Question

Classify all groups of order 1225 upto isomorphism

Answer 1

"Classify all groups of order 12251225". That's all the question says. How in the world do I approach this?? We have the symmetric group of order 12251225, cyclic group of order 1225=5∗5∗7∗71225=5∗5∗7∗7 and so we have that as a group.. but the list just seems so big. How do we classify all groups of this order, it's huge! We had a similar question on groups of order 88 the other week and it wasn't easy..

Thanks for any help guys!