Determine the highest order of an element of a Rubik's Cube group The period of a sequence of moves on a Rubik's Cube is the number of times it must be performed on a solved cube before the cube returns to its solved state. For example, a $90$° clockwise turn on the right face has a period of four; a $180$° clockwise turn on the right face and a $180$° turn on the top face has a period of $12$.
Let's make a $3\times3\times3$ Rubik's Cube group $G$. Each element of $G$ corresponds to each possible scramble of the cube - the result of any sequence of rotations of the cube's faces. Any position of the cube can be represented by detailing the rotations that put a solved cube into that state. With a solved cube as a starting point, each of the elements of $G$ directly align to each of the possible scrambles of the Rubik's Cube.
The cardinality of $G$ is $|G|=43{,}252{,}003{,}274{,}489{,}856{,}000=2^{27}3^{14}5^{3}7^{2}11$ and the largest order/period of any element in $G$ is $1260$. To elaborate, no algorithm needs to be performed on a cube more than $1260$ times to return it to the solved state.
Now let's say we extended $G$ for other sizes of cubes, so $G_3$ is the group of a $3\times3\times3$ and $G_4$ is a the group of a $4\times4\times4$. (If this isn't a valid naming convention, forgive me, I've just begun learning group theory).
Is there a way to find the highest order for any sequence of moves in $G_x$? For example, could I define a function $f$ such that $f(x)$ would give the highest order for any sequence of moves in $G_x$? What would $f$ look like? Would such a function be possible for any size of cube?
Thanks a lot in advance. Once again I apologize for any mistakes I've made; feel free to point them out or correct them.

Notations are from https://ruwix.com/the-rubiks-cube/notation/
$RY$ is an element of order 1260.
It's easy to check that $(RY)^{36}$ keeps all the corners intact but permutes the edges in 2 disjoint groups of order 5 and 7, respectively. So, the total order is $36*5*7=1260$.
$RY$ applied 36 times - https://ruwix.com/saved-rubiks-cube/?moves=RYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRYRY
