           einige charakterentafeln von symmetrien\n           symmetrischer gruppen\n           mitt.math.sem. giessen\n           heft 98 [1973], 21 - 38\n    comments:wreath-product of s3 with s2\n    test: orth.1, minus, sym(3)   \ntests: 1.o.r., pow[2,3]"],
["s3wrs3","origin: CAS library,\nnames:=s3wrs3\n    order: 2^4.3^4 = 1,296\n    number of classes: 22\n    source:generated by dixon-algorithm\n          aachen [1980]\n    comments:wreath-product of s3 with s3,\n            degree: 9\n            generators: a = (1,2,3); b = (1,2);\n                        c = (1,4,7)(2,5,8)(3,6,9);\n                        d = (1,4)(2,5)(3,6)\n    test: orth.1, minus,sym(3)   \ntests: 1.o.r., pow[2,3]"],
["s3xpsl(2,8).3","origin: CAS library,\nmaximal subgroup of Co3,\nRestricted characters decompose properly.\ntests: 1.o.r., pow[2,3,7]"],
["s4","origin: CAS library,\n    names:=     s4\n    order:     2^3.3 = 24\n    number of classes: 5\n    source:    generated by dixon-algorithm aachen [1982]\n    comments:  symmetric group, catalogue nr.24.15\n    test:      orth, min, sym(3)                            \nconstructions: AGL(2,2),\ntests: 1.o.r., pow[2,3]"],
["s4wrs2","solvable subgroup of maximal order in M22.2,\norigin: CAS library,\nnames:=s4wrs2\n    order: 2^7.3^2 = 1,152\n    number of classes: 20\n    source:saenger, f.\n           einige charakterentafeln von symmetrien\n           symmetrischer gruppen\n           mitt.math.sem. giessen\n           heft 98 [1973], 21 - 38\n    comments:wreath-product of s4 with s2\n    test: orth.1, minus, sym(3)   \ntests: 1.o.r., pow[2,3]"],
["s4xpsl(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]"],
["s5wrs2","origin: CAS library,\nnames:=s5wrs2;\n     order: 2^7.3^2.5^2 = 28,800\n     number of classes: 35\n     source:saenger, f\n            einige charakterentafeln von symmetrien\n            symmetrischer gruppen\n            mitt.math.sem. giessen\n            heft 98 [1973], 21 - 38\n     comments:wreath-product of s5 with s2\n     test: orth.1, minus, sym(3)   \ntests: 1.o.r., pow[2,3,5]"],
["s61p","origin: CAS library,\nnames:=s61p; s6[1]+\n order: 2^6 = 64\n number of classes: 16\n source:dye, r.h.\n        the classes and characters of\n        certain maximal and other subgroups\n        of o 2n+2[2]\n        ann.mat.pura appl.[4] 107\n        [1975], 13-47\n comments:table blown up using cas-system.\nThe element orders on the CAS table were incorrect,\nthe correct power map was computed from the group (T. Breuer, July 1999)."],
["sl25ex","origin: CAS library,\nnames:=sl25ex; 3**[1+4].sl2(5)\n order: 29,160\n number of classes: 33\n source: koichiro harada\n         on the simple group f of order\n         2^14.3^6.5^6.7.11.19\n         proceedings of the conference\n         on finite groups,\n         park city, utah (1975)\n comments:     \ntests: 1.o.r., pow[2,3,5],\n3rd power map determined only up to matrix automorphisms,"],
["suzd2","origin: CAS library,\ntests: 1.o.r., pow[2,3]"],
["suzdx","origin: CAS library,\ntests: 1.o.r., pow[2,3,5]"],
["suzs2","Sylow 2 subgroup in sporadic simple group Suz,\norigin: CAS library,\n2nd power map computed from the group"],
["twd5a","origin: CAS library,\ntests: 1.o.r., pow[2,3,5]"],
["w(d4)","origin: CAS library,\ntests: 1.o.r., pow[2,3]"],
["w(d5)","origin: CAS library,\ntests: 1.o.r., pow[2,3,5]"],
["w(f4)","origin: CAS library,\ntests: 1.o.r., pow[2,3]"]
],
"nonautomatic": [
]
}