Let a = U L and b = F R B, then <a, b> is the whole cube group


UTM (a2 = 2 moves, a' = a104 = 104 moves, etc.) R (59*) bbbaaaaababbbabaabbbabbbbaaabbbabaabaaabaaaaaabaababaababab D (61*) aaaabababbbaaababbaaababbaabaababbbabbaaabbabbaababbbaaababab B (64*) abbbbbababaaaaababbbbbabbababaabbaaaababbaaababbbababababaababab U (65*) bbbbbaabaaabbabbbbbababbaababaaababbaabbaababbbbbaaabbaabbaaaaaaa L (65*) ababbabababaabbaaabaaabbbbbbbabbabababaabaaabbbabbbbaabaaaaabbaab F (65*) bbbbbbbbbabbbaaabaabbaaabbabbbababbabbbbaabbaababbbbabaaababbaaba M2 E2 S2 (65*) baaaababbbababaaababbbababbbbaaaaabbaababababbbabababbaababaababa