As we know, the character of cats and dogs are different, for example, dogs usually follow their owners but cats usually not. But if a kitten is adopted with a group of puppies and grow up together, will it gain the character of dogs?
Yes and no. The cat will behave as much like a dog as a cat raised by humans behaves like a human.
It will learn how to read canine body language and noises, and figure out how to start and stop play, and the other essentials for living with the dogs. It will probably think of the dogs as big confused cats, just as it will think of the humans in the household as big confused cats. (Dogs think they're inferior humans; cats think we are inferior cats.)
So the cat may adopt some habits and tricks to get along with the dogs better. It will certainly consider the dogs good warm things for sleeping with and on. But it will remain essentally a cat; a lot of the basic behavior is built in. (A lot of ours is too, but we combine training the ape to follow directions and making up justifications for behaviors the ape does on its own.)
A friend of mine had a dog that had a pet cat. That was clearly the relationship; the cat spent more time with the dog than with the human, and the dog would carry the cat around as if it was a puppy or toy. But outside of that friendship, and always smelling like dog drool from being carried and washed all day, the cat was a cat.
I have a cat who was raised by my dog since he was five weeks old. Delilah nursed him, bathed him, cleaned his bottom, let him eat first - just like he was her puppy. (She is spayed so she only has this adopted child.) Blue behaves like a dog in many ways. He follows his people like a dog does. He sleeps on people beds every night, even though he is an indoor-outdoor cat. He grooms his dog-Mama's face! They regularly bump noses. Blue is now three-and-a-half. Still a puppy to Delilah.