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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
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( 12, 14, 81, 55, 68)( 15, 90, 31, 56, 37)( 18, 69, 45, 84, 76)
( 19, 59, 79, 35, 93)( 21, 22, 64, 39,100)( 26, 58, 96, 85, 77)
( 33, 52, 94, 75, 44)( 34, 62, 87, 78, 50)( 36, 82, 60, 74, 72)
( 41, 80, 70, 49, 67)( 57, 63, 71, 99, 97) ] ],
[ 4, 88704000, 0, "2", [ [ 22, 1 ], [ 77, 1 ] ], 1, "HS:2",
[ "Spor", "HS", 1 ],
[ ( 1, 86)( 4, 54)( 5, 30)( 6, 57)( 8, 44)( 9, 52)( 11, 14)( 13, 42)
( 18, 43)( 19, 85)( 20, 65)( 22, 91)( 23, 71)( 24, 87)( 25, 50)
( 26, 78)( 27, 88)( 29, 73)( 31, 76)( 33, 84)( 34, 72)( 35, 97)
( 36, 53)( 37, 63)( 39, 47)( 40, 99)( 45, 80)( 55, 81)( 58, 79)
( 62, 83)( 66, 77)( 67, 98)( 68,100)( 69, 93)( 74, 89),
( 1, 49, 14, 37, 74)( 2, 16, 52, 96, 44)( 3, 99, 38, 18, 61)
( 5, 62, 64, 65, 95)( 6, 8, 40, 85, 58)( 7, 68, 80, 9, 39)
( 10, 19, 31, 97, 72)( 11, 77, 93, 84, 98)( 12, 46, 86, 78, 42)
( 13, 23, 54, 29, 15)( 17, 82, 69, 34, 30)( 21, 28, 56, 88, 89)
( 22,100, 73, 87, 35)( 24, 79, 67, 59, 32)( 25, 43, 27, 66, 75)
( 26, 92, 47, 50, 94)( 33, 36, 57, 70, 81)( 41, 83, 55, 91, 51)
( 45, 90, 60, 48, 71) ] ],
[ 5, 7200, 0, "4c", [ [ 12, 1 ], [ 36, 2 ], [ 6, 1 ], [ 9, 1 ] ], 1,
"Alt(5) wreath Sym(2)", [ "A", 5, 2 ],
[ ( 1, 20, 57, 28, 84, 32)( 2, 10, 60, 58, 88, 82)( 3, 70, 56, 98, 85, 42
)( 4, 40, 51, 18, 87, 22)( 5, 50, 53, 68, 86, 92)( 6,100, 55, 48,
83, 62)( 7, 30, 54, 38, 81, 12)( 8, 90, 52)( 9, 80, 59, 78, 89,
72)( 11, 17, 27, 24, 34, 31)( 13, 67, 26, 94, 35, 41)( 14, 37, 21)
( 15, 47, 23, 64, 36, 91)( 16, 97, 25, 44, 33, 61)( 19, 77, 29, 74,
39, 71)( 43, 63, 66, 96, 95, 45)( 46, 93, 65)( 49, 73, 69, 76, 99,
75), ( 1, 13, 85, 44)( 2, 33, 88, 64)( 3, 83, 84, 4)
( 5, 43, 81, 14)( 6, 23, 87, 94)( 7, 93, 86, 24)( 8, 63, 82, 34)
( 9, 53, 89, 54)( 10, 73, 90, 74)( 11, 15, 45, 41)( 12, 35, 48, 61)
( 16, 25, 47, 91)( 17, 95, 46, 21)( 18, 65, 42, 31)( 19, 55, 49, 51)
( 20, 75, 50, 71)( 22, 37, 98, 66)( 26, 27, 97, 96)( 28, 67, 92, 36)
( 29, 57, 99, 56)( 30, 77,100, 76)( 32, 38, 68, 62)( 39, 58, 69, 52)
( 40, 78, 70, 72)( 60, 79) ] ],
[ 6, 14400, 0, "4c", [ [ 12, 1 ], [ 36, 2 ], [ 6, 1 ], [ 9, 1 ] ], 1,
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[ ( 1, 13, 44, 80)( 2, 93, 42,100)( 3, 43, 50, 10)( 4, 73, 41, 20)
( 5, 83, 45, 90)( 6, 53, 48, 70)( 7, 33, 49, 30)( 8, 63, 46, 60)
( 9, 23, 47, 40)( 11, 14, 74, 71)( 12, 94, 72, 91)( 15, 84, 75, 81)
( 16, 54, 78, 61)( 17, 34, 79, 21)( 18, 64, 76, 51)( 19, 24, 77, 31)
( 22, 97, 32, 99)( 25, 87, 35, 89)( 26, 57, 38, 69)( 27, 37, 39, 29)
( 28, 67, 36, 59)( 52, 98, 62, 96)( 55, 88, 65, 86)( 56, 58, 68, 66)
( 82, 95), ( 1, 27, 65, 56, 31, 47, 5, 26, 61, 57, 35, 46)
( 2, 24, 68, 53, 32, 44, 8, 23, 62, 54, 38, 43)( 3, 22, 64, 58, 33,
42, 4, 28, 63, 52, 34, 48)( 6, 21, 67, 55, 36, 41, 7, 25, 66, 51,
37, 45)( 9, 30, 69, 60, 39, 50)( 10, 29, 70, 59, 40, 49)
( 11, 77, 95, 16, 71, 97, 15, 76, 91, 17, 75, 96)( 12, 74, 98, 13, 72,
94, 18, 73, 92, 14, 78, 93)( 19, 80, 99, 20, 79,100)( 81, 87, 85, 86)
( 82, 84, 88, 83)( 89, 90) ] ],
[ 7, 14400, 0, "4c", [ [ 12, 1 ], [ 36, 2 ], [ 6, 1 ], [ 9, 1 ] ], 1,
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[ ( 1, 57, 85, 6, 51, 87, 5, 56, 81, 7, 55, 86)( 2, 54, 88, 3, 52, 84,
8, 53, 82, 4, 58, 83)( 9, 60, 89, 10, 59, 90)( 11, 47, 35, 96, 21,
67, 15, 46, 31, 97, 25, 66)( 12, 44, 38, 93, 22, 64, 18, 43, 32, 94,
28, 63)( 13, 42, 34, 98, 23, 62, 14, 48, 33, 92, 24, 68)
( 16, 41, 37, 95, 26, 61, 17, 45, 36, 91, 27, 65)( 19, 50, 39,100, 29,
70)( 20, 49, 40, 99, 30, 69)( 71, 77, 75, 76)( 72, 74, 78, 73)
( 79, 80), ( 1, 76, 47, 14, 40, 95, 51, 72, 67, 19, 30, 98)
( 2, 66, 49, 24, 38, 5, 56, 42, 64, 39, 25, 58)( 3, 86, 43, 84, 33,
85, 53, 82, 63, 89, 23, 88)( 4, 36, 45, 54, 32, 65, 59, 22, 68, 9,
26, 48)( 6, 46, 44, 34, 35, 55, 52, 62, 69, 29, 28, 8)
( 7, 16, 50, 94, 31, 75, 57, 12, 70, 99, 21, 78)( 10, 96, 41, 74, 37,
15, 60, 92, 61, 79, 27, 18)( 11, 80, 97)( 13, 90, 93, 81, 73, 87)
( 17, 20,100, 91, 71, 77) ] ],
[ 8, 28800, 0, "4c", [ [ 12, 1 ], [ 36, 2 ], [ 6, 1 ], [ 9, 1 ] ], 1,
"Sym(5) wreath Sym(2)", [ "A", 5, 2 ],
[ ( 1, 60, 18, 75, 39, 86, 2,100, 17, 25, 33, 66)( 3, 70, 11, 55, 38, 76,
9, 90, 12, 95, 37, 26)( 4, 50, 14, 45, 34, 46)( 5, 40, 16)
( 6, 10, 20, 15, 35, 36)( 7, 30, 13, 65, 31, 56, 8, 80, 19, 85, 32,
96)( 21, 53, 68, 71, 59, 88, 72, 99, 87, 22, 93, 67)( 23, 63, 61, 51,
58, 78, 79, 89, 82, 92, 97, 27)( 24, 43, 64, 41, 54, 48, 74, 49, 84,
42, 94, 47)( 28, 73, 69, 81, 52, 98, 77, 29, 83, 62, 91, 57),
( 1, 14, 91, 54)( 2, 12, 92, 52)( 3, 20, 93, 60)( 4, 11, 94, 51)
( 5, 15, 95, 55)( 6, 18, 96, 58)( 7, 19, 97, 59)( 8, 16, 98, 56)
( 9, 17, 99, 57)( 10, 13,100, 53)( 21, 64)( 22, 62)( 23, 70)( 24, 61)
( 25, 65)( 26, 68)( 27, 69)( 28, 66)( 29, 67)( 30, 63)( 31, 74, 41, 84
)( 32, 72, 42, 82)( 33, 80, 43, 90)( 34, 71, 44, 81)( 35, 75, 45, 85)
( 36, 78, 46, 88)( 37, 79, 47, 89)( 38, 76, 48, 86)( 39, 77, 49, 87)
( 40, 73, 50, 83) ] ],
[ 9, 6584094720000, 0, "4c", [ [ 81, 1 ], [ 18, 1 ] ], 1,
"Alt(10) wreath Sym(2)", [ "A", 10, 2 ],
[ ( 1, 10,100, 97, 27, 23, 13, 12, 72, 75, 35, 34, 54, 51)( 2, 80, 95, 37,
24, 53, 11)( 3, 20, 92, 77, 25, 33, 14, 52, 71, 5, 40, 94, 57, 21)
( 4, 60, 91, 7, 30, 93, 17, 22, 73, 15, 32, 74, 55, 31)
( 6, 50, 98, 87, 29, 63, 16, 42, 78, 85, 39, 64, 56, 41, 8, 90, 99,
67, 26, 43, 18, 82, 79, 65, 36, 44, 58, 81, 9, 70, 96, 47, 28, 83,
19, 62, 76, 45, 38, 84, 59, 61)( 46, 48, 88, 89, 69, 66)
( 49, 68, 86), ( 1, 60)( 2, 58, 6, 55, 3, 52, 8, 56, 5, 53)
( 4, 54)( 7, 59)( 9, 57)( 10, 51)( 11, 80, 41, 90, 31, 20, 71, 50,
81, 40)( 12, 78, 46, 85, 33)( 13, 72, 48, 86, 35)( 14, 74, 44, 84,
34)( 15, 73, 42, 88, 36)( 16, 75, 43, 82, 38)( 17, 79, 47, 89, 37,
19, 77, 49, 87, 39)( 18, 76, 45, 83, 32)( 21, 30)( 22, 28, 26, 25,
23)( 27, 29)( 61,100)( 62, 98, 66, 95, 63, 92, 68, 96, 65, 93)
( 64, 94)( 67, 99)( 69, 97)( 70, 91) ] ],
[ 10, 13168189440000, 0, "4c", [ [ 81, 1 ], [ 18, 1 ] ], 1, "Alt(10)^2.2^2",
[ "A", 10, 2 ],
[ ( 1, 69, 84, 51, 66, 74, 55, 6, 79, 85)( 2, 29, 87, 11, 63, 34, 58, 96,
80, 45)( 3, 39, 88, 91, 70, 44, 52, 26, 77, 15)( 4, 59, 86, 71, 65)
( 5, 9, 89, 81, 61, 64, 54, 56, 76, 75)( 7, 19, 83, 31, 68, 94, 60,
46, 72, 25)( 8, 99, 90, 41, 62, 24, 57, 16, 73, 35)( 10, 49, 82, 21,
67, 14, 53, 36, 78, 95)( 12, 23, 37, 18, 93, 40, 48, 92, 30, 47)
( 13, 33, 38, 98,100, 50, 42, 22, 27, 17)( 20, 43, 32, 28, 97),
( 1, 88, 6, 68, 5, 98, 2, 18)( 3, 78, 7, 28)( 4, 58)( 9, 38)
( 10, 48)( 11, 81, 86, 66, 65, 95, 92, 12)( 13, 71, 87, 26, 63, 75,
97, 22)( 14, 51, 84, 56, 64, 55, 94, 52)( 15, 91, 82, 16, 61, 85,
96, 62)( 17, 21, 83, 76, 67, 25, 93, 72)( 19, 31, 89, 36, 69, 35,
99, 32)( 20, 41, 90, 46, 70, 45,100, 42)( 23, 73, 77, 27)
( 24, 53, 74, 57)( 29, 33, 79, 37)( 30, 43, 80, 47)( 34, 59)( 40, 49)
