Let A = L F R B', then <U,A> is the whole cube group


HTM (U^n and A^n) L (11): A121 U A103' U A46 U A34' U' A12' U' A18' R (11): A90 U A96 U A111' U' A41' U A79' U A123' B (11): U' A77' U A189 U2 A188 U' A183 U A189 U' F (13): A32 U A63 U' A75 U A75' U2 A155' U' A43' U' A2' D (13): A62' U' A95 U' A203' U A159 U' A194' U2 A46' U' A'
QTM (A2 = 2 moves, etc.) L (37): U' A2' U A U A3 U' A2' U A U A' U' A' U A U A U' A' U' A2 U A3' U' A' U' A2 U F (39): A3 U' A' U A' U A' U A U' A4' U A4 U' A' U' A3' U' A5 U' A U A3'