OT: Can't remember name of science fiction novel

[dmm]

Hey dudes, long time no post. I've got a tough one for you. Hope you can help me out. I've searched all over and can't figure out the name of a sci fi book I read once. Here is a plot synopsis:

A young woman is a weak telepath in a world that has discovered telepathy and outlawed it. She wants to link up with other telepaths but she only seems to be good at reading minds, not sending info, so she can't send out a telepathic SOS. The plot thickens as the authorities begin to suspect her. A lot of stuff happens that I forget, including a love story, but in the end she finds out that she is actually a master telepath who is especially gifted at receiving. Somehow she ends up on the Moon with a bunch of other telepaths and they all beam away (telepathically of course), aided by telepathic aliens.

OK, now that you're done laughing, please help! My plot synopsis does not do the book justice. I'm going nuts that I can't find this book again. It was published some time before 1979.

First one to answer correctly will get some sort of prize.