Dear GAP forum,

I'd like to generate a group using two elements A and S: G = <A,S>. I
don't know if this group is finite. Someone can help me?

S = diag(1,1,-1,-1)

A =
[0,                 0,             cos(s),     -sin(s)]
[-sin(t),         cos(t),             0,             0]
[cos(t),         sin(t),             0,             0]
[0,                 0,             sin(s),     cos(s)]

with

cos(t) := 1/4 + 1/4 sqrt(5)

sin(t) := 1/4 sqrt(2) sqrt(5 - sqrt(5))

cos(s):= 3/4 - 1/4 sqrt(5)

sin(s):= 1/4 sqrt(2 + 6 sqrt(5))

Thank you, Nicola.