
print "Imprimitive group of degree 100 constructed by Cappel. ";
print "The minimal systems of imprimitivity are as follows:-";
print "five systems comprising 50 blocks of size 2;";
print "one system comprising 20 blocks of size 5. ";
print "The group is soluble. ";
print "Order 7 812 500 = 2^2 * 5^9;  Base 1,3,5,7,9,11,13,15 ";
print "Group: G";

G := PermutationGroup<100 |
    \[   21,  82,  23,  84,  25,  86,  27,  88,  29,  90,  31,  92,
33,  94,  35,  96,  37,  98,  39, 100,  41,   2,  43,   4,  45,   6,  47,
 8,  49,  10,  51,  12,  53,  14,  55,  16,  57,  18,  59,  20,  61,  22,
63,  24,  65,  26,  67,  28,  69,  30,  71,  32,  73,  34,  75,  36,  77,
38,  79,  40,  81,  42,  83,  44,  85,  46,  87,  48,  89,  50,  91,  52,
93,  54,  95,  56,  97,  58,  99,  60,   1,  62,   3,  64,   5,  66,   7,
68,   9,  70,  11,  72,  13,  74,  15,  76,  17,  78,  19,  80],
    \[    4,   3,   5,   6,   8,   7,  10,   9,   2,   1,  19,  20,
12,  11,  14,  13,  15,  16,  17,  18,  24,  23,  25,  26,  28,  27,  30,
29,  22,  21,  39,  40,  32,  31,  34,  33,  35,  36,  37,  38,  44,  43,
45,  46,  48,  47,  50,  49,  42,  41,  59,  60,  52,  51,  54,  53,  55,
56,  57,  58,  64,  63,  65,  66,  68,  67,  70,  69,  62,  61,  79,  80,
72,  71,  74,  73,  75,  76,  77,  78,  84,  83,  85,  86,  88,  87,  90,
89,  82,  81,  99, 100,  92,  91,  94,  93,  95,  96,  97,  98],
    \[   11,  12,  13,  14,  16,  15,  17,  18,  20,  19,   2,   1,
 4,   3,   5,   6,   8,   7,   9,  10,  31,  32,  33,  34,  36,  35,  37,
38,  40,  39,  22,  21,  24,  23,  25,  26,  28,  27,  29,  30,  51,  52,
53,  54,  56,  55,  57,  58,  60,  59,  42,  41,  44,  43,  45,  46,  48,
47,  49,  50,  71,  72,  73,  74,  76,  75,  77,  78,  80,  79,  62,  61,
64,  63,  65,  66,  68,  67,  69,  70,  91,  92,  93,  94,  96,  95,  97,
98, 100,  99,  82,  81,  84,  83,  85,  86,  88,  87,  89,  90]>;
AssertAttribute(G, "Order", 2^2 * 5^9);
