# Coset Tables and Transversals

The functions described in this section apply only to finite groups for which a base and strong generating set may be constructed.

## `CosetTable(G, H): Grp, Grp -> Hom(Grp)`

The (right) coset table for the group $G$ over subgroup $H$ relative to its defining generators.

## `Transversal(G, H): GrpMat, GrpMat -> { @ GrpMatElt  @}, Map`

## `RightTransversal(G, H): GrpMat, GrpMat -> { @ GrpMatElt  @}, Map`

Given a matrix group $G$ and a subgroup $H$ of $G$, this function returns

**(a)**
A set of elements $T$ of $G$ forming a right transversal for $G$ over $H$; and

**(b)**
The corresponding transversal mapping $\phi: G \rightarrow T$. If $T = [t_1, \ldots, t_r]$ and $g \in G$, $\phi$ is defined by $\phi(g) = t_i$, where $g\in H*t_i$.