what would happen if you connect the live from a portable generator into the ground of mains?

depends on the rest of the connections you make. If the neutral and ground of the generator are unconnected and you connect the hot wire of the generator to ground, nothing much will happen BUT the body of the generator will become hot and dangerous to touch.

If the neutral and/or ground of the generator are connected to the neutral and/or ground of the mains and you connect the hot wire of the generator to ground, you will be shorting out the generator and breakers will pop.

Connecting live to live, assuming the neutral and ground of the generator are connected also, is OK only if the frequency, phase, and amplitude are correctly matched. If not you will get high currents and a breaker will pop. When one generator is at + peak, and the other (or mains) is at – peak, you get high currents.  I doubt that portable generators have the ability to do this matching.

Just connecting the generator ground to either a ground rod or mains ground should have no adverse effect at all.

Connecting generator and mains neutral would likely trip any earth leakage breaker in the system due to unbalanced loads.

If that did not break the circuit, then cross connecting lives as well would cause a catastrophic fault due to excess current, with the voltage out of phase between two different AC systems.

Power from two different AC sources must be synchronised in frequency then phase and amplitude for them to not conflict and cause extreme current flow between them.