Hi,
I believe I found a bug in CharacterTable.
It is concluded that there exist 3-modular spin
irreducible representations of dimension 1440-144=1296
of the Schur cover of the symmetric group of degree 11
in the paper:
Morris, A. O.(4-WALA); Yaseen, A. K.(4-WALA)
Decomposition matrices for spin characters of symmetric groups.
Proc. Roy. Soc. Edinburgh Sect. A 108 (1988), no. 1-2, 145
However, in gap, the command:
c:=CharacterTable("2.A11.2") mod 3;
Display(c);
displays the following infomation
on the spin irreducible representations:
X.28 32 -32 . . . . . -8 8 2 -2 4 -4 . . -1 1 .
X.29 144 -144 . . . . . -16 16 -1 1 4 -4 . . 1 -1 .
X.30 144 -144 . . . . . -16 16 -1 1 4 -4 . . 1 -1 .
X.31 528 -528 . . . . . -12 12 -2 2 -4 4 . . . . .
X.32 640 -640 . . . . . 20 -20 . . -4 4 . . 2 -2 .
X.33 1440 -1440 . . . . . 20 -20 . . -2 2 . . -1 1 .
X.34 1440 -1440 . . . . . 20 -20 . . -2 2 . . -1 1 .
I believe X.33 and X.34 are not irreducible and
contain X.29 and X.30 as their composition factors.
Sincerely,
Shunsuke Tsuchioka
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