# Groups¶

- Examples of Groups
- Base class for groups
- Set of homomorphisms between two groups.
- Group homomorphisms for groups with a GAP backend
- LibGAP-based Groups
- Generic LibGAP-based Group
- Mix-in Class for GAP-based Groups
- PARI Groups
- Miscellaneous generic functions
- Free Groups
- Finitely Presented Groups
- Named Finitely Presented Groups
- Braid groups
- Indexed Free Groups
- Right-Angled Artin Groups
- Functor that converts a commutative additive group into a multiplicative group.
- Semidirect product of groups
- Miscellaneous Groups
- Semimonomial transformation group
- Elements of a semimonomial transformation group.
- Class functions of groups.
- Conjugacy classes of groups

## Abelian Groups¶

- Multiplicative Abelian Groups
- Finitely generated abelian groups with GAP.
- Automorphisms of abelian groups
- Multiplicative Abelian Groups With Values
- Dual groups of Finite Multiplicative Abelian Groups
- Base class for abelian group elements
- Abelian group elements
- Elements (characters) of the dual group of a finite Abelian group.
- Homomorphisms of abelian groups
- Additive Abelian Groups
- Wrapper class for abelian groups

## Permutation Groups¶

## Matrix and Affine Groups¶

- Library of Interesting Groups
- Base classes for Matrix Groups
- Matrix Group Elements
- Finitely Generated Matrix Groups
- Homomorphisms Between Matrix Groups
- Matrix Group Homsets
- Binary Dihedral Groups
- Coxeter Groups As Matrix Groups
- Linear Groups
- Orthogonal Linear Groups
- Groups of isometries.
- Symplectic Linear Groups
- Unitary Groups \(GU(n,q)\) and \(SU(n,q)\)
- Heisenberg Group
- Affine Groups
- Euclidean Groups
- Elements of Affine Groups