
print "The automorphism group of the 4 x 4 x 4 Rubik cube.";
print "The group is represented as a permutation group of degree 72.";
print "Its order is";
print "2^50 * 3^29 * 5^9 * 7^7 * 11^4 * 13^2 * 17^2 * 19^2 * 23^2.";
print "Group: G";

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