Neon tetra care question?

I have a 6 gallon Eclipse System 6 (6 gallon tank with a built in filter that filters 75 gph) and I was wondering if that would be large enough for 5 or 6 neon tetras, though I believe that it's not enough. Also, I have water conditioner, a filter, a 3 gallon bucket, a thermometer, a water test kit (includes ammonia, nitrate, nitrite and ph test kits), a gravel vacuum, and fish food. What else would I need to support neon tetras?