( 44, 60) ] ],
[ 11, 13168189440000, 0, "4c", [ [ 81, 1 ], [ 18, 1 ] ], 1, "Alt(10)^2.4",
[ "A", 10, 2 ],
[ ( 1, 27, 48, 75, 63, 10, 87, 42, 55, 66, 40, 84, 12, 59, 96, 31, 24, 18,
79, 93)( 2, 57, 46, 35, 64, 20, 89, 92, 51, 26, 38, 74, 13, 9, 97,
41, 25, 68, 80, 83)( 3, 7, 47, 45, 65, 70, 90, 82, 52, 56, 36, 34,
14, 19, 99, 91, 21, 28, 78, 73)( 4, 17, 49, 95, 61, 30, 88, 72, 53,
6, 37, 44, 15, 69,100, 81, 22, 58, 76, 33)( 5, 67, 50, 85, 62, 60,
86, 32, 54, 16, 39, 94, 11, 29, 98, 71, 23, 8, 77, 43),
( 1, 58, 37, 26, 19, 83, 92, 45, 70, 71, 54, 7, 28, 39, 86, 12, 43,
100, 75, 64)( 2, 48, 40, 76, 14, 3, 98, 35, 66, 11, 53, 97, 25, 69,
81, 52, 47, 30, 79, 84)( 4, 8, 38, 36, 16, 13, 93, 95, 65, 61, 51,
57, 27, 29, 89, 82, 42, 50, 80, 74)( 5, 68, 31, 56, 17, 23, 99, 85,
62, 41, 60, 77, 24, 9, 88, 32, 46, 20, 73, 94)( 6, 18, 33, 96, 15,
63, 91, 55, 67, 21, 59, 87, 22, 49, 90, 72, 44, 10, 78, 34) ] ],
[ 12, 26336378880000, 0, "4c", [ [ 81, 1 ], [ 18, 1 ] ], 1,
"Sym(10) wreath Sym(2)", [ "A", 10, 2 ],
[ ( 1, 29, 15, 81, 28, 55, 82, 48, 60, 2, 49, 20)( 3, 69, 16, 71, 27, 95,
83, 68, 56, 72, 47,100)( 4, 39, 14, 31, 24, 35, 84, 38, 54, 32, 44,
40)( 5, 89, 18, 51, 22, 45, 90, 8, 59, 12, 41, 30)
( 6, 79, 17, 91, 23, 65, 86, 78, 57, 92, 43, 70)( 7, 99, 13, 61, 26,
75, 87, 98, 53, 62, 46, 80)( 9, 19, 11, 21, 25, 85, 88, 58, 52, 42,
50, 10)( 33, 64, 36, 74, 37, 94)( 63, 66, 76, 77, 97, 93)
( 67, 96, 73), ( 1, 47, 70, 79, 3, 17, 64, 39, 2, 87, 61, 49, 10,
77, 63, 19, 4, 37, 62, 89)( 5, 57, 65, 59)( 6, 97, 68, 29)
( 7, 67, 69, 9)( 8, 27, 66, 99)( 11, 44, 40, 72, 83)
( 12, 84, 31, 42, 90, 71, 43, 20, 74, 33)( 13, 14, 34, 32, 82, 81, 41,
50, 80, 73)( 15, 54, 35, 52, 85, 51, 45, 60, 75, 53)( 16, 94, 38, 22,
86, 91, 48, 30, 76, 93, 18, 24, 36, 92, 88, 21, 46,100, 78, 23)
( 25, 56, 95, 58)( 26, 96, 98, 28) ] ],
[ 13, 259200, 0, "4c", [ [ 81, 1 ], [ 18, 1 ] ], 1, "Alt(6) wreath Sym(2)",
[ "A", 6, 2 ],
[ ( 1, 43, 62, 9, 50, 61, 3, 42, 69, 10, 41, 63, 2, 49, 70)
( 4, 47, 65, 8, 46, 64, 7, 45, 68, 6, 44, 67, 5, 48, 66)
( 11, 93, 22, 19,100, 21, 13, 92, 29, 20, 91, 23, 12, 99, 30)
( 14, 97, 25, 18, 96, 24, 17, 95, 28, 16, 94, 27, 15, 98, 26)
( 31, 33, 32, 39, 40)( 34, 37, 35, 38, 36)( 51, 73, 82, 59, 80, 81,
53, 72, 89, 60, 71, 83, 52, 79, 90)( 54, 77, 85, 58, 76, 84, 57, 75,
88, 56, 74, 87, 55, 78, 86),
( 1, 56, 18, 90, 25, 62)( 2, 6, 16, 20, 30, 22)( 3, 76, 17,100, 24,
32)( 4, 36, 13, 80, 27, 92)( 5, 66, 11, 60, 28, 82)
( 7, 96, 14, 40, 23, 72)( 8, 86, 15, 70, 21, 52)( 9, 46, 19, 50,
29, 42)( 10, 26, 12)( 31, 53, 78, 87, 95, 64)( 33, 73, 77, 97, 94,
34)( 35, 63, 71, 57, 98, 84)( 37, 93, 74)( 38, 83, 75, 67, 91, 54)
( 39, 43, 79, 47, 99, 44)( 41, 59, 48, 89, 45, 69)( 51, 58, 88, 85,
65, 61)( 55, 68, 81) ] ],
[ 14, 518400, 0, "4c", [ [ 81, 1 ], [ 18, 1 ] ], 1, "Alt(6)^2.2^2",
[ "A", 6, 2 ],
[ ( 1, 32, 15, 6, 31, 12, 5, 36, 11, 2, 35, 16)( 3, 38, 14, 9, 33, 18,
4, 39, 13, 8, 34, 19)( 7, 37, 17)( 10, 40, 20)( 21, 22, 25, 26)
( 23, 28, 24, 29)( 41, 62, 75, 46, 61, 72, 45, 66, 71, 42, 65, 76)
( 43, 68, 74, 49, 63, 78, 44, 69, 73, 48, 64, 79)( 47, 67, 77)
( 50, 70, 80)( 51, 82, 95, 56, 81, 92, 55, 86, 91, 52, 85, 96)
( 53, 88, 94, 59, 83, 98, 54, 89, 93, 58, 84, 99)( 57, 87, 97)
( 60, 90,100), ( 1, 4, 44, 41)( 2, 34, 47, 21, 3, 74, 49, 81)
( 5, 54, 46, 91, 8, 14, 50, 61)( 6, 94, 48, 11, 10, 64, 45, 51)
( 7, 24, 43, 71, 9, 84, 42, 31)( 12, 40, 67, 25, 53, 76, 99, 88)
( 13, 80, 69, 85, 52, 36, 97, 28)( 15, 60, 66, 95, 58, 16,100, 68)
( 17, 30, 63, 75, 59, 86, 92, 38)( 18, 20, 70, 65, 55, 56, 96, 98)
( 19, 90, 62, 35, 57, 26, 93, 78)( 22, 33, 77, 29, 83, 72, 39, 87)
( 23, 73, 79, 89, 82, 32, 37, 27) ] ],
[ 15, 518400, 0, "4c", [ [ 81, 1 ], [ 18, 1 ] ], 1, "Alt(6)^2.2^2",
[ "A", 6, 2 ],
[ ( 1, 22, 91, 28, 71, 27)( 2, 92, 98, 78, 77, 7)( 3, 12, 99, 88, 75, 67
)( 4, 42, 96, 38, 80, 57)( 5, 62, 93, 18, 79, 87)( 6, 32,100, 58,
74, 47)( 8, 72, 97)( 9, 82, 95, 68, 73, 17)( 10, 52, 94, 48, 76,
37)( 11, 29, 81, 25, 61, 23)( 13, 19, 89, 85, 65, 63)
( 14, 49, 86, 35, 70, 53)( 15, 69, 83)( 16, 39, 90, 55, 64, 43)
( 20, 59, 84, 45, 66, 33)( 24, 41, 26, 31, 30, 51)( 34, 50, 56)
( 36, 40, 60, 54, 44, 46), ( 1, 70, 92, 74, 29, 85, 56, 33, 47, 18)
( 2, 80, 99, 84, 26, 35, 57, 13, 41, 68)( 3, 50, 98, 4, 30, 95, 54,
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88)( 7, 20, 91, 64, 22, 75, 59, 83, 46, 38)( 8, 10,100, 94, 24, 25,
55, 53, 43, 48)( 9, 90, 96, 34, 27, 15, 51, 63, 42, 78)
( 11, 61, 62, 72, 79, 89, 86, 36, 37, 17)( 12, 71, 69, 82, 76, 39, 87,
16, 31, 67)( 19, 81, 66, 32, 77) ] ],
[ 16, 518400, 0, "4c", [ [ 81, 1 ], [ 18, 1 ] ], 1, "Alt(6)^2.4",
[ "A", 6, 2 ],
[ ( 1, 21, 61, 91, 81)( 2, 27, 66,100, 82, 7, 26, 70, 92, 87, 6, 30, 62,
97, 86, 10, 22, 67, 96, 90)( 3, 24, 69, 98, 83, 4, 29, 68, 93, 84,
9, 28, 63, 94, 89, 8, 23, 64, 99, 88)( 5, 25, 65, 95, 85)
( 11, 41, 51, 31, 71)( 12, 47, 56, 40, 72, 17, 46, 60, 32, 77, 16, 50,
52, 37, 76, 20, 42, 57, 36, 80)( 13, 44, 59, 38, 73, 14, 49, 58, 33,
74, 19, 48, 53, 34, 79, 18, 43, 54, 39, 78)( 15, 45, 55, 35, 75),
( 1, 22, 18, 35, 49, 66, 97, 10, 82, 13, 75, 44, 56, 91, 30, 88, 33,
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28, 38, 39, 69, 67, 7)( 3, 72, 14, 55, 41, 26, 98, 40, 89, 63, 77,
4, 52, 11, 25, 48, 36, 99, 70, 87)( 5, 42, 16, 95, 50, 86, 93, 80,
84, 53, 71, 24, 58, 31, 29, 68, 37, 9, 62, 17)( 6, 92, 20, 85, 43,
76, 94, 60, 81, 23, 78, 34, 59, 61, 27, 8, 32, 19, 65, 47) ] ],
[ 17, 518400, 0, "4c", [ [ 81, 1 ], [ 18, 1 ] ], 1, "Alt(6)^2.2^2",
[ "A", 6, 2 ],
[ ( 1, 41, 45, 15, 20, 10)( 2, 81, 49, 25, 13,100)( 3, 91, 42, 85, 19, 30
)( 4, 31, 48, 65, 16, 80)( 5, 11, 50)( 6, 71, 44, 35, 18, 70)
( 7, 51, 47, 55, 17, 60)( 8, 61, 46, 75, 14, 40)( 9, 21, 43, 95,
12, 90)( 22, 83, 99)( 23, 93, 92, 82, 89, 29)( 24, 33, 98, 62, 86,
79)( 26, 73, 94, 32, 88, 69)( 27, 53, 97, 52, 87, 59)
( 28, 63, 96, 72, 84, 39)( 34, 38, 68, 66, 76, 74)( 36, 78, 64)
( 37, 58, 67, 56, 77, 54), ( 1, 12, 78, 94, 81, 42, 58, 24)
( 2, 18, 74, 91, 82, 48, 54, 21)( 3, 17, 80, 95, 83, 47, 60, 25)
( 4, 11, 72, 98, 84, 41, 52, 28)( 5, 13, 77,100, 85, 43, 57, 30)
( 6, 16, 76, 96, 86, 46, 56, 26)( 7, 20, 75, 93, 87, 50, 55, 23)
( 8, 14, 71, 92, 88, 44, 51, 22)( 9, 19, 79, 99, 89, 49, 59, 29)
( 10, 15, 73, 97, 90, 45, 53, 27)( 31, 62, 38, 64)( 32, 68, 34, 61)
( 33, 67, 40, 65)( 35, 63, 37, 70)( 36, 66)( 39, 69) ] ],
[ 18, 518400, 0, "4c", [ [ 81, 1 ], [ 18, 1 ] ], 1, "Alt(6)^2.4",
[ "A", 6, 2 ],
[ ( 1, 88, 76)( 2, 83, 77)( 3, 87, 72)( 4, 85, 80)( 5, 90, 74)
( 6, 81, 78)( 7, 82, 73)( 8, 86, 71)( 9, 89, 79)( 10, 84, 75)
( 11, 98, 66)( 12, 93, 67)( 13, 97, 62)( 14, 95, 70)( 15,100, 64)
( 16, 91, 68)( 17, 92, 63)( 18, 96, 61)( 19, 99, 69)( 20, 94, 65)
( 21, 38, 46)( 22, 33, 47)( 23, 37, 42)( 24, 35, 50)( 25, 40, 44)
( 26, 31, 48)( 27, 32, 43)( 28, 36, 41)( 29, 39, 49)( 30, 34, 45)
