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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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1
#############################################################################

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##

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#W  nor3.f                 GAP library of groups           Hans Ulrich Besche

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##                                               Bettina Eick, Eamonn O'Brien

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##

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7
SMALL_GROUP_LIB[ 117 ] := [

8
[ [ 1 ], -1, [ 1, -2, 3 ], [ 1, 3 ], -4, -4, [ 1, 3, 4 ], [ 1, 3, 4, 7 ], -4,

9
[ 1, 3, 7 ], -10, -4, -8, -8, -8, -4, -4, -4, -4, -4, -4, [ 1, 3, -2 ], -4,

10
-1, -3, -4, -4, -10, -10, -22, [ 1, -2, 3, -2 ], [ 1, 3, -2, 7, -2 ], -32,

11
[ 1, 7 ], -32, [ 1, -2, 4, 7, -2 ], -34, [ 1, -2, 3, 7, -2 ], -36,

12
[ 1, 4, 7 ], [ 1, -2, 3, -2, 4, -2, 7, -2 ], -36, [ 1, -2, 4, -2, 7 ],

13
[ 1, -2, 3, 4, -2 ], -7, -41, [ 1, -2, 3, -2, 4 ], -32, -10, -41, -38, -38,

14
-41, -10, -32, -43, -1, -4, -3, -3, -4, -4, -10, -10, -4, -22, -3, -3, -31,

15
-3, -3, -22, -4, -3, -38, -3, -3, -22, -4, -3, -38, -3, -3, -7, -47, -44, -47

16
, -47, -47, -41, -22, -31, -4, -3, -4, -4, -10, -10, -8, -8, -8, -1, -4, -4,

17
[ 1, 3, 9, 10 ], [ 1, 3, -2, 9, 10 ], [ 1, 9 ], [ 1, 3, 7, 9, -2 ],

18
[ 1, 3, 9 ], [ 1, 7, 9 ], [ 1, 9, -2 ], -107, [ 1, 4, 9, -2 ], -111,

19
[ 1, 3, 9, 12 ], [ 1, 3, -2, 7, -2, 9, 12, -2 ],

20
[ 1, 3, 7, -2, 9, 12, 19, 25 ], [ 1, -2, 3, 9, 12 ],

21
[ 1, -2, 3, 7, -2, 9, 12, 16, -2, 19, -2, 21, 25, -2 ],

22
[ 1, 3, -2, 9, -2, 12, 19, -2 ], [ 1, 3, -2, 9, -2, 12, -2, 19, -2, 21, -2 ],

23
-1, [ 1, 3, -2, 9, 19 ], [ 1, 19 ],

24
[ 1, -2, 3, 9, -2, 10, -2, 19, -2, 25, -2 ],

25
[ 1, -2, 3, -2, 7, 9, -2, 10, 12, 16, -2, 19, -2, 22 ], [ 1, 7, 19 ],

26
[ 1, 19, -2 ], -124, [ 1, 4, 19, -2 ], -128, [ 1, 19, 21 ],

27
[ 1, 3, -2, 19, 21, -2, 25, -2 ], [ 1, 3, 9, -2, 19, -2, 21, -2 ],

28
[ 1, -2, 3, -2, 10, -2, 12, -2, 19, -2 ], [ 1, -2, 3, 10, 12, -2, 22, -2 ],

29
[ 1, -2, 10, 25, -2 ], [ 1, 3, 21 ], -115, [ 1, 3, 9, 12, 21 ],

30
[ 1, 3, 9, 21 ], -109, [ 1, 3, 4, 7, 9, 19, 21, 22, 25 ], -141,

31
[ 1, 3, 7, 9, 19 ], -4, -143, [ 1, 3, 9, 19, 25 ], -138,

32
[ 1, -2, 3, 9, 12, 21 ], -141, -150, -141, -150,

33
