Let F=GF(p^k) be any finite field. Let G be a group of all affine permutations on F (i.e. permutations of form ax+b). Then the set of all functions from F to \bar{F} is a linear representation of G, where g(f)=f(gx).

What are all sub-representations of this representation? Is it possible to characterize them?

Note: that in this case gcd(|G|,F) not equal to 1.

Let $F=\mathrm{GF}\left(p^k\right)$ be any finite field. Let $G$ be the group of all affine permutations on $F$ (i.e. permutations of form $x\mapsto ax+b$). Then the set of all functions from $F$ to $\bar{F}$ is a linear representation of $G$, where $g(f)(x)=f(gx)$.

What are all sub-representations of this representation? Is it possible to characterize them?

Note: that in this case $\mathrm{gcd}\left(\left|G\right|,F\right)$ not equal to $1$.

Let F=GF(p^k) be any finite field. Let G be a group of all affine permutations on F (i.e. permutations of form ax+b). Then the set of all functions from F to \bar{F} is linear represintation of G, where g(f)=f(gx).

What are all sub-represintations of represintation? Does it possible to charitirize them? Note: that in this case gcd(|G|,F) not equal to 1.

Let F=GF(p^k) be any finite field. Let G be a group of all affine permutations on F (i.e. permutations of form ax+b). Then the set of all functions from F to \bar{F} is a linear representation of G, where g(f)=f(gx).

What are all sub-representations of this representation? Is it possible to characterize them?

Note: that in this case gcd(|G|,F) not equal to 1.