# Standard Action

Every finite Coxeter group $W$ has a standard action. For example, the standard action group of a Coxeter group of type $A_n$ is the symmetric group of degree $n+1$ acting on $\{1,\dots,n\}$.

## `StandardAction(W): GrpFPCox -> Map`

## `StandardAction(W): GrpPermCox -> Map`

The standard action of the finite Coxeter group $W$.

## `StandardActionGroup(W): GrpFPCox -> GrpPerm, Map`

## `StandardActionGroup(W): GrpPermCox -> GrpPerm, Map`

The group $G$ of the standard action of the finite Coxeter group $W$, together with an isomorphism $W\to G$.

## `Example: Standard Action (ex-eff773)`

```magma
> W := CoxeterGroup("A3");
> G, h := StandardActionGroup(W);
> IsSymmetric(G);
true
> h(W.1); h(W.2); h(W.3);
(1, 2)
(2, 3)
(3, 4)

```