[ 1, 3, 4, 7, 9, -2, 19, -2, 21, -2, 22, -2, 25, -2 ], -150, -141, -150, -138

34
, -150, -155, -150, -138, -150, -150, -155, -138, [ 1, -2, 3, 12, 21 ], -150,

35
-150, -150, -150,

36
[ 1, -2, 3, -2, 4, -2, 7, -2, 9, -2, 10, -2, 12, -2, 13, -2, 16, -2, 19, -2,\

37
 21, -2, 22, -2, 25, -2 ], -150, -150, -138, -168, -173, -138, -168, -173,

38
[ 1, -2, 3, -2, 10, -2, 12, 16, -2, 19, -2, 21, -2, 22, -2, 25, -2 ], -173,

39
-173, [ 1, -2, 3, -2, 4, -2, 7, -2, 10, -2, 12, 19, -2, 21, -2, 25, -2 ],

40
-173, [ 1, -2, 3, -2, 7, -2, 10, -2, 12, 13, -2, 16, -2, 19, -2, 21, -2 ],

41
[ 1, -2, 3, 9, 21 ], -150, -188, -150, -188, -150,

42
[ 1, -2, 3, -2, 4, -2, 7, -2, 9, 19, -2, 21, -2, 22, -2, 25, -2 ], -188, -188

43
, -188, [ 1, -2, 3, -2, 7, -2, 9, 19, -2 ], -188, -150, -188, -150, -188,

44
-150, -194, -150, -150, -150, [ 1, -2, 3, -2, 9, -2, 19, -2, 25, -2 ],

45
[ 1, -2, 3, 7, -2, 9, -2, 10, -2, 16, -2, 19, -2, 21, -2, 25, -2 ], -173,

46
-210, -173, -210, -173, -138, -150, -188, -150, -150, -150, [ 1, -2, 3, 9 ],

47
-109, -173, -222, -150, -118, -118,

48
[ 1, -2, 3, -2, 7, -2, 9, -2, 10, -2, 12, 13, -2, 16, -2, 19, -2 ], -4, -150,

49
-173, -109, -173, -4,

50
[ 1, -2, 3, -2, 9, -2, 10, -2, 12, 16, -2, 19, -2, 22, -2, 25, -2 ],

51
[ 1, -2, 3, -2, 4, -2, 7, -2, 9, -2, 10, -2, 12, 19, -2, 25, -2 ], -109,

52
[ 1, 3, -2, 9 ], [ 1, -2, 3, 7, -2, 9 ], [ 1, 3, 9, 19, 21 ], -109, -222,

53
-141, -109, -109, -109, [ 1, 3, 4, 7, 9 ], -222, -222, -222,

54
[ 1, -2, 3, -2, 4, -2, 7, -2, 9 ], -109, -222, -115, -140, [ 1, 3, 7, 9, 12 ]

55
, -118, -150, [ 1, -2, 3, -2, 7, -2, 9, -2, 12 ], -115, -118, -115, -118,

56
[ 1, 3, 9, -2 ], [ 1, -2, 3, 9, -2 ], [ 1, 3, 9, -2, 21, -2 ], -267, -267,

57
[ 1, 3, 7, 9 ], -240, [ 1, 3, 7, 9, 21 ], -272, [ 1, 3, 10 ],

58
[ 1, -2, 3, 7, 9, -2, 10 ], [ 1, 3, 7, 9, 10, 16, 21 ], -276,

59
[ 1, 3, 7, 9, 10 ], -278, [ 1, -2, 3, 7, -2, 9, 10, -2, 16, -2, 21 ], -280,

60
[ 1, -2, 3, 7, -2, 9, 10, -2 ], -282, [ 1, 3, 4, 7, 9, 10 ],

61
[ 1, -2, 3, -2, 4, -2, 7, -2, 9, 10, -2 ], [ 1, -2, 3, 9, -2, 10, 16 ],

62
[ 1, -2, 3, -2, 9, -2, 10, 16, -2 ],

63
[ 1, -2, 3, 7, -2, 9, -2, 10, 16, 21, -2 ], -288, -141, -141, -109, -109,

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[ 1, 3, 4, 7, 9, 22 ], -188, -188, -222, -222,

65
[ 1, -2, 3, -2, 4, -2, 7, -2, 9, 22, -2 ], -115, -115, -115, -140, -140, -140

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, [ 1, 3, 7, 9, 10, 12, 16, 19, 25 ], [ 1, 7, 9, 10, 16 ],

