Abstract Algebra mathematica add on

hey,

I have this group I've been trying to generate using the GenerateGroupoidByRelations[] function but it keeps giving me an error,

G = GenerateGroupoidByRelations[{a, b}, {a^4 == e, b^4 == e, a ** b ** a ** b == e, a^3 ** b ** a^3 ** b == e}, SizeLimit -> 60]

gives

GenerateGroupoid::size: The size of the set generated thus far exceeds the current value of 25 given by the option SizeLimit. (The elements generated thus far are shown below.)

It outputs a list of elements after this, but it depends on what i set the sizelimit too, if i set it to a large number ,it will spit out hundreds, if set it to 60 it will spit out 60

This group only has 16 elements which I found after an hour of todd coxeter,

Does anyone know how I could get mathematica to generate this group?