Counting groups based on PSU(4,3)

Question

How many almost quasisimple extensions of PSU(4,3) are there?

As noted in Constructing central extensions or Schur cover of U4(3) in GAP this group is too large to be in the perfect groups library (the order 3,265,920 is over 2 million) and it has abnormally large Schur Multiplier (36) and large automorphism group ($D_{8}$) so there are many almost quasisimple groups associated with it.

The Atlas only lists these eleven https://brauer.maths.qmul.ac.uk/Atlas/v3/clas/U43/ :

U4(3)

2.U4(3)

U4(3).2_1

U4(3).4

U4(3).2_2

U4(3).2_3

3_2.U4(3).2_3

3_2.U4(3).2_3'

U4(3):D8

3_2.U4(3):D8

2.U4(3).D8

I know GAP already contains some thing on this list such a CharacterTable("6_1.U4(3).2_2");

Is there a way to convince GAP to print out a list of all groups in the character table library defined by a string that contains "U4(3)" ? Because I guess that would be a good start. Does GAP character table library even contain all the almost quasisimple groups based on PSU(4,3)?

Answer 1

To get groups mapping onto $U_4(3)$, you could use:

c:=CharacterTable("U4(3)");
NamesOfFusionSources(c);

and eliminate the ones that are subgroups. You could do similarly for U4(3).2_1 and so on.