67
[ 1, 4, 7, 9, 10, 13, 16 ], [ 1, 3, 7, 9, 10, 16, 19, 21, 25 ],

68
[ 1, 3, 4, 7, 9, 10, 12, 13, 16, 19, 21, 22, 25 ],

69
[ 1, 4, 7, 9, 10, 13, 16, 19, 22 ], -311, -311, [ 1, 3, 9, 10, 19 ], -314,

70
-306, -257, -257, -257, [ 1, 7, 9, 19, 25 ], [ 1, 9, 19 ],

71
[ 1, 3, 7, 9, 12, 16, 19, 21, 25 ], -322, -322, -239, -252, -239, -239, -239,

72
-252, -239, -239, -239, -252, -239, -239, -106, -106, -106,

73
[ 1, -2, 3, -2, 7, -2, 9, -2, 10, 12, -2, 16, -2, 21, -2, 25, -2 ],

74
[ 1, 3, -2, 9, 10, 19 ], -341, -341,

75
[ 1, 3, 7, 9, -2, 19, -2, 21, -2, 25, -2 ], -344, [ 1, 3, 7, 9, -2, 21, -2 ],

76
[ 1, -2, 3, 7, -2, 9, -2, 21, -2 ],

77
[ 1, 3, -2, 7, -2, 9, -2, 12, -2, 16, -2, 19, -2, 21, -2, 25, -2 ], -348,

78
[ 1, 3, -2, 7, -2, 9, -2, 12, -2, 21, -2 ],

79
[ 1, -2, 3, -2, 4, -2, 7, -2, 9, -2, 12, -2, 21, -2 ], -288, -288, -288, -340

80
, -340, -340, -210, -210, -210, -173, -173, -173, [ 1, 3, 9, 19 ], -341, -364

81
, -341, -364, -341, -119, -364, -341, -134, -341, -341, -341,

82
[ 1, -2, 3, -2, 9, -2, 10, -2, 12, -2, 19, -2, 21, -2 ], -341, -341, -341,

83
-341, -341, -341, -341, -341, -341, -173, -222, -222, -222, -107, -239, -321,

84
-267, -109, -239, [ 1, 3, 7, 9, 25 ], [ 1, -2, 3, 9, -2, 21, -2 ], -109, -239

85
, [ 1, -2, 3, -2, 7, 9, 16, 25 ], [ 1, 3, -2, 9, 21, -2 ], -402, -402, -341,

86
-402, -402, -402, -341, -341, [ 1, -2, 3, 7, -2, 9, 19, -2, 21, 25, -2 ],

87
-194, -210, -173, -107, [ 1, 9, 27 ], [ 1, 9, 27, -2 ], [ 1, 3, 9, 21, 27 ],

88
[ 1, 3, 9, 30 ], [ 1, 3, -2, 9, 27, -2, 30, 48 ], [ 1, 3, 9, 30, 55 ],

89
[ 1, 3, 27 ], [ 1, 3, -2, 9, 27 ], [ 1, 3, -2, 19, 27, -2, 57 ], -422,

90
[ 1, 3, 9, -2, 27 ], [ 1, 3, 9, 21, 27, -2, 63, -2 ], [ 1, 3, 9, 27, 57 ],

91
[ 1, 3, 7, 9, 19, 27, 55 ], [ 1, 3, -2, 9, 21, -2, 27, -2, 63, -2 ], -423,

92
[ 1, 3, -2, 7, -2, 9, 19, 27 ], [ 1, 3, 21, 27, 57, 75, -2 ],

93
[ 1, 3, 27, -2, 57, -2 ], [ 1, 3, 27, 57 ],

94
[ 1, 3, 12, 27, -2, 57, -2, 66, -2 ],

95
[ 1, 3, 4, 7, 9, 19, 21, 22, 25, 27, 55, 63, 73, -2 ], -434,

96
[ 1, 3, 9, 10, 19, 25, 27, -2, 55, -2, 57, -2 ], -4, [ 1, -2, 3, 9, 27 ],

97
[ 1, 3, -2, 9, 21, -2, 27, 63 ], -423, [ 1, 3, -2, 7, -2, 9, 21, -2, 27 ],

98
[ 1, 3, -2, 9, 21, -2, 27 ], [ 1, 3, -2, 9, -2, 27 ],

99
[ 1, 3, -2, 7, -2, 9, 10, 19, 27, -2, 30, -2, 57, -2, 73, -2 ],

100
[ 1, -2, 3, 7, -2, 9, 21, 27, 63 ], -448, -448,

101
[ 1, -2, 3, 7, -2, 9, -2, 10, -2, 16, -2, 19, -2, 21, -2, 25, -2, 27, 30, 48\

102
, -2, 57, 63, -2, 75, -2 ],

103
[ 1, -2, 3, -2, 7, -2, 9, 12, -2, 16, -2, 19, -2, 21, -2, 25, -2, 27, -2, 28\

