[GAP Forum] Group with complex matrices

[Marek Mitros]

Hi,

I have diagonal matrix f1 with vector [1, E(5), E(5)^2, etc,... on the
diagonal. The order of the matrix is 5. When I perform Size(Group(f1))
it hangs for a minute or so before it gives the answer 5. Why it takes
so long ? For human being it is obvious, that group generated by one
element of order 5 will be of size 5 and it is abelian.

Can you explain what calculation GAP does when determining size of the
matrix group ?
I observed that matrices over finite fields are processed quicker than
complex matrices.

Regards,
Marek