Irr: "Failed to calculate eigenspaces" for a solvable group when IrrDixonSchneider is seeded with a partial IrrBaumClausen list

[BenjaminSambale]

Observed behaviour

In GAP 4.16.1, from a fresh session:

N := SmallGroup(192, 1025);;
A := AutomorphismGroup(N);;
G := Image(IsomorphismPermGroup(A));;
Irr(G);

Here G is solvable of order 61440, and the last line stops with

Error, Failed to calculate eigenspaces.
*[1] Error( "Failed to calculate eigenspaces." );
   @ /usr/share/gap/lib/ctblgrp.gi:674
 [2] DxEigenbase( N )
   @ /usr/share/gap/lib/ctblgrp.gi:790
 [3] SplitStep( D, bsm );
   @ /usr/share/gap/lib/ctblgrp.gi:2206
 [4] DixonSplit( D )
   @ /usr/share/gap/lib/ctblgrp.gi:2284
 [5] IrrDixonSchneider( G, opt )
   @ /usr/share/gap/lib/ctblgrp.gi:2323

The error does not depend on the representation (the isomorphic pc group behaves
the same) and not on the random state (it occurs in a fresh session and after
Reset(GlobalMersenneTwister, s) for s = 1 and s = 42).

Where it comes from

The Irr method for [ IsGroup, IsZeroCyc ] in lib/ctblgrp.gi calls
IrrBaumClausen first if the group is solvable and, when that list is
incomplete, passes it to IrrDixonSchneider as knownirreducibles. For this
group the Baum-Clausen list is incomplete, and it is only the seeded
Dixon-Schneider run that fails:

H := Image(IsomorphismPcGroup(G));;
bc := IrrBaumClausen(H);;
Length(bc);                 # 31
Sum(bc, c -> c[1]^2);       # 15360, while |H| = 61440
NrConjugacyClasses(H);       # 39

ds := IrrDixonSchneider(H);;  # works
Length(ds);                  # 39
Sum(ds, c -> c[1]^2);         # 61440

IrrDixonSchneider(H, rec(knownirreducibles := bc));;   # same error as above

So IrrDixonSchneider computes all 39 irreducible characters on its own, but
fails as soon as it is given the 31 characters found by IrrBaumClausen.

Expected behaviour

Irr(G) returns the 39 irreducible characters of G.

Workaround

Calling IrrDixonSchneider(G) directly.

Version

GAP 4.16.1 on arch linux. The
lib/ctblgrp.gi of this installation agrees with the one in current master (2718
lines, and the line numbers in the traceback match it), so master looks affected
as well. The seeding of IrrDixonSchneider with knownirreducibles was
introduced for #6134.

[ThomasBreuer]

The problem is in IrrBaumClausen.