PermCharInfo( tbl, permchars )
Let tbl be the character table of the group G, and permchars the
permutation character (1_U)^G for a subgroup U of G, or a list of
such characters. PermCharInfo
returns a record with components
contained
:
bound
:permchars[k]
be the permutation character (1_U)^G. Then the
class length in U of an element in class i of tbl must be a
multiple of the value
'bound[<k>][<i>]' = |U| / gcd( |U|, '<tbl>.centralizers[<i>]' ),
display
:DisplayCharTable
to display the permutation characters and the corresponding components
contained
and bound
, for the classes where at least one character
of permchars is nonzero,
ATLAS
:tbl.irreducibles
in ATLAS notation.
gap> t:= CharTable("A6");; gap> PermCharInfo( t, [ 15, 3, 0, 3, 1, 0, 0 ] ); rec( contained := [ [ 1, 9, 0, 8, 6, 0, 0 ] ], bound := [ [ 1, 3, 8, 8, 6, 24, 24 ] ], display := rec( classes := [ 1, 2, 4, 5 ], chars := [ [ 15, 3, 0, 3, 1, 0, 0 ], [ 1, 9, 0, 8, 6, 0, 0 ], [ 1, 3, 8, 8, 6, 24, 24 ] ], letter := "I" ), ATLAS := [ "1a+5b+9a" ] ) gap> DisplayCharTable( t, last.display ); A62 3 3 . 2 3 2 . 2 . 5 1 . . .
1a 2a 3b 4a 2P 1a 1a 3b 2a 3P 1a 2a 1a 4a 5P 1a 2a 3b 4a
I.1 15 3 3 1 I.2 1 9 8 6 I.3 1 3 8 6
GAP 3.4.4