4.5 The group id database

The function group_id requires that the Small Groups Library of E. A. O'Brien, B. Eick, and H. U. Besche be installed (you can do this by typing ./sage -i database_gap-4.4.9 in the Sage home directory).

sage: G = PermutationGroup(['(1,2,3)(4,5)', '(3,4)'])
sage: G.order()
120
sage: G.group_id()      # requires optional GAP database package
[120, 34]

Another example of using the small groups database:

sage: gap_console()
GAP4, Version: 4.4.6 of 02-Sep-2005, x86_64-unknown-linux-gnu-gcc
gap> G:=Group((4,6,5)(7,8,9),(1,7,2,4,6,9,5,3));
Group([ (4,6,5)(7,8,9), (1,7,2,4,6,9,5,3) ])
gap> StructureDescription(G);
"(((C3 x C3) : Q8) : C3) : C2"

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