The Brauer character tables in GAP do not yet have
a ``native'' Sage interface. To access them you can directly
interface with GAP using pexpect and the gap.eval
command.
The example below using the GAP interface illustrates the syntax.
sage: print gap.eval("G := Group((1,2)(3,4),(1,2,3))") Group([ (1,2)(3,4), (1,2,3) ]) sage: print gap.eval("irr := IrreducibleRepresentations(G,GF(7))") # random arch. dependent output [ [ (1,2)(3,4), (1,2,3) ] -> [ [ [ Z(7)^0 ] ], [ [ Z(7)^4 ] ] ], [ (1,2)(3,4), (1,2,3) ] -> [ [ [ Z(7)^0 ] ], [ [ Z(7)^2 ] ] ], [ (1,2)(3,4), (1,2,3) ] -> [ [ [ Z(7)^0 ] ], [ [ Z(7)^0 ] ] ], [ (1,2)(3,4), (1,2,3) ] -> [ [ [ Z(7)^2, Z(7)^5, Z(7) ], [ Z(7)^3, Z(7)^2, Z(7)^3 ], [ Z(7), Z(7)^5, Z(7)^2 ] ], [ [ 0*Z(7), Z(7)^0, 0*Z(7) ], [ 0*Z(7), 0*Z(7), Z(7)^0 ], [ Z(7)^0, 0*Z(7), 0*Z(7) ] ] ] ] sage: gap.eval("brvals := List(irr,chi->List(ConjugacyClasses(G),c->BrauerCharacterValue(Image(chi,Representative(c)))))") '' sage: print gap.eval("Display(brvals)") # random architecture dependent output [ [ 1, 1, E(3)^2, E(3) ], [ 1, 1, E(3), E(3)^2 ], [ 1, 1, 1, 1 ], [ 3, -1, 0, 0 ] ] sage: print gap.eval("T := CharacterTable(G)") CharacterTable( Alt( [ 1 .. 4 ] ) ) sage: print gap.eval("Display(T)") CT3 <BLANKLINE> 2 2 2 . . 3 1 . 1 1 <BLANKLINE> 1a 2a 3a 3b 2P 1a 1a 3b 3a 3P 1a 2a 1a 1a <BLANKLINE> X.1 1 1 1 1 X.2 1 1 A /A X.3 1 1 /A A X.4 3 -1 . . <BLANKLINE> A = E(3)^2 = (-1-ER(-3))/2 = -1-b3
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