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FORTRAN 90 help!

Could anyone help me with using fortan 90? I'm doing a project on group theory and i am supposed to use fortran 90 and create various programs, e.g. one which will calculate the order of any element of a groups, etc...(the groups in question are up to order 12)
I am trying to define my own variabe type GroupElement and to overload * with group multiplication but i am really confused how to because up to order 12 groups there re abelian and non abelian...

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