The database of simple groups of order less than 1020 is intended to make it easy for a user to access any of the small simple groups. There are 403,874 simple groups in the database. The groups are arranged in order of increasing cardinality which makes it trivial to scan the simple groups of small order.
This intrinsic returns a group isomorphic to the simple group specified in the argument. The simple group can be specified by any one of the following:-The group returned is generally the permutation group od smallest degree that is isomorphic to the simple group.
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- An integer N that is the number of the requested simple group in the database.
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- A string S giving the standard name of the simple group.
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- A tuple T containing three integers that give the internal designation of the simple group.
A group isomorphic to a simple group whose order is given by the argument. The order may be an integer M or a factored integer F.
The number of groups in the simple groups database.
This intrinsic returns the standard name of the simple group which has database number N.
This intrinsic returns the database number of the simple group which has standard name number S.
This intrinsic returns the database number of the simple group whose internal designation is T.
This intrinsic returns the database number of the simple group whose internal designation is T.