What variety strawberry do I have?

I can post a picture later if anyone thinks it's necessary, but it just looks like a typical, medium-sized red strawberry. It doesn't put out long runners, but spreads slowly at the edges of the clump. I torture it terribly, so it's a little hard to tell if it's everbearing or not. It fruits heavily early summer, stops for the dry season when I don't water, then fruits a little again in the fall once it cools down and the rains start again. Everyone moans a bit the first time they eat one of the berries and then goes on a rant about crappy supermarket berries or starts reminiscing about their childhood.

I bought it from a co-worker whose daughter was doing a dry grad fundraiser or something. I'm hoping that's a clue. Maybe a certain type is often used in commercial hanging baskets or something :D

It spreads so slowly, that I'd like to buy more to plant around the property. Every other strawberry I've got from the local nurseries tastes like nothing compared to this one. I've ended up ripping them all out again.

A picture of the plant and fruit would help. I'm tempted to say it's an alpine strawberry but haven't seen one yet with medium sized fruit.  Does it ever put out runners or just clumps.

My daughter received a Seascape strawberry as part of a local festival that was cancelled. Planted it several months ago, it put out a few berries and sat there.  Since we're not seeing mid-90's temps, it has started to grow and finally put out a lone runner and is fruiting again.  I don't know if this particular variety doesn't produce many runners or if it was just stressed from the heat and dry conditions

I don't think it's an alpine. It has put out a few runners over the four years I've had it. Like, six maybe? The longest one was about 8" long.  The crappy strawberries planted in the same bed and equally abused put out endless amounts of very long runners.

Seascape sounds like a good variety to try out, even if it's not what I have. I suppose I should just be looking for good varieties to try, regardless of what I have already.

Jan, I have no clue what variety that could be. Would it be possible to dig a few plants from the edges of the clump to plant elsewhere?  

I'm currently getting a patch of wild strawberries established and I think they put out a runner every few minutes. Many years ago I kept the runners pulled off a single plant for a year and it had formed a small clump by the end of the season.  It was a lot of work but I did get several sweet tiny berries from that clump the next spring.