I am in a group of 5 that needs to get from Geneva airport to Chamonix this summer to hike the Haute Route? Any suggestions?

yup, there is a bus you can take. takes a while with all the stops.

I used Mountain Drop-Offs when I went climbing in Chamonix 2 years ago. It's probably a bit more expensive than a public bus but it was very convenient.

https://www.mountaindropoffs.com/

If you've got time you could try to hitch hike. Better to hitch hike to get there than to get back on account of the smell factor.

You have a few options. I used Chamonix Express. It costs only about thirty euro each way. They will wait for you at the airport and drop you to your accommodation. Its a great service. If money or time isn't too much of an problem I would really recommend taking the train via Martigny. It is a stunning trip. Either way, enjoy.

Yeah, as Mallowman above says, there are a lot of minibus companies that'll do the job for about 30 euros each way. Personally I use Alpybus but mostly 'cos it's a cute name and they've never let me down