Is the DNA freely swimming in the nucleus?

Of course not, the DNA is enveloped into chromosomes, together with some proteins.

Click on a chromosome to get a description.

Each organism has a specific number of chromosomes.

Organism	Number of chromosomes
Carp	104
Dog	78
Horse	64
Chimpanzee	48
Human	46
Rat	42
Mouse	40
Cat	38

Each chromosome contains a piece of DNA, which has hundreds and thousands of nucleotides.