( 51, 58, 56)( 52, 53, 57)( 54, 55, 60),
( 1, 25, 37, 52, 8, 65, 33, 72, 6, 15, 34, 92, 9, 85, 40, 42)
( 2, 5, 35, 32)( 3, 75, 36, 12, 4, 95, 39, 82, 10, 45, 31, 22, 7,
55, 38, 62)( 11, 24, 97, 59, 88, 70, 43, 71, 26, 17, 54, 98, 69, 83,
80, 46)( 13, 74, 96, 19, 84,100, 49, 81, 30, 47, 51, 28, 67, 53, 78,
66)( 14, 94, 99, 89, 90, 50, 41, 21, 27, 57, 58, 68, 63, 73, 76, 16)
( 18, 64, 93, 79, 86, 20, 44, 91, 29, 87, 60, 48, 61, 23, 77, 56) ] ],
[ 19, 518400, 0, "4c", [ [ 81, 1 ], [ 18, 1 ] ], 1, "Alt(6)^2.2^2",
[ "A", 6, 2 ],
[ ( 1, 20, 83, 96, 4, 17, 81,100, 3, 16, 84, 97)( 2, 12, 82, 92)
( 5, 18, 89, 95, 8, 19, 85, 98, 9, 15, 88, 99)( 6, 14, 87, 91, 10,
13, 86, 94, 7, 11, 90, 93)( 21, 50, 23, 46, 24, 47)( 22, 42)
( 25, 48, 29, 45, 28, 49)( 26, 44, 27, 41, 30, 43)( 31, 80, 53, 66,
34, 77, 51, 70, 33, 76, 54, 67)( 32, 72, 52, 62)( 35, 78, 59, 65,
38, 79, 55, 68, 39, 75, 58, 69)( 36, 74, 57, 61, 40, 73, 56, 64, 37,
71, 60, 63), ( 1, 63, 87, 40, 94, 46)( 2, 53, 85, 30, 98, 76)
( 3, 83, 90,100, 96, 6)( 4, 43, 81, 70, 97, 36)( 5, 23, 88, 80,
92, 56)( 7, 33, 84, 50, 91, 66)( 8, 73, 82, 60, 95, 26)
( 9, 13, 89, 20, 99, 16)( 10, 93, 86)( 11, 69, 17, 39, 14, 49)
( 12, 59, 15, 29, 18, 79)( 21, 68, 77, 32, 54, 45)( 22, 58, 75)
( 24, 48, 71, 62, 57, 35)( 25, 28, 78, 72, 52, 55)( 27, 38, 74, 42,
51, 65)( 31, 64, 47)( 34, 44, 41, 61, 67, 37) ] ],
[ 20, 1036800, 0, "4c", [ [ 81, 1 ], [ 18, 1 ] ], 1, "Alt(6)^2.D_8",
[ "A", 6, 2 ],
[ ( 1, 46, 34, 88, 13, 30, 95, 79, 67, 52)( 2, 6, 36, 38, 18, 20,100, 99,
69, 62)( 3, 26, 35, 78, 17, 60, 91, 49, 64, 82)( 4, 86, 33, 28, 15,
80, 97, 59, 61, 42)( 5, 76, 37, 58, 11, 50, 94, 89, 63, 22)
( 7, 56, 31, 48, 14, 90, 93, 29, 65, 72)( 8, 16, 40, 98, 19, 70, 92,
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( 9, 82, 60,115)( 10, 87, 98, 67)( 12,106, 40, 45)( 13, 51,110, 21)
( 14, 78, 46, 86)( 16, 97)( 17,104,108, 74)( 18, 22, 42, 68)
( 19, 93, 85, 25)( 20, 48, 66, 81)( 24, 75)( 26, 54, 96, 83)
( 28, 35, 72, 70)( 29,100)( 31, 58, 33, 49)( 34,111, 95, 76)
( 41, 62, 80,117)( 43, 69, 53,114)( 50, 55)( 52, 57, 84, 61)
( 63,103, 73,107)( 65, 94)( 71, 92)( 77, 90, 99, 79),
( 1,115, 83)( 2, 95, 98, 66, 68, 46, 60, 11,106)( 3, 34,114,111, 85,
20, 50, 30, 61, 28, 47, 62, 58, 73, 16,105, 81, 63)( 4, 99, 55, 64,
19, 53, 10, 88, 51)( 5, 22, 72, 79, 17,116, 41, 44, 14, 23, 94, 9,
48,117, 90, 67, 43, 59)( 6, 93, 18)( 7, 13, 71, 15, 35, 54, 25,
37, 24,107,103, 12, 82, 52, 65, 70, 91, 42)( 8,113, 76, 92,108, 33,
86, 77, 45, 74, 21, 69, 26, 78, 87, 49,100, 75)( 27,102, 84, 32, 38,
109, 36,101,110)( 29,104, 80, 31, 39, 96, 57, 97,112)( 40, 56, 89) ]
],
[4, Factorial(117)/2,1,"2",[[116,1]],115, "Alt(117)", ["A",117, 1], "Alt"],
[5, Factorial(117),0,"2",[[116, 1]],117, "Sym(117)", ["A",117, 1], "Sym"]];
PRIMGRP[118]:=
[[1, Factorial(118)/2,1,"2",[[117,1]],116, "Alt(118)", ["A",118, 1], "Alt"],
[2, Factorial(118),0,"2",[[117, 1]],118, "Sym(118)", ["A",118, 1], "Sym"]];
PRIMGRP[119]:=
[[ 1, 197406720, 1, "2", [ [ 64, 1 ], [ 54, 1 ] ], 1, "O-(8, 2)",
[ "2D", [ 4, 2 ], 1 ],
[ ( 1, 2)( 3, 5)( 4, 7)( 6, 10)( 8, 12)( 9, 13)( 14, 19)( 15, 20)
( 16, 22)( 17, 23)( 18, 25)( 24, 31)( 26, 33)( 27, 34)( 28, 36)
( 29, 38)( 30, 39)( 35, 45)( 37, 46)( 41, 48)( 42, 50)( 43, 51)
( 44, 53)( 47, 57)( 49, 59)( 52, 62)( 54, 64)( 55, 65)( 56, 67)
( 58, 70)( 60, 73)( 61, 74)( 63, 77)( 66, 80)( 68, 82)( 69, 75)
( 71, 84)( 72, 85)( 76, 88)( 78, 90)( 79, 91)( 81, 94)( 83, 97)
( 86,100)( 87,101)( 89,102)( 92,104)( 93,105)( 95,103)( 96,106)
( 99,107)(108,114)(109,115)(110,112)(113,117)(118,119),
( 1, 3, 6)( 2, 4, 8)( 5, 9, 14)( 7, 11, 16)( 10, 15, 21)
( 12, 17, 24)( 13, 18, 26)( 19, 27, 35)( 20, 28, 37)( 22, 29, 36)
( 23, 30, 40)( 25, 32, 42)( 31, 41, 49)( 33, 43, 52)( 34, 44, 54)
( 38, 39, 47)( 45, 55, 66)( 46, 56, 68)( 48, 58, 71)( 50, 60, 65)
( 51, 61, 75)( 53, 63, 78)( 57, 69, 73)( 59, 72, 86)( 62, 76, 89)
( 64, 79, 92)( 67, 81, 95)( 70, 83, 98)( 74, 87, 77)( 80, 93, 88)
( 82, 96, 97)( 84, 99,108)( 85, 90,103)( 91,101,110)( 94,100,109)
(102,111,104)(105,112,116)(106,113,118)(114,115,117) ] ],
[ 2, 394813440, 0, "2", [ [ 64, 1 ], [ 54, 1 ] ], 1, "PSO-(8, 2)",
[ "2D", [ 4, 2 ], 1 ],
[ ( 3, 25)( 8, 21)( 9, 36)( 12, 74)( 15, 22)( 16, 63)( 17, 52)( 19, 77)
( 24, 60)( 27, 59)( 28, 32)( 30, 39)( 35, 86)( 40, 75)( 43, 71)
( 47, 57)( 48, 64)( 49,102)( 50, 95)( 51,101)( 68,116)( 80,109)
( 81,112)( 84, 87)( 94,106)( 97,107)( 98,103)(104,110),
( 1,103, 72, 21, 9, 92, 16, 19, 58, 52, 62, 70, 75, 82)
( 2, 20, 38, 44, 17, 61, 98)( 3, 77, 88, 13, 68,105, 57)
( 4, 95, 31,116,111, 6, 45, 12, 34, 64, 89, 86, 49,106)
( 5,115, 48, 46, 29, 79, 50)( 7, 99, 8, 84,110,119, 74)
( 10, 47, 22, 65, 39, 73, 97,104, 55, 66, 27, 14, 60, 76)
( 11, 78, 24, 96, 40, 23, 59)( 15, 53, 37,107, 43,102, 81)
( 18, 26,117, 33,118, 32,112, 25, 51, 87, 71,109, 42, 85)
( 28, 94, 56, 41, 35, 80, 93)( 30, 91, 69,114, 54,100, 90)
( 36,108, 67,113, 83, 63,101) ] ],
[3, Factorial(119)/2,1,"2",[[118,1]],117, "Alt(119)", ["A",119, 1], "Alt"],
[4, Factorial(119),0,"2",[[118, 1]],119, "Sym(119)", ["A",119, 1], "Sym"]];
PRIMGRP[120]:=
[[ 1, 5040, 0, "2", [ [ 14, 2 ], [ 7, 1 ], [ 42, 1 ], [ 21, 2 ] ], 1,
"Sym(7)", [ "A", 7, 1 ],
[ ( 1, 2, 4, 6, 9, 14, 3)( 5, 8, 12, 19, 29, 44, 64)
( 7, 11, 17, 26, 39, 58, 61)( 10, 16, 24, 37, 56, 78, 99)
( 13, 21, 32, 49, 70, 93, 80)( 15, 23, 35, 54, 76, 96,109)
( 18, 28, 42, 62, 84, 48, 25)( 20, 31, 47, 68, 91,100, 50)
( 22, 34, 52, 74, 77, 98, 73)( 27, 41, 60, 83,103,110,119)
( 30, 46, 66, 89, 97,105, 88)( 33, 51, 72, 82,102,107,104)
( 36, 55, 43, 63, 40, 59, 81)( 38, 57, 79,101,113,111,112)
( 45, 65, 87, 94, 95,108,116)( 53, 75, 67, 90, 71, 85, 86)
( 69, 92,106,114,120,117,118), ( 1, 3)( 2, 5)( 4, 7)( 6, 10)
( 8, 13)( 9, 15)( 11, 18)( 12, 20)( 14, 22)( 16, 25)( 17, 27)
( 19, 30)( 21, 33)( 23, 36)( 24, 38)( 26, 40)( 28, 43)( 29, 45)
( 31, 48)( 32, 50)( 34, 53)( 35, 52)( 37, 54)( 39, 56)( 41, 61)
( 42, 62)( 44, 58)( 46, 67)( 47, 69)( 49, 71)( 51, 73)( 55, 77)
( 57, 80)( 59, 82)( 60, 79)( 63, 85)( 64, 86)( 65, 88)( 66, 81)
( 68, 83)( 70, 84)( 72, 89)( 74, 94)( 75, 95)( 76, 97)( 78,100)
( 87, 93)( 90,104)( 91,105)( 92,107)( 96,110)( 98,111)( 99,112)
(101,114)(102,106)(103,115)(108,117)(109,118)(113,119)(116,120) ] ],
[ 2, 181440, 1, "2", [ [ 56, 1 ], [ 63, 1 ] ], 1, "Alt(9)", [ "A", 9, 1 ],
[ ( 1, 2, 4, 8, 15, 27, 47)( 3, 6, 12, 22, 39, 64, 94)
( 5, 10, 19, 34, 20, 36, 58)( 7, 14, 25, 43, 38, 63, 92)
( 9, 17, 31, 53, 80, 91, 70)( 11, 21, 37, 62, 71, 98,112)
( 13, 24, 42, 67, 96,102,116)( 16, 29, 50, 75, 46, 61, 90)
( 18, 33, 57, 86, 23, 40, 59)( 26, 45, 56, 85, 97, 28, 41)
( 30, 52, 32, 55, 83,108, 79)( 35, 60, 88,104,114,117,107)
( 44, 69, 48, 73,101, 68, 81)( 49, 74,103, 78,106, 95, 82)
( 51, 77, 87, 93, 65, 84, 54)( 66, 76,105,100,115,111,120)
( 72, 99,113,109,118,110,119), ( 1, 3, 7)( 2, 5, 11)( 4, 9, 18)
