Linearly primitive group
This article defines a property that can be evaluated for finite groups (and hence, a particular kind of group property)
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A finite group is said to be linearly primitive if it has a faithful irreducible representation over an algebraically closed field of characteristic zero (or equivalently, over the algebraic closure of rationals or over the complex numbers).
Definition with symbols
A group is said to be linearly primitive if there is a homomorphism for some vector space over the complex numbers, such that has no proper nonzero -invariant subspace.