What's For Multiplication... As summation symbol ($\sum$) is for summing up terms, is there a similar notation for multiplication (except factorial notation)?

$\prod$ (\prod) is the multiplicative analogue of $\sum$. It multiplies things together, where multiplication is assumed commutative.
But there's more! For some other commutative binary operations, the result of applying that operation to a list of objects may be denoted in a $\sum$-like notation, but with an enlarged operator taking $\sum$'s place. For example, $\bigwedge$ performs a logical AND ($\wedge$) of whatever follows, $\bigvee$ logical OR ($\vee$) and $\bigoplus$ logical XOR ($\oplus$).