( 6, 13, 22)( 8, 16, 30)( 10, 20, 37)( 12, 23, 41)( 14, 26, 46)
( 15, 28, 49)( 17, 32, 56)( 19, 35, 61)( 21, 38, 43)( 24, 27, 48)
( 25, 44, 70)( 29, 51, 78)( 31, 54, 82)( 33, 58, 75)( 34, 59, 87)
( 36, 45, 71)( 39, 65, 95)( 40, 66, 57)( 42, 68, 97)( 47, 72,100)
( 50, 76, 90)( 52, 79, 67)( 53, 81,107)( 55, 84,110)( 60, 89, 77)
( 62, 91, 80)( 63, 93, 69)( 64, 83,109)( 73,102,101)( 74,104, 92)
( 85,111,119)( 86,106, 88)( 94, 99,114)( 96,105, 98)(103,117,108)
(112,120,116)(113,115,118) ] ],
[ 3, 4080, 1, "2", [ [ 17, 7 ] ], 1, "PSL(2, 16)", [ "L", [ 2, 16 ], 1 ],
[ ( 1, 40)( 2, 78)( 3,118)( 4,112)( 5, 94)( 6,102)( 7, 88)( 8, 12)
( 9, 85)( 10, 91)( 11, 84)( 13, 19)( 14,114)( 15, 18)( 17,108)
( 20, 66)( 21, 47)( 22, 53)( 23,106)( 24, 41)( 25, 46)( 26, 58)
( 27,105)( 28, 57)( 29,115)( 31, 90)( 32, 52)( 33, 49)( 34, 76)
( 35, 51)( 36, 43)( 37,103)( 39, 44)( 42, 56)( 45, 71)( 48, 60)
( 50, 59)( 54, 98)( 55, 72)( 61, 69)( 62,111)( 63,109)( 65, 83)
( 67, 74)( 68,104)( 70, 73)( 75, 96)( 77, 80)( 79, 95)( 82, 99)
( 86, 93)( 87,100)( 92,113)( 97,107)(101,110)(117,120),
( 1,116, 18)( 2, 56,113)( 3, 70, 58)( 4, 65,105)( 5, 42, 43)
( 6, 50, 27)( 7, 16, 69)( 8, 89,106)( 9, 28, 55)( 10, 91, 59)
( 11, 98, 63)( 12, 92,120)( 13, 44, 76)( 14,100, 21)( 15,104, 94)
( 17, 82, 37)( 19, 74, 62)( 20,103, 67)( 22,112, 31)( 23, 40, 87)
( 24, 78, 34)( 25,119, 83)( 26, 96, 46)( 29, 90,117)( 30,107, 72)
( 32, 33, 97)( 35,114, 52)( 36, 79, 66)( 38,111, 81)( 39, 45,108)
( 41, 75, 84)( 47, 51, 54)( 48, 71, 80)( 49, 86, 95)( 53,109, 64)
( 57,102, 88)( 60,101, 73)( 61, 93,118)( 68, 85, 77)( 99,110,115) ] ],
[ 4, 8160, 0, "2", [ [ 34, 2 ], [ 17, 3 ] ], 1, "PSL(2, 16).2",
[ "L", [ 2, 16 ], 1 ],
[ ( 1, 82)( 2,110)( 3, 73)( 4,102)( 5, 41)( 6, 60)( 7,108)( 8, 63)
( 9, 14)( 10,117)( 11, 33)( 12, 97)( 13, 72)( 15, 92)( 16, 96)
( 17,120)( 18, 94)( 19, 67)( 20,111)( 21, 54)( 22, 74)( 23,106)
( 24,113)( 25, 32)( 26, 59)( 27, 57)( 28, 78)( 29, 30)( 31, 46)
( 34, 87)( 35, 83)( 36, 48)( 37, 49)( 38, 80)( 39, 84)( 40, 99)
( 42, 65)( 43,112)( 44,103)( 45, 71)( 47, 85)( 50, 66)( 51,104)
( 52, 61)( 53, 55)( 56, 68)( 58, 62)( 64, 93)( 69, 90)( 70, 76)
( 75, 81)( 77,119)( 79,107)( 86, 89)( 88, 91)( 95,109)( 98,114)
(100,118)(101,105)(115,116), ( 1, 44, 19, 34)( 2, 77, 88, 50)
( 3,110, 56, 31)( 4, 83, 21, 14)( 5, 93, 55, 97)( 6, 48, 41, 42)
( 7,103, 66,102)( 8, 49, 17, 18)( 9, 87, 95, 30)( 10, 80, 62, 26)
( 11,109)( 12, 54, 47,115)( 13, 64, 58, 67)( 15, 68, 94, 23)
( 16, 69,104, 32)( 20, 38,101, 28)( 22,111, 39, 79)( 24, 36, 82, 89)
( 25, 84, 99,100)( 29, 63,116, 45)( 33, 52, 75, 81)( 35, 61)
( 37, 96, 46, 72)( 40, 60, 59, 86)( 43, 85, 51,113)( 53, 90, 65, 78)
( 57,105, 70, 74)( 71,108,119,120)( 76,118,114,107)( 91,112, 92,117)
] ],
[ 5, 16320, 0, "2", [ [ 34, 1 ], [ 68, 1 ], [ 17, 1 ] ], 1, "PSigmaL(2, 16)",
[ "L", [ 2, 16 ], 1 ],
[ ( 1, 52)( 2,109)( 3,101)( 4, 13)( 5, 72)( 6, 74)( 7, 45)( 8, 47)
( 9, 78)( 10,111)( 11, 94)( 12, 33)( 14, 40)( 15, 63)( 16, 39)
( 17, 83)( 18, 35)( 19, 50)( 20,102)( 21, 87)( 22, 79)( 23,100)
( 24, 28)( 25, 37)( 26, 71)( 27, 62)( 29, 84)( 30, 43)( 31, 66)
( 32, 92)( 34, 55)( 36,112)( 38, 91)( 41,117)( 42,107)( 44,105)
( 46, 80)( 48, 96)( 49, 85)( 51,106)( 53, 56)( 54, 89)( 57,103)
( 58, 73)( 59, 81)( 60, 70)( 61,110)( 64,113)( 65, 76)( 67, 88)
( 68, 86)( 69,108)( 75, 90)( 77, 95)( 82,119)( 93, 99)( 97,120)
( 98,104)(114,116)(115,118),
( 1, 86, 74, 49,106, 44,110, 53, 70, 8, 98, 3)( 2,114, 65, 15, 68,
73, 77,118, 60, 47, 54, 27)( 4, 95,105, 28,100, 23, 5, 82, 57, 64,
51,115)( 6, 75, 94, 62, 26, 18, 79,108, 12,103, 7, 17)
( 9,117, 83, 58, 37, 43, 24, 72, 97,101, 92, 84)( 10, 59,113, 42, 11,
55,102, 90, 99, 22, 35, 21)( 13, 25, 76, 14, 89, 34, 20, 85,107, 93,
87, 56)( 16, 19, 52, 39, 50, 32, 29, 31,119, 48, 88, 63)
( 30, 61,111, 67, 40,104, 36,109, 41, 38, 78,116)( 33, 96, 81, 45, 91,
66,120,112, 71, 69, 46, 80) ] ],
[ 6, 20160, 1, "2", [ [ 56, 1 ], [ 42, 1 ], [ 21, 1 ] ], 1, "PSL(3, 4)",
[ "L", [ 3, 4 ], 1 ],
[ ( 1, 58)( 2, 95)( 3, 34)( 4,106)( 5, 36)( 6, 57)( 7, 13)( 8, 31)
( 9, 56)( 10,104)( 11, 39)( 12, 30)( 14,117)( 15, 85)( 16, 53)
( 17, 73)( 18, 45)( 19, 77)( 20, 81)( 21, 28)( 22, 86)( 23, 26)
( 24,114)( 27, 55)( 29,100)( 32, 70)( 33, 91)( 35, 62)( 37, 46)
( 38, 97)( 40, 79)( 43,105)( 44,110)( 47, 50)( 48, 92)( 49, 59)
( 51, 94)( 52, 72)( 54, 76)( 60,112)( 61, 88)( 63, 98)( 64, 82)
( 65,115)( 66,109)( 68,118)( 69, 83)( 71,101)( 74,116)( 78, 84)
( 80, 90)( 87,108)( 93, 99)( 96,103)(102,111)(107,120),
( 1, 75, 86,117)( 2, 30, 66, 13)( 3, 38, 94,104)( 4, 42, 28,107)
( 5, 20, 92, 15)( 6, 22, 55, 95)( 7, 33, 72, 62)( 8, 64,119,108)
( 9, 37, 41,106)( 10, 18,118,112)( 11, 36,100, 35)( 12, 24,115, 25)
( 14, 45,111, 68)( 16,109, 82, 69)( 17,110, 27, 39)( 19, 98, 48, 67)
( 21, 50, 99, 93)( 23,102)( 26, 73, 56, 85)( 29, 49, 84, 53)
( 31, 91,116, 77)( 32, 54, 59,120)( 40, 60, 63, 97)( 43, 74)
( 44, 51,101, 89)( 46, 96, 47,113)( 52, 61, 90,103)( 57, 83, 81, 58)
( 65, 70, 80, 87)( 71,105, 78,114) ] ],
[ 7, 40320, 0, "2", [ [ 56, 1 ], [ 42, 1 ], [ 21, 1 ] ], 1, "PSL(3, 4).2",
[ "L", [ 3, 4 ], 1 ],
[ ( 1, 36)( 3, 67)( 4, 64)( 5, 99)( 6, 54)( 7,118)( 8, 56)( 9, 21)
( 10,119)( 11, 57)( 12, 74)( 13, 94)( 14, 58)( 15,113)( 17, 33)
( 18,120)( 19, 43)( 22, 26)( 23, 24)( 27, 73)( 28, 76)( 29, 65)
( 30, 98)( 31, 39)( 32, 97)( 35, 89)( 37, 53)( 38, 88)( 40,110)
( 41,109)( 42, 95)( 46,101)( 47, 90)( 49, 51)( 50,117)( 59, 77)
( 61, 86)( 66,102)( 68,105)( 69, 81)( 70,114)( 72,107)( 75,111)
( 79,108)( 80, 93)( 82, 96)( 83, 84)( 92,100)(103,106),
( 1, 21, 8,119)( 2, 96, 40, 23)( 3, 92, 65, 10)( 4, 54, 79, 17)
( 5, 41, 35, 61)( 6, 22, 85, 69)( 7, 33, 51,112)( 9,110, 26,102)
( 11, 42, 89, 49)( 12, 75, 52, 84)( 13, 73,117, 87)( 14,103, 94, 56)
( 15,116, 16, 66)( 18, 67, 45, 50)( 19, 44, 91, 90)( 20, 93, 24, 83)
( 25,105, 82, 27)( 28, 78)( 29, 98, 30, 58)( 31, 72, 63,100)
( 32, 36, 43,118)( 34, 57, 71, 53)( 37, 81,109,107)( 38, 86,104, 99)
( 39, 59)( 46, 48, 74, 97)( 47,113)( 55, 62, 70, 68)( 60, 95, 77,106)
( 64, 88)( 76, 80,108,111)(101,114,115,120) ] ],
[ 8, 40320, 0, "2", [ [ 56, 1 ], [ 42, 1 ], [ 21, 1 ] ], 1, "PSL(3, 4).2",
[ "L", [ 3, 4 ], 1 ],
[ ( 1, 23)( 2,120)( 3,111)( 4, 88)( 6, 13)( 7, 17)( 8,103)( 9, 99)
( 10, 40)( 11,114)( 12, 91)( 14, 63)( 15,105)( 16,117)( 18, 94)
( 19,104)( 20, 49)( 21,113)( 22, 39)( 24, 29)( 25, 54)( 26, 95)
( 27, 31)( 28, 52)( 30, 75)( 32, 46)( 33,119)( 34, 48)( 35,116)
( 36, 67)( 37,102)( 38, 60)( 41, 50)( 43,115)( 44, 97)( 45, 86)
( 47, 76)( 51,100)( 53, 98)( 56, 58)( 59, 90)( 61,109)( 62, 80)
( 64, 74)( 65, 66)( 69, 70)( 71,108)( 72, 89)( 77, 78)( 79,101)
( 81, 82)( 83, 92)( 84, 87)( 85,106)( 93,107),
( 1,110, 48, 22)( 2, 41, 83, 38)( 3, 8,114, 79)( 4, 75, 37, 6)
( 5, 82, 25, 42)( 7, 84,120, 69)( 9, 32, 78, 73)( 10, 54, 94, 23)
