Diameter of the M24 Conway puzzle is 45

This is a well know puzzle in which there are two moves, one which rotates the central "clock" by one position
clockwise or counter-clockwise.

The other switches or swaps each pair of numbers with matching colours.

I decided to plug these values into GAP to investigate God's number for the underlying group for this puzzle

as it still seemed be unknown or undocumented anywhere at least.

Feeding these numbers into GAP we get:

S := (1,24)(2,23)(3,4)(5,22)(6,11)(7,8)(9,10)(12,21)(13,14)(15,20)(16,17)(18,19);