Go see an OT, a play group is nice for socialization, but he needs to be evaluated and get therapy started. He has all that energy because he is seeking what he needs. My son is 8 with SPD. I suggest all the heavy work you can give hi, watch his diet, heavy work would include:
have him carry in the milk, laundry detergent, things like that. Get him a backpack he loves and fill it with heavy things, get a small trampoline for in the house so he can jump on that, punishment cards and chart. Deep pressure, push ups for punishment, there is a conversation on here about that, it Is a good one.
Second, DO NOT allow him o be labeled as the "problem child" !!!!!!!! Go in there to his teacher and your special ed department and get him screened and started with an IEP. HE is not a behavior problem and you do not want them to label him as such!!!! He needs help within the classroom and they need to provide it ( is this a public school?) You go in with the tools to start the teacher off. Sit fit cushion for class, they are like $25 or so you can find one on therapy shoppe online. Fidget toy for at the desk, wing nut pencil toppers are great. They are not noisy. He is hurting, he is overwhelmed and over stimulated!! Have him pulled from the cafeteria, could be that it is too noisy and he doesn't have a chance to re-group. He needs a quiet moment to pull himself together. My son was coming home with migraines from school because he was never given a chance to have a time to himself. He eats lunch everyday in a separate room with a teacher and a few other students. No more headaches. Have the teacher allow him to be the "back captian" he is then allowed to hold the "heavy" door and gives him a moment to get the input he needs. She can watch him for signs he is going to meltdown or get out of control and he can run a message to the office or another teacher (even if nothing is on the paper) my son's teacher does this for him. You HAVE to be your sons advocate nobody else is going to be. Get that teacher on track. Visual cues are great, watch him for different signs and then you can work from there. Consistancy is key, have a calendar for him posted so he knows what is coming next. These kids thrive on structure but also need to know that things don't always go the way they want them too. Start with an OT, look online for different resources that fit him and your home. I highly recommend heavy work. I can't stress enough the importance of getting in that school and getting his teacher on track, go in armed with information and get him an IEP, then he can get pull outs which are great for his system!!!!!!! Good Luck to you!!!!!!

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If they are seeking out excessive proprioceptive input, they are looking for a way to calm and organize their nervous system. They may seem disruptive, full of excessive energy, or even unsafe. These are the crashers, jumpers, movers, and shakers! These are the children we ABSOLUTELY want to target with heavy work activities. It WILL make a difference in them!
this is from a sensory site, forgot the name, let me look it up again!!!!! lol

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playing with playdoh if he can stand the smell, that is hard work also builds strength in fine motor which a lot of these kids lack. here is the site where it explains what he is seeking by doing all the jumping and crashing!!! sensory-processing-disorder/heavywork.com