Does this stand any chance of being an ICS appeal?

[Markmyplace13]

I have been allocated a school almost 4 miles away (and an hour to travel to on public transport) for my dd starting reception this Sept. I missed out on all of my preferences for the local schools which are literally a street or a couple of streets away in each direction and missed my first choice which is 0.024 miles away by 48 feet (I live in over subscribed North London).
I was apparently allocated the closest school in the borough with a space.

Looking at the offers by school on my council website I have noticed that a school that I did not apply for because it is just less than a mile away and I thought I would be well out of catchment has a two form entry and a total intake of 56. I am struggling to find any grounds to make an appeal at the moment apart from just the general unfairness of it which I know the LEA will not consider but seeing this schools intake of 56 when all of the other surrounding schools have 30,60 or 90 has made me wonder if it is worth looking into.
Could I find out the PAN for this school and then make an appeal on infant class size even though I didn't list this school on the original application?
Surely making space for one extra child would not be too detrimental to the school and would be a better alternative than making a 4 year old child travel an 8 mile round trip every day?
If a PAN is set at less than 60 for a 2 form entry is there normally a good reason for this and are they quite rigid about it?
Sorry for all of the questions. If anyone can help I would be very grateful.

If its intake is 56 that is its PAN. You can't appeal on infant class size. You can apply to this school and appeal when your child is refused entry. With a PAN of 56 this would not be an ICS appeal. That is a good thing as it means you can try to make the case that this is the right school for your daughter. Having said that, an 8 mile round trip is not usually grounds for a successful appeal so you will need to look for other factors to boost your case.

A PAN of 56 suggests the school has some small classrooms. It is for the appeal panel to decide whether the classrooms are really too small to take any extra pupils. If they think the classrooms are big enough it is quite likely the appeal panel will admit up to 4 pupils.

Thank you both prh and twiggy for taking time out to give really helpful replies. I must have been confused about the ICS conditions for an appeal but you have given me a little more hope if a non ICS appeal stands a slightly better chance.
My dd has speech and language difficulties and receives speech therapy but because she doesn't have a statement I didn't put this on the application. She is quiet and very shy because of her speech difficulties and finds it hard to feel comfortable in a group however at least one of the friends she has made in nursery are starting at the school that has a PAN of 56. I wonder if a letter of support from her speech therapist suggesting that it would help her to start school with some children she is familiar with might help in an appeal? I know I'm probably grasping at straws.

Thanks so much Tiggytape. I will get to work! Really your help on this forum is invaluable!

You will qualify for home to school transport if you stick with the school that's almost 4 miles away. Below the age of 8, it is recommended that school journeys shouldn't take longer than 45 minutes, so you may qualify for something like a cab.