On HP-UX 10.20 the "file" command can tell you a little bit about the core file:
> file core
core: core file from 'sleep' - received SIGQUIT

That is the output I get from a core file that I intentionally created. And it's right, I did a "sleep 500" and then I sent a quit signal to the process.

To take it further, I would need to use a debugger. Usually that implies that the program needed to be built in a special way to enable the use of a particular debugger.

I could always do something like:
adb /usr/bin/sleep core
but this will be very rough since the sleep program has been stripped. adb, like all debuggers, is an interactive program. Knowing how to use it will require a lot of assembly language knowledge.

A core file is (basicly) the data and stack segments of the process. You can use programs like "strings" and "od" on it if you're looking for something in particular.