104
, -2, 34, -2, 43, -2, 46, -2, 52, -2, 55, -2, 57, 61, -2, 63, -2, 66, 70, -2, \

105
73, -2, 75, 79, -2 ],

106
[ 1, 55 ], [ 1, 3, 21, 27, 55 ], [ 1, -2, 3, 9, 55, -2, 63 ],

107
[ 1, -2, 3, 7, -2, 9, 21, 27, 36, 55, -2, 63 ], [ 1, 3, -2, 21, -2, 27, 55 ],

108
[ 1, -2, 4, -2, 7, 9, 55, -2, 63 ],

109
[ 1, -2, 3, -2, 4, -2, 7, -2, 9, 21, -2, 27, 36, 55, -2, 63 ],

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[ 1, 3, -2, 21, -2, 27, 55, 57, -2, 75, -2 ],

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[ 1, -2, 3, -2, 4, -2, 7, -2, 9, -2, 12, -2, 21, -2, 27, 55, -2, 57, -2, 58,\

112
 -2, 61, -2, 63, -2, 66, -2, 75, -2 ], [ 1, 4, 7, 9, 55, 63 ], -459,

113
[ 1, 3, 4, 7, 9, -2, 19, -2, 21, -2, 22, -2, 25, -2, 27, 28, 46, -2, 55, 63,\

114
 -2, 73, -2 ], [ 1, -2, 4, -2, 7, 9, 36, 55, -2, 63 ], -458,

115
[ 1, -2, 3, -2, 4, -2, 7, -2, 9, -2, 12, -2, 21, -2, 27, -2, 28, -2, 30, -2,\

116
 31, -2, 34, -2, 36, -2, 39, -2, 48, -2, 55, -2, 57, -2, 58, -2, 61, -2, 63, -\

117
2, 66, -2, 75, -2 ],

118
[ 1, 10, -2, 12, -2, 16, -2, 19, -2, 21, -2, 25, -2, 28, -2, 30, -2, 36, -2,\

119
 37, -2, 39, 40, 46, -2, 48, -2, 55, -2, 63, -2, 64, -2, 66, -2, 70, -2, 73, -\

120
2, 75, -2, 76, -2, 79 ],

121
-1, [ 1, -2, 3, -2, 4, 9, 27, 63 ], [ 1, -2, 3, -2, 7, 9, 27 ],

122
[ 1, -2, 3, 4, -2, 9 ], -109,

123
[ 1, -2, 3, -2, 4, -2, 9, 10, -2, 12, -2, 19, -2, 21, -2, 22, -2, 27, -2, 28\

124
, -2, 31, -2, 37, -2, 46, -2, 49, -2, 55, -2, 57, 58, -2, 63, -2, 64, -2, 66, \

125
73, -2, 75, 76, -2 ],

126
[ 1, 27 ], [ 1, 9, -2, 27 ], -435, [ 1, -2, 3, 27 ], [ 1, 9, 27, 63 ], -479,

127
-416, -416, [ 1, 3, 9, 12, 21, 27, 66 ], [ 1, 3, -2, 9, 27, 63 ], -484, -423,

128
-423, [ 1, 3, -2, 9, -2, 12, -2, 21, -2, 27, 66, -2 ],

129
[ 1, 3, -2, 7, -2, 9, 10, 19, 27, 64 ], [ 1, 9, 19, 27, 63 ], -490,

130
[ 1, 9, 19, 27 ], -492, [ 1, -2, 3, 9, 12, 19, -2, 21, 27, 66 ],

131
[ 1, -2, 3, 9, 12, 19, -2, 21, 27, 75 ],

132
[ 1, -2, 3, 9, 12, 19, -2, 21, 27, 57 ], [ 1, 81 ], -475, [ 1, 27, -2, 81 ],

133
[ 1, 9, 27, 171 ], -4, [ 1, 3, -2, 9, 81 ], [ 1, 3, 163 ], -1 ], 

134
[ [ 1 ], -1, [ 1, -2, 9 ], [ 9, 15 ], -4, -4, -4, [ 9, 12, 15 ], [ 9 ], -9,

135
-9, -9, -8, -8, -8, -4, -9, -9, -4, -9, -9, [ 9, -2, -4, -5, -7, -8, 15, -2 ]

