Dicyclic group

The dicyclic group of order $4n$ has generatorsEvery element has a unique form $a^k$ or $a^{k}b$, with $0\le k<2n$.

Four one-dimensional characters and $n-1$ two-dimensional characters exhaust a dicyclic group of order $4n$. In the two-dimensional rows, the values at $a^r$ are $2\cos (\pi jr/n)$ and those on the two noncyclic cosets are zero. The one-dimensional rows depend on whether $n$ is odd or even.