( 11,113,119, 12)( 13, 53, 74,105)( 14, 20,112, 19)( 15, 33, 80, 56)
( 16, 95, 96, 91)( 17,108,111, 24)( 18, 21, 89, 30)( 26, 98, 88, 60)
( 27, 81, 40, 34)( 28,100)( 29, 52, 45, 39)( 31,102, 65, 85)
( 35, 36,118, 49)( 43, 77, 58, 87)( 44, 61,107, 46)( 47, 68, 64, 67)
( 50, 62)( 51, 97, 63,109)( 55,117, 71,104)( 57, 70, 93, 90)
( 76, 92,106,103)( 86,101,116,115) ] ],
[ 9, 40320, 0, "2", [ [ 56, 1 ], [ 42, 1 ], [ 21, 1 ] ], 1, "PSL(3, 4).2",
[ "L", [ 3, 4 ], 1 ],
[ ( 1,104)( 2,101)( 3, 5)( 4, 71)( 6, 87)( 7, 91)( 9,103)( 10,102)
( 11, 97)( 12,114)( 14, 64)( 15, 29)( 16,105)( 17, 44)( 18,109)
( 19,113)( 20, 48)( 21, 38)( 22, 40)( 23, 60)( 24, 54)( 25,117)
( 26, 94)( 27, 79)( 28,120)( 30, 68)( 31, 52)( 34, 81)( 35, 39)
( 37,116)( 41, 43)( 42, 51)( 47, 63)( 49, 78)( 50, 90)( 53, 69)
( 55, 89)( 56, 59)( 57,100)( 58,115)( 61, 80)( 62, 95)( 65, 76)
( 66, 74)( 67, 83)( 70, 93)( 72, 73)( 75,112)( 77, 82)( 85, 98)
( 86,119)( 88,108)(106,107)(111,118),
( 1, 44, 68, 96,109, 34)( 2, 17,118, 5, 16, 93)( 3, 98,101, 60,110,
15)( 4,111, 67,117, 79, 13)( 6, 57,114, 24, 47,104)
( 7, 11,100, 29,102, 23)( 8,115, 48, 75, 86, 51)( 9, 97, 94, 37,
78,116)( 12, 45,103, 73, 88, 20)( 14,119, 39, 76, 26, 32)
( 18, 92, 53, 33, 27,112)( 19, 89,106, 90, 54, 41)( 21, 66, 49, 62,
82, 99)( 22, 83, 63,107, 64, 91)( 25, 95, 74, 81,108, 35)
( 28, 52, 85, 56,120,113)( 30, 31, 61, 59, 71, 69)( 36, 42, 55, 43,
58, 46)( 38,105, 87)( 40, 70, 77)( 65, 84, 72) ] ],
[ 10, 80640, 0, "2", [ [ 56, 1 ], [ 42, 1 ], [ 21, 1 ] ], 1, "PSL(3, 4).2^2",
[ "L", [ 3, 4 ], 1 ],
[ ( 1, 2)( 3, 5)( 6, 9)( 7, 11)( 8, 13)( 10, 16)( 14, 20)( 15, 22)
( 18, 26)( 19, 28)( 21, 31)( 23, 27)( 24, 35)( 25, 37)( 29, 40)
( 30, 42)( 33, 45)( 34, 47)( 38, 52)( 39, 54)( 41, 56)( 43, 59)
( 48, 64)( 49, 66)( 51, 68)( 55, 72)( 57, 75)( 60, 79)( 61, 62)
( 63, 81)( 65, 82)( 67, 83)( 70, 85)( 73, 89)( 74, 78)( 76, 77)
( 80, 95)( 84, 99)( 87,103)( 91, 97)( 93, 98)( 94,109)( 96,110)
(100,112)(101,104)(102,105)(111,118)(113,120)(116,117),
( 1, 3, 6, 10, 17, 25)( 2, 4, 7, 12, 18, 27)( 5, 8, 14, 21, 32,
44)( 9, 15, 23, 34, 48, 65)( 13, 19, 29, 41, 57, 76)
( 16, 24, 36, 50, 59, 78)( 20, 30, 43, 60, 80, 96)( 22, 33, 46, 62,
47, 63)( 26, 38, 53, 66, 64, 31)( 28, 39, 55, 73, 90, 99)
( 35, 49, 67, 75, 92,107)( 37, 51, 69, 72, 88,104)( 42, 58, 77, 93,
108,118)( 45, 61, 68, 84,100,113)( 52, 70, 86,102,115,120)
( 54, 71, 87, 83, 79, 94)( 56, 74, 91,106,117,109)( 81, 97,103)
( 82, 98,111)( 85,101,114)( 89,105,116,110,112,119) ] ],
[ 11, 40320, 0, "2", [ [ 56, 1 ], [ 14, 1 ], [ 28, 1 ], [ 21, 1 ] ], 1,
"Sym(8)", [ "A", 8, 1 ],
[ ( 1, 2, 4, 7)( 3, 6, 10, 14, 21, 32, 48, 57)( 5, 9, 13, 19, 29,
44, 66, 89)( 8, 12, 17, 26, 39, 58, 82, 85)( 11, 16, 24, 25, 38,
56, 72, 95)( 15, 23, 35, 53, 27, 41, 61, 83)( 18, 28, 42, 63)
( 20, 31, 46, 68, 91,110,108,118)( 22, 34, 51, 73, 49, 71, 94, 30)
( 33, 50)( 36, 54, 77, 64, 86, 43, 65, 87)( 37, 55, 79,101)
( 40, 60, 78,100)( 45, 67, 90,106)( 47, 70, 93,111, 88,107,116, 98)
( 52, 75, 97, 76, 99,114,115,117)( 62, 84,104,112,120, 81,103,105)
( 69, 92, 80,102, 96,113,109,119),
( 1, 3)( 2, 5)( 4, 8)( 6, 11)( 7, 9)( 10, 15)( 12, 18)( 13, 20)
( 14, 22)( 16, 25)( 17, 27)( 19, 30)( 21, 33)( 23, 36)( 24, 37)
( 26, 40)( 28, 43)( 29, 45)( 31, 47)( 32, 49)( 34, 52)( 35, 48)
( 38, 57)( 39, 59)( 41, 62)( 42, 64)( 44, 60)( 46, 69)( 50, 72)
( 51, 74)( 53, 76)( 54, 78)( 55, 80)( 56, 81)( 58, 67)( 61, 82)
( 63, 85)( 65, 88)( 66, 71)( 68, 86)( 70, 77)( 73, 96)( 75, 98)
( 79, 94)( 83, 92)( 84,105)( 87,106)( 89,108)( 90,109)( 91, 99)
( 93,111)( 95,112)( 97,101)(100,115)(102,116)(103,113)(104,117)
(107,110)(114,119)(118,120) ] ],
[ 12, 979200, 1, "2", [ [ 68, 1 ], [ 51, 1 ] ], 1, "PSp(4, 4)",
[ "B", [ 2, 4 ], 1 ],
[ ( 1,115, 59, 18, 29, 46,103, 94, 36, 19,119, 78, 57, 2,110, 64, 34)
( 3,101, 43, 32, 56,106, 91, 21, 14,116,100, 5, 84, 49, 79, 61, 24)
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[3, Factorial(132)/2,1,"2",[[131,1]],130, "Alt(132)", ["A",132, 1], "Alt"],
[4, Factorial(132),0,"2",[[131, 1]],132, "Sym(132)", ["A",132, 1], "Sym"]];
PRIMGRP[133]:=
[[ 1, 212427600, 1, "2", [ [ 132, 1 ] ], 2, "PSL(3, 11)",
[ "L", [ 3, 11 ], 1 ],
[ ( 4, 74, 66,106,112)( 5, 60,113,126,107, 19, 67, 23, 75,102)
( 6, 71, 54, 40, 13, 20, 49, 41,116, 33)( 7, 57, 9, 45, 28, 51,109,
48, 81, 83)( 8, 96, 10, 46,120, 36,104, 78, 25,122)( 11, 30,118, 70,
114, 62, 35,132, 77, 24)( 12,103, 43,128,115, 29,108, 72, 80, 82)
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38, 64, 55)( 16, 44, 27, 32, 95, 90, 91, 39, 34, 56)( 17,124,111, 21,
58, 73,105, 65,100,133)( 18,125, 59,101, 22)( 26,110, 94, 89, 69,130,
119, 37,131, 79)( 47, 85, 61, 92, 63, 93,123, 68,129, 84),
( 1, 21,103, 19, 18, 58, 8,122, 35, 89, 62, 20, 60, 59,100, 95,109,
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61, 23, 22, 65, 30, 15, 39, 11, 99, 90, 48, 40, 94,116, 55, 80, 45,
119, 93, 49,104,127,102,101,111, 51, 56,118, 77,114, 75, 74,133, 47,
98, 91, 26, 42,128, 24,126,125, 73, 88,132, 9, 53, 32, 34, 29, 46,
10, 96, 79, 50, 43, 16, 70, 81,121, 97, 52,120, 7,108, 5, 4, 3,
2)( 6, 67, 66,124, 33,131, 83, 87, 44, 38, 57, 69) ] ],
[2, Factorial(133)/2,1,"2",[[132,1]],131, "Alt(133)", ["A",133, 1], "Alt"],
[3, Factorial(133),0,"2",[[132, 1]],133, "Sym(133)", ["A",133, 1], "Sym"]];
PRIMGRP[134]:=
[[1, Factorial(134)/2,1,"2",[[133,1]],132, "Alt(134)", ["A",134, 1], "Alt"],
[2, Factorial(134),0,"2",[[133, 1]],134, "Sym(134)", ["A",134, 1], "Sym"]];
PRIMGRP[135]:=
[[ 1, 1451520, 1, "2", [ [ 56, 1 ], [ 14, 1 ], [ 64, 1 ] ], 1, "PSp(6, 2)",
[ "B", [ 3, 2 ], 1 ],
[ ( 1, 2)( 3, 5)( 4, 7)( 6, 10)( 8, 13)( 9, 15)( 11, 18)( 12, 20)
( 14, 23)( 16, 26)( 17, 28)( 19, 31)( 21, 34)( 22, 36)( 24, 39)
( 25, 40)( 27, 43)( 30, 46)( 32, 47)( 33, 48)( 35, 51)( 37, 54)
( 38, 56)( 41, 59)( 42, 61)( 49, 65)( 50, 67)( 52, 70)( 53, 71)
( 55, 58)( 62, 79)( 63, 81)( 64, 83)( 66, 86)( 68, 89)( 69, 91)
( 72, 94)( 73, 76)( 75, 97)( 78,100)( 80,103)( 82,101)( 84,106)
( 85,108)( 87,111)( 88,113)( 92,110)( 93,109)( 95,112)( 96,117)
( 98,119)( 99,121)(102,123)(104,122)(105,124)(114,125)(116,131)
(120,128)(127,133)(129,134),
( 1, 3, 6, 11, 19, 32)( 2, 4, 8, 14, 24, 31)( 5, 9, 16, 27, 26,
42)( 7, 12, 21, 35, 52, 61)( 10, 17, 29, 45, 63, 82)
( 13, 22, 37, 55, 73, 95)( 15, 25, 41, 60, 78,101)( 18, 30)
( 20, 33, 49, 66, 87,112)( 23, 38, 57, 75, 98,120)( 28, 44, 62, 80,
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( 40, 58, 76, 99, 70, 43)( 48, 64, 84,107,127,123)( 51, 69, 92,116,
71, 93)( 54, 59, 77, 97,119,131)( 56, 74, 96,118,133,103)
( 65, 85,109, 67, 88,114)( 81,104, 89,115,130,135)( 83,105,125)
( 91,111,121)( 94,108)(100,122,113,129,106,126)(117,132)(124,134) ] ],
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( 5, 15, 43,106,131,121, 22, 65, 92, 99, 87,125)( 6, 60, 71, 35, 30,
