[GAP Forum] Extra-special group acting on an elementary abelian group

[Goodson, Joshua E]

Hello,

I am trying to count the orbits of an extra-special group of order 3^5 acting on an elementary abelian group of order 7^9.  I start with the automorphism group of the elementary abelian group and then try to find the isomorphic image of the extra-special group, but because of the size of the automorphism group the computer cannot finish.  I also try to find the group myself by first finding the Sylow subgroup of the automorphism group, but again the computer has a problem finishing.  I believe in each case it mentions running out of memory.  So I was wondering if there is another way I can perform the desired action GAP or would a better computer be able to find the subgroup of the automorphism group that I want?

Thank you