Examples of Groups - Groups

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# Examples of Groups

The `groups` object may be used to access examples of various groups. Using tab-completion on this object is an easy way to discover and quickly create the groups that are available (as listed here).

Let `<tab>` indicate pressing the `Tab` key. So begin by typing `groups.<tab>` to the see primary divisions, followed by (for example) `groups.matrix.<tab>` to access various groups implemented as sets of matrices.

- Permutation Groups (`groups.permutation.<tab>`)

  - `groups.permutation.Symmetric`

  - `groups.permutation.Alternating`

  - `groups.permutation.KleinFour`

  - `groups.permutation.Quaternion`

  - `groups.permutation.Cyclic`

  - `groups.permutation.ComplexReflection`

  - `groups.permutation.Dihedral`

  - `groups.permutation.DiCyclic`

  - `groups.permutation.Mathieu`

  - `groups.permutation.Suzuki`

  - `groups.permutation.PGL`

  - `groups.permutation.PSL`

  - `groups.permutation.PSp`

  - `groups.permutation.PSU`

  - `groups.permutation.PGU`

  - `groups.permutation.Transitive`

  - `groups.permutation.RubiksCube`

- Matrix Groups (`groups.matrix.<tab>`)

  - `groups.matrix.QuaternionGF3`

  - `groups.matrix.GL`

  - `groups.matrix.SL`

  - `groups.matrix.Sp`

  - `groups.matrix.GU`

  - `groups.matrix.SU`

  - `groups.matrix.GO`

  - `groups.matrix.SO`

- Finitely Presented Groups (`groups.presentation.<tab>`)

  - `groups.presentation.Alternating`

  - `groups.presentation.Cactus`

  - `groups.presentation.Cyclic`

  - `groups.presentation.Dihedral`

  - `groups.presentation.DiCyclic`

  - `groups.presentation.FGAbelian`

  - `groups.presentation.KleinFour`

  - `groups.presentation.Quaternion`

  - `groups.presentation.Symmetric`

- Affine Groups (`groups.affine.<tab>`)

  - `groups.affine.Affine`

  - `groups.affine.Euclidean`

- Lie Groups (`groups.lie.<tab>`)

  - `groups.lie.Nilpotent`

- Miscellaneous Groups (`groups.misc.<tab>`)

  - Coxeter, reflection and related groups

    - `groups.misc.Braid`

    - `groups.misc.Cactus`

    - `groups.misc.CoxeterGroup`

    - `groups.misc.PureCactus`

    - `groups.misc.ReflectionGroup`

    - `groups.misc.RightAngledArtin`

    - `groups.misc.WeylGroup`

  - other miscellaneous groups

    - `groups.misc.AdditiveAbelian`

    - `groups.misc.AdditiveCyclic`

    - `groups.misc.Free`

    - `groups.misc.SemimonomialTransformation`