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114,132)( 16, 79,107,108, 41, 56,105, 40,103, 26, 37, 27)
( 17, 78, 72, 67,128, 32, 34, 45, 19, 57,135, 51)( 24,110,119, 29, 63,
129)( 33, 68, 42)( 36, 85, 98,126, 84, 52)( 44, 77, 69,109,113,122,
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( 1, 58, 76, 21, 49, 55, 50, 73, 31, 16, 22, 25,134,123,122)
( 2, 52, 74,119,131,115,133, 40, 83, 41, 6, 59, 99,124, 51)
( 3,108, 88, 86, 18, 77, 23, 9, 39, 12, 17, 53, 11,109, 84)
( 4, 75, 33, 43,121, 61, 44, 56, 36, 47, 20, 98,101, 80,135)
( 5, 13,104,102, 62, 8, 46, 48, 72, 28,100, 97, 54,112, 14)
( 7,105,107, 19,118,127, 81, 68, 30, 95, 87,120,103, 37, 32)
( 10, 67,117, 85, 79,129, 89, 26, 63, 45,114,126, 91, 42,128)
( 15, 65, 38, 93,110,130,125, 60, 34, 96, 78,106, 90,132, 27)
( 24, 71,116, 57, 35, 92,113, 69, 29, 70,111, 64, 66, 82, 94) ] ],
[ 3, 348364800, 0, "2", [ [ 70, 1 ], [ 64, 1 ] ], 1, "PSO+(8, 2)",
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[ ( 1, 70, 6, 82, 13, 37, 45, 23, 95, 64,133, 25)( 2, 40, 43, 55, 65, 87,
80,104,118, 26, 83, 59)( 3, 33, 47, 98, 96,126)( 4, 77, 12,135, 86,
88,100, 61, 18, 39, 28,117)( 5, 14, 76, 50,115,123)( 7, 79, 91,106,
93, 60, 78, 11,108,105, 67, 75)( 8, 27, 62, 72, 22,127, 17,103,121,
81, 35, 69)( 9, 30, 99,114,120, 15, 94, 10, 54, 58, 57, 92)
( 16, 41, 89, 97,102,131,132, 38, 49,116,113, 44)( 19, 56, 32)
( 20, 31,134,109, 34, 90)( 21, 63, 73, 36,101,129)( 24,130,110,125,
119, 48, 52, 46, 42, 71, 29, 74)( 51,122,107)( 53, 68,128, 85)
( 66,112,111,124), ( 1, 38, 39)( 2, 74, 43, 54, 97, 91,101,124, 31,
3,130, 50)( 4, 73, 24)( 5, 15, 76, 6, 26,111, 83, 18,132, 34,
28, 14)( 7, 47, 9, 51)( 8, 96,109, 22, 16,134, 23, 66, 99, 10,
21, 80)( 11, 53,102)( 12, 48, 17,116, 46,114,112, 92,106, 86, 55, 35
)( 13, 69, 87,129, 40, 85,120,100, 60, 84, 37, 52)( 19, 95, 58, 56,
107,105,108,122,103,118, 65, 72)( 20,128, 42,113, 75,131, 90,135, 29,
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( 27, 81, 30, 70)( 32, 68,127)( 41, 67,121)( 57,119, 77,133,110,117)
( 63,123, 78, 98,115, 94)( 71, 79, 89) ] ],
[4, Factorial(135)/2,1,"2",[[134,1]],133, "Alt(135)", ["A",135, 1], "Alt"],
[5, Factorial(135),0,"2",[[134, 1]],135, "Sym(135)", ["A",135, 1], "Sym"]];
PRIMGRP[136]:=
[[ 1, 2448, 1, "2", [ [ 18, 4 ], [ 9, 7 ] ], 1, "PSL(2, 17)",
[ "L", [ 2, 17 ], 1 ],
[ ( 1,101)( 2, 79)( 3, 93)( 4, 59)( 6, 98)( 7, 50)( 8, 85)( 9, 75)
( 10, 31)( 11,104)( 12, 68)( 13, 46)( 14,129)( 15,100)( 16, 91)
( 17, 44)( 18, 77)( 19, 83)( 20, 52)( 21, 71)( 22,103)( 23, 87)
( 24,106)( 25, 95)( 26, 33)( 27,123)( 28,119)( 29, 38)( 30, 42)
( 32, 64)( 34, 65)( 35, 62)( 37, 90)( 40,130)( 41,121)( 43,117)
( 45,110)( 47, 56)( 48, 67)( 49,116)( 51, 96)( 53,102)( 54, 92)
( 55,127)( 57, 89)( 58,120)( 60,114)( 61, 69)( 63, 70)( 66, 99)
( 72,126)( 76, 81)( 78,131)( 80,133)( 84, 94)( 97,112)(105,125)
(107,109)(108,124)(111,128)(113,132)(115,134)(118,136)(122,135),
( 1, 15, 12)( 2, 49, 93)( 3, 20, 48)( 4,120,129)( 5, 32, 61)
( 6,125, 67)( 7, 38, 36)( 8, 23,117)( 9, 87, 22)( 10,103,104)
( 11, 90,102)( 13, 60, 14)( 16, 35, 66)( 17, 43, 44)( 18, 75, 98)
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( 28, 76,105)( 29,134, 89)( 30,108,110)( 31, 69, 45)( 34,106, 63)
( 37,126,133)( 39, 71, 80)( 40, 59,135)( 41, 88,122)( 42, 68,121)
( 46, 99, 55)( 47,112,131)( 50, 72, 94)( 52, 73, 78)( 53, 81,114)
( 54,100,118)( 58, 84,136)( 62,107, 70)( 64,127,109)( 65, 96,123)
( 82,101, 91)( 83,113,111)( 85,128, 92)( 86,124,119)( 97,130,132) ] ],
[ 2, 4896, 0, "2", [ [ 18, 7 ], [ 9, 1 ] ], 1, "PGL(2, 17)",
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[ ( 2, 46)( 3, 45)( 4, 69)( 6, 70)( 7,107)( 8,124)( 9, 53)( 10, 47)
( 13, 66)( 14,105)( 15, 98)( 16,125)( 17,110)( 18,127)( 19, 94)
( 21, 51)( 22,112)( 23,111)( 24, 25)( 27, 37)( 28, 32)( 29, 31)
( 30,103)( 33,130)( 34,135)( 35,104)( 36,106)( 39, 75)( 40,122)
( 41,123)( 43, 76)( 44, 89)( 48, 81)( 49, 86)( 50, 54)( 52, 71)
( 55,134)( 56,115)( 57,114)( 58, 85)( 59, 83)( 60, 74)( 61, 73)
( 62,121)( 63,120)( 64, 84)( 65,128)( 67, 80)( 68, 79)( 72, 82)
( 77, 97)( 78,126)( 87,109)( 88,108)( 90, 99)( 91,116)( 93,132)
( 95,119)( 96,118)(100,131)(101,117)(102,113)(133,136),
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( 6, 44,130)( 7,126, 30)( 8,123, 24)( 9,113,106)( 10,136, 15)
( 11,125, 94)( 12, 48,131)( 13,122,111)( 14, 18,124)( 16, 58,134)
( 17, 83, 29)( 20, 92,104)( 21,110,103)( 22, 25,129)( 23, 73, 38)
( 26,114,120)( 28,127, 96)( 32,101, 34)( 33, 90,109)( 35, 59,116)
( 36, 77,105)( 39, 52,117)( 40, 76, 95)( 42, 89,118)( 43, 79, 98)
( 45,102, 54)( 46, 68, 49)( 50, 71,121)( 55, 56,108)( 57,128, 81)
( 61, 78, 82)( 62, 88,119)( 63, 75, 85)( 64, 66, 99)( 67,115, 70)
( 72, 86, 91)( 74, 80,135)( 84,133, 97)( 87,112,100)( 93,132,107) ] ],
[ 3, 4080, 1, "2", [ [ 15, 7 ], [ 30, 1 ] ], 1, "PSL(2, 16)",
[ "L", [ 2, 16 ], 1 ],
[ ( 1,131)( 2, 12)( 4, 67)( 5,117)( 6, 76)( 7, 49)( 8, 79)( 9,128)
( 10, 50)( 11, 32)( 13, 15)( 14, 24)( 16, 62)( 17,125)( 18, 36)
( 19, 93)( 20, 59)( 21,110)( 22, 23)( 25, 61)( 26, 88)( 27,102)
( 28, 96)( 29, 92)( 30, 31)( 33, 83)( 34, 82)( 37,104)( 38, 66)
( 39, 58)( 40, 46)( 41,118)( 42, 68)( 44, 52)( 45,130)( 47, 70)
( 48, 54)( 51, 89)( 55, 65)( 56, 74)( 57, 63)( 60, 64)( 69,120)
( 71,135)( 72,114)( 75,108)( 77, 81)( 78,122)( 80,115)( 84,107)
( 85, 98)( 86, 90)( 87,119)( 91,105)( 95,134)( 97,116)( 99,132)
(100,124)(101,133)(103,136)(106,123)(112,113)(121,126)(127,129),
( 1, 36,100)( 2, 11, 48)( 3,130, 55)( 4, 56, 91)( 5, 99,112)
( 6,124, 47)( 7,128, 14)( 8, 76, 24)( 9, 70, 38)( 10, 72,109)
( 12, 35, 58)( 13,105, 73)( 15, 45, 64)( 16, 49, 92)( 17, 85,126)
( 18,115, 33)( 19, 82, 65)( 20, 87, 43)( 21, 44, 75)( 22, 25,132)
( 23, 63,122)( 26, 62, 95)( 27, 80,101)( 28, 66,120)( 29,102, 67)
( 30,116,111)( 31, 94, 69)( 32, 93, 71)( 34, 50, 51)( 37,129,119)
( 39, 90, 52)( 40, 88,107)( 41, 54, 89)( 42, 98,103)( 46,131,113)
( 53,135,127)( 57, 86,114)( 59, 68,134)( 60, 78, 96)( 61,108,106)
( 74,117,125)( 77, 97, 79)( 81,110,104)( 83,123,136)( 84,133,118) ] ],
[ 4, 8160, 0, "2", [ [ 15, 3 ], [ 30, 3 ] ], 1, "PSL(2, 16).2",
[ "L", [ 2, 16 ], 1 ],
[ ( 1, 81)( 2, 60)( 3,116)( 4,122)( 5, 13)( 6, 93)( 7, 72)( 10,113)
( 11, 28)( 12, 37)( 14,130)( 15, 55)( 16,112)( 17, 34)( 18,125)
( 19, 63)( 22, 80)( 25, 70)( 26,117)( 27,103)( 29, 64)( 30, 57)
( 31, 76)( 32, 77)( 33, 62)( 35,107)( 36, 98)( 38,105)( 39,118)
( 41, 56)( 42, 49)( 43, 97)( 44, 86)( 46, 75)( 47, 90)( 48, 79)
( 50, 83)( 51, 91)( 52, 61)( 53,133)( 58,126)( 59,132)( 65, 88)
( 66,106)( 67, 78)( 68,100)( 69, 94)( 71,102)( 73,101)( 74,121)
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( 3, 94, 31,128)( 4,108, 99, 33)( 5, 59, 75, 36)( 6, 55,127, 9)
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( 13,106,116,129)( 14, 71,134,105)( 15, 53, 41, 20)( 16,103, 46, 78)
