# Automatic Groups of 3-Manifolds

This database contains automatic groups for 5,389 of the 10,986 small-volume closed hyperbolic manifolds in the Hodgson–Weeks census.

## `AutomaticGroup(i): RngIntElt -> GrpAtc`

## `AutomaticGroup(name): MonStgElt -> GrpAtc`

## `AutomaticGroup(r): Rec -> GrpAtc`

Returns the automatic group associated with the specified hyperbolic manifold, if present in the database. The manifold may be specified as an index $i$ ($1 \le i \le 5800$), a name from the Hodgson–Weeks census, or a record from the manifold database (as described in Section [Fundamental Groups of 3-Manifolds](3-manifolds-database.md#sectthreemanifolds)).

## `AutomaticGroupIndices() -> [RngIntElt]`

Returns a sequence of the valid indices for use with `AutomaticGroup`.

## `AutomaticGroupNames() -> [MonStgElt]`

Returns a sequence of the valid names for use with `AutomaticGroup`.