Hi
The core switch is usually your most powerful switch and depending on the design its the one with routing on it and connected to your firewall , there is no command which will tell you what the core switch is , it will be based on the topology and design of the network , are the switches all layer 2 whats there default-gateway where they are sending traffic too and if there routing where is the routing pointing to that may give you another indication as traffic is usually processed through teh core switch , run a trace from a local pc and see where the traffic path is going whats the last switch it hits before breaking out of the network that's usually your core switch 2 as path goes up through access/distribution layers and hits core and break out to internet or ISP network