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( 26, 85,135, 73)( 27, 56, 51, 95)( 28, 89,117, 92)( 29, 87, 45,104)
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( 39,101,119,113)( 44, 58, 98,124)( 48, 96, 83, 54)( 50,132, 74,126)
( 60, 82,121,136)( 65,133)( 67, 77, 93,100)( 70,123,118, 90)
( 76,111,107,114) ] ],
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(111,116)(122,129)(124,128),
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91,105, 7)( 8,133, 93, 51,131, 84, 69, 52, 29,126,109,127)
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65, 71,101, 66, 58,125)( 32,114, 40, 74, 49, 99, 47,111, 82, 95,110,
92) ] ],
[ 6, 47377612800, 1, "2", [ [ 135, 1 ] ], 2, "PSp(8, 2)",
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( 14, 21)( 16, 23)( 18, 25)( 22, 29)( 24, 32)( 28, 37)( 30, 40)
( 31, 42)( 35, 47)( 36, 49)( 38, 52)( 39, 53)( 41, 56)( 45, 61)
( 46, 62)( 50, 65)( 51, 67)( 54, 69)( 55, 71)( 59, 75)( 60, 77)
( 63, 80)( 68, 84)( 70, 87)( 74, 91)( 78, 95)( 79, 96)( 83, 94)
( 85,103)( 86,105)( 90,110)( 92,112)( 99,108)(100,113)(101,117)
(102,104)(109,122)(111,124)(114,121)(116,120)(118,125)(126,128)
(130,133)(132,135), ( 2, 3, 5, 8, 13, 20, 28, 38)( 4, 6, 10, 16,
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( 69, 86,106,110, 96,115, 91,111)( 71, 89,109,123,130,134,135,112)
( 84,102,105,119,122,129,132,124)(133,136) ] ],
[ 7, 979200, 1, "2", [ [ 60, 1 ], [ 75, 1 ] ], 1, "PSp(4, 4)",
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[ ( 1,102, 66, 64, 9, 99,114, 85, 89, 71,126, 2, 96,129, 52)
( 3, 4, 25, 78, 80,104, 79, 47,116, 18,100,117, 13, 37, 67)
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119,136, 56)( 15, 29,130, 28, 59,135, 87, 65, 16, 21, 83, 48, 43, 91,
49)( 24, 32, 69, 51,122, 42, 35, 38, 75, 53,115,125, 88,118,133)
( 30,101,124)( 41, 73,132),
( 1, 77, 89, 93,125, 41)( 2, 23, 39,101,126, 70)( 3,102, 43,122, 71,
40)( 4, 20, 88, 68, 64,130)( 5, 25,128, 74,105, 27)
( 6, 52, 7, 96,124,133)( 8, 69, 26, 61, 62, 33)( 9,107, 79)
( 10, 75, 94, 11,109, 85)( 12, 35, 17)( 13, 51, 95, 83, 32, 98)
( 14, 90, 76, 42,103, 50)( 15,116, 99, 22, 46, 73)( 16,118,114)
( 18, 24,113,135, 65,117)( 19,108, 66,106, 37,132)( 21, 67,120, 57,
34,127)( 28,100,111,136, 86,129)( 30, 60, 63)( 31,119, 36, 87, 47,
55)( 38, 48,115, 49, 91, 59)( 44,123,131, 58, 92, 56)
( 45, 53, 97,104, 78, 54)( 72, 84,112)( 80, 82,121, 81,110,134) ] ],
[ 8, 1958400, 0, "2", [ [ 60, 1 ], [ 75, 1 ] ], 1, "PSp(4, 4).2",
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[ ( 1, 42, 28, 93, 92, 90)( 2,118, 11, 49,114, 85)( 3, 24, 97, 87,100, 20
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( 22, 58, 36, 78,117, 37)( 25, 75, 62, 61,109, 59)( 31,108,135,122,
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( 35,130, 57, 72,133,119)( 44,121, 54,113, 89, 64)( 56,129, 98)
( 67,102)( 68,116, 84)(104,124)(106,120),
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48, 42)( 5,113, 38, 7, 74,111, 33, 21, 26,101)( 6, 37,108, 8,
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( 11, 70, 87, 81, 63, 12, 73,129, 78, 62)( 14, 96, 61,128, 75, 60, 88,
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( 20,136, 64, 83, 35, 71, 22, 41, 84,106)( 24, 77,115, 28,121, 44,127,
89,118,102) ] ],
[ 9, 197406720, 1, "2", [ [ 72, 1 ], [ 63, 1 ] ], 1, "O-(8, 2)",
[ "2D", [ 4, 2 ], 1 ],
[ ( 1,114, 93, 69,107, 85, 28, 72,135,115, 31,128,131,119, 27, 67,102, 77,
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91, 6, 7, 65, 35, 24,113,111, 58,126, 79)( 4, 16, 56, 84,108, 90,
112, 25, 78, 14,123, 8, 62,104, 34, 59, 89, 97, 99, 51, 10)
( 5, 47, 13, 53, 32, 74, 38, 63, 43, 49, 55, 12, 39, 37,100, 26,105,
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109,106, 70, 60,103, 75, 45,127)( 22, 50,116, 30, 82, 29,124)
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( 3, 74, 27, 86,111,122,135, 14)( 4, 84, 31, 90,118,129,136, 24, 7,
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( 6, 82, 33, 88,120,127,138, 22, 9, 76, 36, 91,114,130,141, 16, 12,
79, 30, 94,117,124,144, 19)( 8, 80, 32, 92,116,128,140, 20)
( 37, 65,107, 49, 41, 71, 97, 53, 47, 61,101, 59)( 38, 63, 98, 51)
( 39, 62, 99, 50)( 40, 72,103, 54, 46, 69,100, 60, 43, 66,106, 57)
( 42, 70,105, 52, 48, 67,102, 58, 45, 64,108, 55)( 44, 68,104, 56),
( 1,136,122, 20, 93, 11,100,121,140, 86, 23,105)( 2, 16,129, 8, 88,
131,104, 85,143, 98, 13,141)( 3, 40,127, 68, 94, 35,108, 49,138, 74,
17,117)( 4,124,128, 92, 95,107, 97,133,134, 14, 21, 9)
( 5,112,123, 44, 91, 71,106, 25,144, 50, 18, 81)( 6, 76,125,116, 87,
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15, 45)( 10, 28,132, 56, 90, 83,101,109,135, 38, 19, 69)
( 12, 52,126, 80, 89,119, 99, 37,139, 62, 22, 33)( 27, 48, 55, 66, 82,
29,120, 51, 42, 79, 65,118)( 30, 84, 53,114, 75, 41,115, 63, 46, 31,
72, 58)( 34, 36, 60, 54, 78, 77,113,111, 39, 43, 67, 70) ] ],
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"Alt(12) wreath Sym(2)", [ "A", 12, 2 ],
[ ( 1, 65, 30,127, 13, 70,114,122, 37, 71, 90,128,133, 72, 78,129)
( 2, 41, 35, 91, 20,142,120, 74, 45, 11, 89, 32,139, 24, 82,117)
( 3,101, 27,103, 15,106,111, 98, 39,107, 87,104,135,108, 75,105)
( 4, 53, 28, 55, 16, 58,112, 50, 40, 59, 88, 56,136, 60, 76, 57)
( 5, 29, 31, 19, 22,118,110, 38, 47, 95, 92,140,144, 84, 81, 9)
( 6,125, 25, 67, 18,130,109, 62, 42,131, 85, 68,138,132, 73, 69)
( 7, 17, 34,115, 14, 46,119, 86, 44,143, 96, 80,141, 12, 77, 33)
( 8,137, 36, 79, 21, 10,113, 26, 43, 23, 94,116,134, 48, 83, 93)
( 49, 64, 54,124)( 51,100)( 61, 66,126,121)( 63,102,123, 97),
( 1,138, 47, 81)( 2,136, 41, 75, 10,140, 48, 79)( 3,142, 44, 84, 7,
134, 40, 77)( 4,137, 39, 82, 8,144, 43, 74)( 5,135, 46, 80, 12,
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( 13,102, 35,129, 49, 90, 23,105, 25,126, 59, 93)( 14,100, 29,123, 58,
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125, 51, 94, 20,108, 31,122, 52, 89)( 18,107, 33,121, 54, 95, 21, 97,
30,131, 57, 85)( 61, 66, 71, 69)( 62, 64, 65, 63, 70, 68, 72, 67)
(109,114,119,117)(110,112,113,111,118,116,120,115) ] ],
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"Alt(12)^2.2^2", [ "A", 12, 2 ],
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13, 14)( 3,112, 66, 80,137,105, 27,109, 18, 74, 5,100, 63,116,138,
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( 7,124, 72, 92,139,129, 36, 85, 19,122, 12, 88, 67,128,144, 93, 31,
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22, 50, 11, 40, 70, 56,143, 45, 34, 49, 23, 38)( 39,118, 54, 83, 41,
106, 51,119, 42, 82, 53,107)( 43,130, 60, 95)( 46, 58, 59, 47)
( 48, 94, 55,131)( 75,113,102)( 77,101, 99,111,114, 78)
( 79,125,108, 87,115,126, 84, 89,103,123,120, 90)( 91,127,132, 96),
( 1, 5, 89, 92, 44, 40,136,142,130,127,115,120, 84, 73)
( 2, 53, 90, 68, 45, 16,135,106,131, 31,110, 60, 78, 61, 9, 17, 87,
