4 fix typo

Is it known how many faithful linear representations a finite group G has on a complex vector space of given dimension? What if G is abelian?

I would even be interested in this special case: the smallest dimension of a faithful representation of an abelian group over C is the number of factors in the group's invariant factor decomposition, how many faithful representations are there of that dimension? Is it It is not just the sum of φ(mi) (where mi are the orders of the "invariant factors") (e.g. Z/2 × Z/2 has 3 faithful two-dimensional representations).

3 strikeout didn't work (though preview was fine). reword instead.

Is it known how many faithful linear representations a finite group G has on a complex vector space of given dimension? What if G is abelian?

I would even be interested in this special case: the smallest dimension of a faithful representation of an abelian group over C is the number of factors in the group's invariant factor decomposition, how many faithful representations are there of that dimension? Is it not just the product sum of φ(mi) (where mi are the orders of the "invariant factors") (i.e. are the only ones sums of e.g. Z/2 × Z/2 has 3 faithful characters of the factors)?two-dimensional representations).

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