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


HTM (a^n and b^n are 1 move) L (11): b5 a33 b2 a34 b21' a39 b34 a6 b31' a11' b25' B (11): a27 b17' a34' b14 a5 b39' a14 b6' a15 b37' a7' U (12): a2 b2 a27 b36' a21 b22' a23' b13' a33' b29 a27' b12' R (12): a b7 a5 b35' a26 b14' a34 b35' a5 b17' a31' b5' F - at least 13 D (13): a b a22 b19 a6 b23 a13 b29' a39 b31' a36' b18 a21'
QTM (a2 = 2 moves, etc.) U - at least 40