print "An imprimitive group of degree 90 with 10 blocks";
print "of size 9. The group acting on the blocks is";
print "A6.2^3, while the kernel of this action is";
print "a group of order 2^3 * 3^4. ";
print "Order: 466 560 = 2^7 * 3^6 * 5;  Base: 1,2,3. ";
print "Group: G";

G := PermutationGroup<90 |
    \[ 2,   3,   1,   6,   8,  10,  12,  14,  15,   4,  17,  19,
20,   5,  22,  24,  25,  27,   7,  30,  32,   9,  35,  37,  11,  39,  41,
21,  36,  13,  45,  28,  43,  49,  44,  52,  16,  47,  55,  57,  18,  60,
62,  23,  63,  65,  67,  68,  58,  40,  71,  29,  73,  70,  26,  74,  50,
34,  77,  78,  79,  33,  31,  80,  76,  59,  38,  81,  82,  83,  84,  69,
85,  75,  56,  46,  66,  42,  86,  87,  48,  72,  54,  51,  53,  61,  64,
89,  90,  88],
    \[ 1,   4,   5,   7,   9,  11,  13,   2,  16,   3,  18,  12,
15,  21,  23,  19,  26,  28,  29,  31,  33,  34,  36,  24,  38,  40,  42,
43,  44,  30,  46,  47,  48,  50,  51,   8,  53,  54,  56,  58,  59,  61,
39,  10,  64,  66,  20,  69,  70,  71,  72,  45,  17,  68,  25,  75,  14,
76,  73,  60,  67,  32,  63,  55,  62,  65,  35,  52,  49,  57,  80,  82,
81,  74,   6,  79,  22,  41,  37,  88,  83,  27,  85,  77,  89,  86,  87,
84,  78,  90]>;
AssertAttribute(G, "Order", 2^7 * 3^6 * 5);
