# Group algebra of permutation group, error

Why does not

```
GroupAlgebra(PermutationGroup([(1,2,3),(2,3,4)]),QQ).center_basis()
```

work when

```
GroupAlgebra(AlternatingGroup(4),QQ).center_basis()
```

does work?

The first command gives a long error message, terminating with the slightly bizzare

```
RuntimeError: There is a bug in the coercion code in Sage.
Both x (=()) and y (=()) are supposed to have identical parents but they don't.
In fact, x has parent 'Permutation Group with generators [(2,3,4), (1,2,3)]'
whereas y has parent 'Permutation Group with generators [(2,3,4), (1,2,3)]'
Original elements () (parent Permutation Group with generators [(2,3,4), (1,2,3)]) and () (parent Permutation Group with
generators [(2,3,4), (1,2,3)]) and maps
<class 'NoneType'> None
<class 'sage.structure.coerce_maps.DefaultConvertMap_unique'> (map internal to coercion system -- copy before use)
Coercion map:
From: Permutation Group with generators [(2,3,4), (1,2,3)]
To: Permutation Group with generators [(2,3,4), (1,2,3)]
```

It says it's a bug. So it needs to be reported.