Corrections to the ATLAS of Finite Groups

Further errors are listed here:

L2(25). Page 16.

Last maximal subgroup in G.2₃ should read (Q₈ × 3):2.

Sz(8). Page 28.

In the `Suzuki' construction, the oval is incorrectly defined: add the extra condition that when t=0, we have x=y=0.

G2(3). Page 60.

14­dimensional construction, definition of D²: e_i should read 3e_i.

Sz(32). Page 77.

In the `Suzuki' construction, the oval is incorrectly defined: add the extra condition that when t=0, we have x=y=0.

J3. Page 82.

The definition of C_Z only applies when z is nonzero. The image of e(0) is e(0).

3D4(2). Page 89.

Replace top row (but not first column) occurrences of s/4 by its conjugate in 768 matrix orbit.

G2(4). Page 97.

Delete `non­edge' from Graph column of maximal subgroups.

O7(3). Page 109.

In 14th maximal subgroup, replace 2E by 2F.

S6(3). Page 113.

In 7th maximal subgroup, extensions are split.

R(27). Page 123.

First maximal subgroup has shape 3³⁺³⁺³:26 in G and 3³⁺³⁺³:26:3 in G.3.

Suz. Page 131.

In 12th maximal subgroup, the extension is non-split: (A₆ × A₅) ^. 2.

O8+(3). Page 140.

The novelties 2⁷A₈ in O8+(3):2₁ (after the fusion markers for the 10/11th and 12/13th maximal subgroups) should be 2⁶:A₈:2 = 2^{6 .} S₈ (the latter extension being non-split).

Fi22. Page 160.

In the additional 5 columns, on p. 310 of the ABC, the centraliser orders of 12L, 12M, 12N should be 3456, 1296 and 576 respectively.

Fi22. Page 163.

The structure of the 2B­normaliser is (2 × 2¹⁺⁸):U₄(2):2, and correspondingly H.2 in G.2.

2E6(2). Page 191.

16th maximal subgroup has shape 3¹⁺⁶:2³⁺⁶:3²:2 (so there is no quotient S₃ x 3).

Page 241.

Outer automorphism group of G₂(9) is 4, not 2.

Simon Norton's list of improvements to the ATLAS of Finite Groups is also available here in both dvi and PostScript formats.

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