can someone please help me trying to find the centre of the following subgroup

H=

where a,b,c belong to Reals and ac not equal to zero

ive tried

then equating to find the values of a b and c. but have had no luck

also tried replacing f,g,h with 1's and 0's with no luck

the answer is Z(H)=

Got an exam in a couple of days so any help appreciated. Can never do these kinds of questions so a general method would be nice.