question about a front lever

if i want to be able to hold a front lever longer, which muscle group should i focus on strengthening? the lats? the core? please help and thanks.

Both? I suppose the first question you need to answer is can you hold a full front lever....

To be honest, in my experience the people i know who can hold a solid front lever find it less an issue of muscular strength and more an issue of technical proficiency. So in essence, if you want to hold longer front levers - do more front levers. Some good ideas if your bored of straight holds include front lever pulls (or ice-cream makers), yewkis, cranks, 360 pulls etc.

Or if you're a bit more energetic for something different, you could do some bouldering on roofs...

Depends on your weakest link. That will always be the most bang for your buck.