52.5 CAS Tables

All tables of the CAS table library are available in GAP, too. This sublibrary has been completely revised, i.e., errors have been corrected and powermaps have been completed.

Any CAS table is accessible by each of its CAS names, that is, the table name or the filename (see CharTable):

    gap> t:= CharTable( "m10" );; t.name;
    "A6.2_3"

One does, however, not always get the original CAS table: In many cases (mostly ATLAS tables, see ATLAS Tables) not only the name but also the succession of classes and characters has changed; the records in the component CAS of the table (see Character Table Records) contain the permutations which must be applied to classes and characters to get the original CAS table:

    gap> t.CAS;
    [ rec(
          name := "m10",
          permchars := (3,5)(4,8,7,6),
          permclasses := (),
          text := [ 'n', 'a', 'm', 'e', 's', ':', ' ', ' ', ' ', ' ',
              ' ', 'm', '1', '0', '\n', 'o', 'r', 'd', 'e', 'r', ':',
              ' ', ' ', ' ', ' ', ' ', '2', '^', '4', '.', '3', '^', '2',
              '.', '5', ' ', '=', ' ', '7', '2', '0', '\n', 'n', 'u',
              'm', 'b', 'e', 'r', ' ', 'o', 'f', ' ', 'c', 'l', 'a', 's',
              's', 'e', 's', ':', ' ', '8', '\n', 's', 'o', 'u', 'r',
              'c', 'e', ':', ' ', ' ', ' ', ' ', 'c', 'a', 'm', 'b', 'r',
              'i', 'd', 'g', 'e', ' ', 'a', 't', 'l', 'a', 's', '\n',
              'c', 'o', 'm', 'm', 'e', 'n', 't', 's', ':', ' ', ' ', 'p',
              'o', 'i', 'n', 't', ' ', 's', 't', 'a', 'b', 'i', 'l', 'i',
              'z', 'e', 'r', ' ', 'o', 'f', ' ', 'm', 'a', 't', 'h', 'i',
              'e', 'u', '-', 'g', 'r', 'o', 'u', 'p', ' ', 'm', '1', '1',
              '\n', 't', 'e', 's', 't', ':', ' ', ' ', ' ', ' ', ' ',
              ' ', 'o', 'r', 't', 'h', ',', ' ', 'm', 'i', 'n', ',', ' ',
              's', 'y', 'm', '[', '3', ']', ' ', ' ', ' ', ' ', ' ', ' ',
              ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ',
              ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', '\n' ] ) ]

The subgroup fusions were computed anew; their record component text tells if the fusion is equal to that in the CAS library --of course modulo the permutation of classes.

Note that the fusions are neither tested to be consistent for any two subgroups of a group and their intersection, nor tested to be consistent with respect to composition of maps.

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