
print "Imprimitive group of degree 72 due to Cappel. ";
print "Order: 26 778 504 199 680 = 2^9 * 3^21 * 5 ";
print "Base: 1,2,3,4,5,7,9,10,11,12,13,14,15,16,17,18,19,20";
print "Group: G";

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