====== BigObject Group ======
//from application [[..:group|group]]//\\
\\
 Object encoding a finite group.

===== Properties =====

==== Symmetry ====
 These properties capture information of the object that is concerned with the action of permutation groups.
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{{anchor:character_table:}}
  ?  **''CHARACTER_TABLE''**
  :: The character table. NOTE: We do not support complex characters, but for the moment only real ones.
    ? Type:
    :''[[..:common#Matrix |Matrix]]<[[..:common#QuadraticExtension |QuadraticExtension]]<[[..:common#Rational |Rational]]>,[[..:common#NonSymmetric |NonSymmetric]]>''


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{{anchor:conjugacy_class_sizes:}}
  ?  **''CONJUGACY_CLASS_SIZES''**
  :: The sizes of the conjugacy classes
    ? Type:
    :''[[..:common#Array |Array]]<[[..:common#Int |Int]]>''


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{{anchor:facets_action:}}
  ?  **''FACETS_ACTION''**
  :: operates on indices
    ? Type:
    :''[[..:group:PermutationAction |PermutationAction]]<[[..:common#Int |Int]],[[..:common#Rational |Rational]]>''


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{{anchor:facet_normals_action:}}
  ?  **''FACET_NORMALS_ACTION''**
  :: operates on indices
    ? Type:
    :''[[..:group:PermutationAction |PermutationAction]]<[[..:common#Int |Int]],[[..:common#Rational |Rational]]>''


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{{anchor:homogeneous_coordinate_action:}}
  ?  **''HOMOGENEOUS_COORDINATE_ACTION''**
  :: operates on indices, including the '0'-th homogeneous coordinate
    ? Type:
    :''[[..:group:PermutationAction |PermutationAction]]<[[..:common#Int |Int]],[[..:common#Rational |Rational]]>''


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{{anchor:implicit_set_action:}}
  ?  **''IMPLICIT_SET_ACTION''**
  :: an action on sets where only one representative for each orbit is stored
    ? Type:
    :''[[..:group:ImplicitActionOnSets |ImplicitActionOnSets]]''


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{{anchor:inequalities_action:}}
  ?  **''INEQUALITIES_ACTION''**
  :: operates on indices
    ? Type:
    :''[[..:group:PermutationAction |PermutationAction]]<[[..:common#Int |Int]],[[..:common#Rational |Rational]]>''


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{{anchor:input_cones_action:}}
  ?  **''INPUT_CONES_ACTION''**
  :: operates on indices
    ? Type:
    :''[[..:group:PermutationAction |PermutationAction]]<[[..:common#Int |Int]],[[..:common#Rational |Rational]]>''


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{{anchor:input_rays_action:}}
  ?  **''INPUT_RAYS_ACTION''**
  :: operates on indices
    ? Type:
    :''[[..:group:PermutationAction |PermutationAction]]<[[..:common#Int |Int]],[[..:common#Rational |Rational]]>''


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{{anchor:maximal_cones_action:}}
  ?  **''MAXIMAL_CONES_ACTION''**
  ::
    ? Type:
    :''[[..:group:PermutationAction |PermutationAction]]<[[..:common#Int |Int]],[[..:common#Rational |Rational]]>''


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{{anchor:order:}}
  ?  **''ORDER''**
  :: The number of elements in the group
    ? Type:
    :''[[..:common#Integer |Integer]]''


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{{anchor:permutation_action:}}
  ?  **''PERMUTATION_ACTION''**
  :: a permutation action on integers
    ? Type:
    :''[[..:group:PermutationAction |PermutationAction]]<[[..:common#Int |Int]],[[..:common#Rational |Rational]]>''


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{{anchor:rays_action:}}
  ?  **''RAYS_ACTION''**
  :: operates on indices
    ? Type:
    :''[[..:group:PermutationAction |PermutationAction]]<[[..:common#Int |Int]],[[..:common#Rational |Rational]]>''


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{{anchor:regular_representation:}}
  ?  **''REGULAR_REPRESENTATION''**
  ::
    ? Type:
    :''[[..:group:MatrixActionOnVectors |MatrixActionOnVectors]]<[[..:common#Rational |Rational]]>''


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{{anchor:set_action:}}
  ?  **''SET_ACTION''**
  :: a permutation action on a collection of sets of integers
    ? Type:
    :''[[..:group:PermutationAction |PermutationAction]]<[[..:common#Set |Set]]<[[..:common#Int |Int]]>,[[..:common#Rational |Rational]]>''


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{{anchor:simplexity_lower_bound:}}
  ?  **''SIMPLEXITY_LOWER_BOUND''**
  :: The symmetrized version of ''[[..:group:Group#SIMPLEXITY_LOWER_BOUND |SIMPLEXITY_LOWER_BOUND]]''.
    ? Type:
    :''[[..:common#Int |Int]]''


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{{anchor:vector_action:}}
  ?  **''VECTOR_ACTION''**
  :: operates on indices
    ? Type:
    :''[[..:group:PermutationAction |PermutationAction]]<[[..:common#Int |Int]],[[..:common#Rational |Rational]]>''


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