136
, [ 1, 9 ], -1, -3, -23, -23, [ 1, 9, 73 ], -28, [ 1, 9, -2 ],

137
[ 1, -2, 9, -2 ], [ 1, 9, -2, 73, -2 ], -32,,,,,,,,,,,,,,,,,,,,,,,,,

138
[ 1, 9, 15 ], [ 1, -2, 9, 15, -2 ], [ 1, -2, -4, -5, -7, -8, 9, 15, -2 ], -4,

139
-8, -4, -4, -9, [ 9, -2 ], [ 9, 15, -2 ], -9, -66, -67, -67, -66, -9,

140
[ 9, -2, 12 ], -9, -9, -9, -66, -9, [ 9, -2, 15 ], -9, -9, -9, -9, -66, -67,

141
-66, -66, -66, [ 9, -2, 12, -2, 15, -2 ], [ 9, -2, 15, -2 ], -90, -4, -67,,,,

142
,,,, -1, -9, -9, [ 9, 568 ], [ 9, -2, 568 ], [ 81 ], [ 81, -2 ], -107, -107,

143
-108, -107, -108, -108, [ 576 ], [ 576, -2 ], -115, -115, -115, -115, -116,,,

144
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

145
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, [ 9, 81, 87 ], [ 9, -2, 81, 87 ],

146
[ 9, 81, 87, -2 ], [ 9, 81, 87, 657 ], [ 81, 87, 135 ], [ 81, 87, -2, 135 ],

147
-242, -107, -107, -107, -107, -107, -107, -107, -107, [ 81, 87, 108, 135 ],

148
[ 81, 87, -2, 108, 135 ], -107, -107, -107, -107, -107, -108, -242, -243,

149
-242, -243, [ 81, -2, 87, -2, 135, -2 ], [ 81, -2, 84, -2, 87, -2, 141, -2 ],

150
[ 81, -2, 87, -2 ], [ 81, -2, -4, -5, -7, -8, 87, -2 ], -267,

151
[ 81, 87, 135, 141, -2 ], [ 81, 87, -2, 108, 114, -2, 135, 141, -2 ],

152
[ 81, 135 ], -272, [ 82, 568 ], [ 82, 568, -2, 622 ], [ 568 ], -276, -276,

153
-276, [ 568, -2 ], -280, -280, -280, [ 109, 568, 595, 622 ],

154
[ 109, -2, 568, -2, 595, -2, 622, -2 ], [ 82, 136, 568, -2 ],

155
[ 82, -2, 136, 568, -2 ], [ 82, 136, 568, -2, 622, -2 ], -288,,,,,,,,,,,,,,,,

156
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

157
,,,,,,,,, -272, [ 81, 87, 135, -2 ], -272,,,,,,,,,,,,,,,,,,,,,, -107, [ 729 ]

158
, [ 729, -2 ], -416, [ 5112 ], -419, -419, -416, -416, -417,,,,,,,,,,,,,,,,,,

159
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, [ 729, 1215 ], [ 729, 783, 1215, -2 ],

160
[ 729, 735, 1215 ], [ 729, 735, -2, 1215 ],,,,,,,,,,,,,,,,,,, [ 6561 ] ], 

161
rec( pos := [ 1, -8, 22, -23, 58, -59, 61, -64, 91, -94, 238, 242, 265, 270,

162
274, 286, 391, -393, 475 ], val := [ [ 1 ], -1, [ 1, -2 ], [ 27 ], -4, -4, -4

163
, -4, [ 27, -2, -4, -5, -7, -8 ], -4, [ 27, 51 ], [ 27, 51, -2 ], [ 27, 45 ],

164
[ 27, 36, 45 ], -61, -61, [ 27, -2, 45, -2 ], -22, -61, [ 27, 45, -2 ],

165
[ 729 ], -238, [ 729, -2 ], -238, [ 13852 ], -274, [ 729, 1215 ],

166
[ 729, 747, 1215, -2 ], -391, [ 19683 ] ] ), 

167
rec( pos := [ 1, 58, 61, 91, 93, -94, 391 ], val := [ [ 1 ], [ 81 ], -58,

168
[ 81, -2 ], [ 81, 135 ], [ 81, 135, -2 ], [ 6561 ] ] ), 

169
rec( pos := [ 1, 93 ], val := [ [ 1 ], [ 243 ] ] ), 

170
[ [ 1 ] ] ];

171


172