
print "A homomorphic image of the Fibonacci group F(2, 9).";
print "The image is a soluble permutation group of degree 190";
print "and order 2^3 * 5^18 * 19.";
print "Group: G";

G := PermutationGroup<190 |
    \[     2,   4,   6,   8,  10,  12,  13,  15,  17,  16,  18,  21,
 23,  25,  27,  29,  28,  30,  31,  33,  35,  37,  36,  38,  39,  42,  43,
 45,  47,  49,  51,  53,  55,  54,  58,  46,  60,  50,  59,  62,  61,  65,
 64,  67,  69,  71,  72,  70,  74,  75,  68,  78,  77,  81,   1,  80,  83,
 85,  73,  86,  87,  76,  88,  89,  79,  92,  93,  95,  90,  98,  97,  84,
 99, 102,  96,   3, 103, 100, 101, 106, 104, 111, 108, 114,  91,  94, 107,
110, 105, 116, 113, 109, 112, 121, 115, 123, 117, 118, 122, 126,   5, 120,
125, 124, 128, 127, 129,   7, 133, 130, 132, 134, 137, 136, 141, 131, 139,
143, 135, 138, 140, 145, 142,   9, 146, 144, 147, 150, 149, 152,  14,  11,
148, 151, 155, 153, 156, 159, 160, 157, 154, 164, 158, 161, 163, 162, 165,
 19, 166,  22,  24, 168, 170, 172, 167,  20, 171,  26, 169, 174, 177, 176,
173, 175, 179, 178,  32, 180,  34, 182,  41, 181, 184,  40, 185, 186, 183,
187,  44,  48,  56,  52,  63,  66, 188,  57, 189,  82, 190, 119],
    \[     3,   5,   7,   9,  11,  13,  14,  16,  18,  19,  20,  22,
 24,  26,  28,  30,  31,  32,  33,  34,  36,  38,  39,  40,  41,  43,  44,
 46,  48,  50,  52,  54,  56,  57,  51,  59,  53,  61,  62,  63,  64,  66,
 67,  68,  70,   1,  71,  73,  75,  76,  77,  79,  80,  82,  81,  83,  84,
 86,  87,  78,  88,  89,  90,  91,  92,  93,  94,  96,  97,  99, 100,  98,
101, 103, 104, 105, 106, 107, 108, 109, 110, 112, 113, 115,  95,   2, 111,
116, 114, 117, 118, 119, 120, 122, 123, 124, 125,   4,   6, 127, 128, 126,
129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144,
145, 141, 146,   8, 147,  10, 148, 149,  12, 150, 151, 152, 153, 154, 155,
156, 157, 158, 159, 160, 161, 162, 163, 164,  17,  15, 165,  21, 166,  23,
167, 168,  25, 169, 170, 171, 173, 172, 174, 175, 176, 177,  27,  35, 178,
179,  29,  37, 180, 181, 182, 183,  42, 184, 185,  45, 186,  47,  58, 187,
 49,  60,  55, 188,  65,  72,  85, 189,  69,  74, 190, 102, 121]>;
AssertAttribute(G, "Order", 2^3 * 5^18 * 19);
