[GAP Forum] Finding [2,p]-generated groups

[R. Keith Dennis]

I'm doing similar, but more complicated computations now.  In your
case you can eliminate many groups from consideration almost instantly
by using EulerianFunction(G,2) to determine if the group is generated
by 2 elements or not.  After that, I suppose you could save a bit
by letting the first element range over representatives of conjugacy
classes of elements of order 2 (resp p), but for the second element
testing all relevant ones seems like the simplest way to go.  
I guess it depends on how many cases you want to check.

Keith

> I have the following problem: I want to list all the groups of order
>n generated by one element of order 2 and one element of order p>2,
>with p prime (and n divided by 2 and by p, of course). I can achieve
>that goal using the SmallGroup library and testing all the groups of
>order n, but is there any faster way ?  Same question for the groups
>generated by two elements of order p, with p prime.