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141, 22,123,103,119, 36, 74, 49, 6, 65, 93, 20, 39,100,143, 34,122,
55,114, 72, 81, 13, 3,101, 95, 32, 38, 52,138, 70,129, 19,111,108,
83, 25)( 4,137, 94,128, 43,112,144, 82,121, 7,113, 96, 80, 37)
( 8, 41, 88,140, 46,124,139,118,132, 79,109, 12, 77, 85)
( 10,125, 91,116, 48, 76,133)( 14, 51,102, 71, 33)( 15, 99,107, 35,
26, 50, 54, 66, 69, 21)( 18, 63,105, 23, 27, 98, 59, 30, 62, 57) ]
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133,139,103,106, 58, 57, 81, 83, 23, 15, 27, 36, 12)( 3, 26, 72, 6,
38, 64,114, 41,124,116, 89,121,140, 91, 97,142, 55,105, 82, 59, 21,
75, 35, 24)( 4,110, 65,126, 44, 88,109,137,127,104, 94, 49,141, 79,
107, 22, 51, 33, 84, 11, 14, 63, 30, 48)( 5,122, 68, 90, 37,136,115,
101,130, 56, 93, 73,143, 19, 99, 34, 60, 9, 74, 71, 18, 39, 28,120)
( 8, 86, 61,138, 43,100,118, 53,129, 80, 95, 13,135, 31,108, 10, 50,
69, 78, 47, 16,111, 29,132),
( 1, 62, 19, 39, 28, 97, 71, 7, 38, 16, 99, 35)( 2, 14, 15, 27, 25,
61, 67, 43, 40,100,107, 11)( 3, 26, 13, 63, 31, 37, 64,103, 47, 4,
98, 23)( 5, 74, 24,135, 33,109, 68,127, 42, 88,101, 83, 12,134, 21,
111, 32,121, 66, 91, 41, 76,108,143, 9,110, 20,123, 30, 85, 65, 79,
48,136,105,119, 8,122, 18, 87, 29, 73, 72,139, 45,112,104,131, 6,
86, 17, 75, 36,133, 69,115, 44,124,102, 95)( 10, 50, 22, 51, 34, 49,
70, 55, 46, 52,106, 59)( 53, 82, 60,142, 57,118, 56,130, 54, 94)
( 77, 84,144,141,117,116,128,126, 90, 89)( 78, 96,137, 81,120,140,129,
114, 92,125)( 80,132,138, 93,113) ] ],
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25,141, 61, 45)( 2, 78, 56,130,103, 96, 23, 29,136, 62, 42, 8, 82,
55,132,107, 89, 16, 26,138, 68, 46, 7, 84, 59,125,100, 86, 18, 32,
142, 67, 48, 11, 77, 52,122,102, 92, 22, 31,144, 71, 41, 4, 74, 54,
128,106, 91, 24, 35,137, 64, 38, 6, 80, 58,127,108, 95, 17, 28,134,
66, 44, 10, 79, 60,131,101, 88, 14, 30,140, 70, 43, 12, 83, 53,124,
98, 90, 20, 34,139, 72, 47, 5, 76, 50,126,104, 94, 19, 36,143, 65,
40)( 3, 75, 51,123, 99, 87, 15, 27,135, 63, 39)(109,117)
(110,114,116,118,115,120,119,113,112),
( 1,142, 89, 42,119, 80,103,129, 12, 22, 86, 66,111, 56, 97,141, 5,
46, 95, 78,115,128,108, 21, 2, 70, 87, 54,109,140,101, 45, 11, 82,
91,126,120, 20, 98, 69, 3, 58, 85,138,113, 44,107, 81, 7,130, 96,
18,110, 68, 99, 57)( 4, 34, 88, 30,112, 32,100, 33)
( 6,118, 92,102,117, 8,106, 93)( 9, 10, 94, 90,114,116,104,105)
( 13,134, 65, 39, 59, 73,139,125, 48, 23, 74, 67,123, 60)
( 14, 62, 63, 51, 49,133,137, 41, 47, 83, 79,127,132, 24)
( 15, 50, 61,135, 53, 37,143, 77, 43,131, 84, 19,122, 72)
( 16, 26, 64, 27, 52, 25,136, 29, 40, 35, 76, 31,124, 36)
( 17, 38, 71, 75, 55,121,144) ] ],
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( 8, 90, 64, 32, 94,136, 33, 10,138, 69)( 11,114, 71,116, 95,112, 35,
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( 15, 99,101,125,122, 38, 37, 49, 55, 19)( 23,111,107,113,131,110, 47,
109, 59,115)( 24, 75,108, 77,132, 74, 48, 73, 60, 79)( 83,120),
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13)( 4, 94, 81,103, 59, 37)( 5, 34, 80,115, 54,121)
( 6,130, 77, 31, 56,109)( 7, 58, 73)( 8,118, 78,127, 53, 25)
( 9,106, 83, 43, 52, 85)( 11, 46, 76, 91, 57, 97)( 12, 22, 75,139,
50, 61)( 14, 63,144)( 15,135,134, 62, 72, 24)( 16, 87,141, 98, 71,
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( 20,111,138,122, 65, 36)( 21, 99,143, 38, 64, 96)( 23, 39,136, 86,
69,108)( 28, 92,117,102,131, 41)( 29, 32,116,114,126,125)
( 30,128,113)( 33,104,119, 42,124, 89)( 35, 44,112, 90,129,101)
( 40, 88, 93,105,107, 47)( 45,100, 95) ] ],
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3, 34, 67,133, 77, 18,129, 47, 52)( 4, 10, 70, 61, 73, 78,126,131,
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( 5, 22, 69, 37, 76, 6,130, 71, 49, 74,102,128,119, 51, 26,103,140,
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114,123, 35, 55,134,101, 20,117, 39, 28)( 8,118, 63, 25, 79,138,125,
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56, 26, 53)( 3,144, 44, 35, 89)( 4,120, 37, 83, 90, 99,142, 68,
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93, 15,136,116, 25, 77)( 7,132, 43,131, 91,123,139,128, 31,125)
( 8, 36, 41, 11, 96, 39,143, 92, 27,137)( 9, 24, 40,119, 85, 75,138,
104, 34, 65)( 10, 72, 45, 23, 88,111,133, 80, 30,101)
( 13, 76,114, 97, 82, 66,105, 22, 64,117)( 14, 52,110, 49, 74, 54, 98,
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105, 12, 13,112, 27,131,138, 44, 77, 67, 98, 10, 21,120, 25,124,135,
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( 49, 52, 51, 59, 54, 56, 53, 55, 50, 58, 57, 60)( 85, 88, 87, 95, 90,
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( 1,102, 70,134, 21, 48, 31, 59, 75, 8,114, 61, 98, 22,144, 33, 47,
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139, 57, 39, 7, 54, 63)( 3, 6, 66, 62, 14, 24, 36, 35, 83, 80,116,
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96, 29, 95, 77, 92,113, 85,101, 94,137, 93, 41, 91, 53, 87)
( 9, 42, 67, 50, 15, 12, 30, 71, 74, 20,120, 25,107, 82,140,117, 37,
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87, 19, 60, 45, 29,109, 83,100, 62, 10,138,123, 20, 96, 43, 53,117,
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( 9, 30,121, 80, 88, 67, 58,141, 27, 13, 84, 40, 65,118,143, 99, 14,
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( 1, 56, 35, 17,114,142, 2, 51, 33, 24,115,136)( 3, 57, 36, 19,112,
133, 8, 59, 29, 18,118,134)( 4, 49, 32, 23,113,138, 10, 50, 27, 21,
120,139)( 5, 54, 34, 14,111,141, 12, 55, 28, 13,116,143)
( 6, 58, 26, 15,117,144, 7, 52, 25, 20,119,137)( 9, 60, 31, 16,109,
140, 11, 53, 30, 22,110,135)( 37, 92,107,125, 78, 70, 38, 87,105,132,
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( 40, 85,104,131, 77, 66, 46, 86, 99,129, 84, 67)( 41, 90,106,122, 75,
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PRIMGRP[146]:=
[[1, Factorial(146)/2,1,"2",[[145,1]],144, "Alt(146)", ["A",146, 1], "Alt"],
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PRIMGRP[147]:=
[[1, Factorial(147)/2,1,"2",[[146,1]],145, "Alt(147)", ["A",147, 1], "Alt"],
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PRIMGRP[148]:=
[[1, Factorial(148)/2,1,"2",[[147,1]],146, "Alt(148)", ["A",148, 1], "Alt"],
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[[ 1, 149, 3, "1", [ [ 1, 148 ] ], 1, "C(149)", [ "Z", 149, 1 ], [ ] ],
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[ 3, 596, 2, "1", [ [ 4, 37 ] ], 1, "149:4", [ "Z", 149, 1 ],
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[ 4, 5513, 2, "1", [ [ 37, 4 ] ], 1, "149:37", [ "Z", 149, 1 ],
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[ 5, 11026, 2, "1", [ [ 74, 2 ] ], 1, "149:74", [ "Z", 149, 1 ],
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PRIMGRP[150]:=
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