Educate Me: is a pool one bitcoin node?

[xdigital]

I do have a general idea how bitcoin and bitcoin mining work.
As I understand, when a bitcoin client software (bitcoin-qt, bitcoind,...) runs, It is 1 node of the whole p2p bitcoin network.
When you do solo mining, miner communicates with this client to get information to "hash".
With pooled mining (expect P2Ppool.info), all miners connect to one server; which I assume it running one bitcoin client software (am I right?)

I know Ghash.io is the biggest pool and can reach 51% of the total hash rate.
But all of their mining machines are pointed to 1 bitcoin client, which is just 1 node of the whole network.
I don't know exactly how many nodes currently there are in the network, but I would guess more than 100000 nodes.

How could one node (yes with hash power) can affect the network?

Thank

[Bitcoinpro]

its just acting as one node

[Remember remember the 5th of November]

A pool is basically a proxy to a Bitcoin node, but there are many ways one can write a pool, somebody could even integrate it into the bitcoin node directly, or keep it as a separate instance or even have multiple nodes connected to which it sends data.

[bitpop]

They aren't even a node. They use a special slimmed down node. But I'm sure they run several real ones.