print "The automorphism group of the 5 x 5 x 5 Rubik cube.";
print "The group is represented as a permutation group of degree 144.";
print "Its order is";
print "2^91 * 3^44 * 5^15 * 7^11 * 11^7 * 13^3 * 17^3 * 19^3 * 23^3.";
print "Group: G";

G := PermutationGroup<144 |
    (40,88,9,96)(28,76,21,84)(16,64,33,72)(4,52,45,60)(41,5,8,44)
        (42,17,7,32)(43,29,6,20)(18,19,31,30)(101,127,104,126)
        (98,128,107,125)(124,136,129,144),
    (39,87,10,95)(27,75,22,83)(15,63,34,71)(3,51,46,59)(123,135,130,143),
    (52,53,93,44)(51,65,94,32)(50,77,95,20)(49,89,96,8)(9,12,48,45)
        (10,24,47,33)(11,36,46,21)(22,23,35,34)(99,132,108,129)(102,131,105,130)
        (109,137,120,128),
    (54,81,43,64)(66,82,31,63)(78,83,19,62)(90,84,7,61)(138,117,127,112),
    (57,60,96,93)(58,72,95,81)(59,84,94,69)(70,71,83,82)(45,89,37,41)
        (46,90,38,42)(47,91,39,43)(48,92,40,44)(111,144,120,141)(114,143,117,142)
        (108,119,106,107),
    (33,77,25,29)(34,78,26,30)(35,79,27,31)(36,80,28,32)(105,116,103,104),
    (49,52,88,85)(62,63,75,74)(50,64,87,73)(51,76,86,61)(5,1,53,9)
        (6,2,54,10)(7,3,55,11)(8,4,56,12)(109,136,118,133)(112,135,115,134)
        (98,97,110,99),
    (17,13,65,21)(18,14,66,22)(19,15,67,23)(20,16,68,24)(101,100,113,102),
    (57,48,49,1)(69,36,61,13)(81,24,73,25)(93,12,85,37)(89,53,56,92)
        (90,65,55,80)(91,77,54,68)(66,67,79,78)(110,140,119,137)(113,139,116,138)
        (132,133,121,141),
    (94,11,86,38)(82,23,74,26)(70,35,62,14)(58,47,50,2)(131,134,122,142),
    (85,5,60,92)(86,17,59,80)(87,29,58,68)(88,41,57,56)(1,4,40,37)
        (2,16,39,25)(3,28,38,13)(14,15,27,26)(100,123,103,122)(97,124,106,121)
        (118,125,111,140),
    (73,6,72,91)(74,18,71,79)(75,30,70,67)(76,42,69,55)(115,126,114,139)
>;

AssertAttribute(G, "Order", 2^91 * 3^44 * 5^15 * 7^11 * 11^7 * 13^3 * 17^3 * 19^3 * 23^3);
