Dear Gap Forum,

A. R. Ashrafi wrote

I need to the character table of the second maximal subgroups of Co1. How to
compute these tables. Also, I don't know Gap contains these tables or not.

According to the Atlas of Finite Groups,
the groups in the second class of maximal subgroups of Co1
are of type 3.Suz:2, that is, bicyclic extensions of the
sporadic simple Suzuki group.

The GAP library of character tables contains all character
tables of bicyclic extensions that occur in the Atlas of
Finite Groups.

On can access these Atlas tables via names obtained from those
used in the Atlas by omitting subscripts and superscripts,
and replacing colons `:' by simple dots `.'.
In this example, the character table can be fetched from the
library via

gap> tbl:= CharTable( "3.Suz.2" );
CharTable( "3.Suz.2" )

For most of the sporadic simple groups, the GAP library contains
the character tables of all maximal subgroups.
In these cases, the `maxes' component of the character table of
the group lists the names by which the tables of the maximal
subgroups can be accessed.
In this example, one could proceed as follows.

gap> co1:= CharTable( "Co1" );
CharTable( "Co1" )
gap> co1.maxes;
[ "Co2", "3.Suz.2", "2^11:M24", "Co3", "2^(1+8)+.O8+(2)", "U6(2).3.2", 
  "(A4xG2(4)):2", "2^(2+12):(A8xS3)", "2^(4+12).(S3x3S6)", "3^2.U4(3).D8", 
  "3^6:2M12", "(A5xJ2):2", "3^(1+4).2U4(2).2", "(A6xU3(3)):2", 
  "3^(3+4):2(S4xS4)", "A9xS3", "(A7xL2(7)):2", "(D10x(A5xA5).2).2", 
  "5^(1+2):GL2(5)", "5^3:(4xA5).2", "5^2:2A5", "7^2:(3x2A4)" ]
gap> tbl:= CharTable( co1.maxes[2] );
CharTable( "3.Suz.2" )

Kind regards,
Thomas

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