ATLAS of Finite Group representations
What's new
 7th January 1998

 Representations of 2.Sz(8) as permutations on 1040 points, as 40 × 40 matrices over GF(7) and as 24 × 24 matrices over GF(13).
 19th December 1997

 Lots of representations of decorations of A9 and A13.
 14th December 1997

 Lots of representations of and information about L2(8) and L2(8):3.
 12th December 1997

 Lots of representations of A11, 2.A11, S11 and 2.S11.
 10th December 1997

 Standard generators defined for all decorations of A6. Added representation of 3.A6 as permutations on 18 points.
 6th December 1997

 Representation of L5(2):2 as 30 × 30 matrices over Z[r2].
 Standard generators of L2(27) and SL2(27) defined and implemented.
 5th December 1997

 All faithful irreducible representations of U4(2) and 2.U4(2) in characteristic 3.
 1st December 1997

 Lots of representations of A8, 2.A8 and S8.
 29th November 1997

 Standard generators for L3(9), L3(11) and U3(11) defined and implemented. Representations for these groups added.
 27th November 1997

 Representations of 2.A12 in 16 dimensions over GF(3) and 32 dimensions over GF(5), GF(7) and GF(11).
 20th November 1997

 Standard generators for O10(2) and O10(2):2 defined and implemented. Representations of O10(2):2 in 32, 44 and 100 dimensions over GF(2).
 19th November 1997

 Standard generators for L2(25) and SL2(25) defined and implemented.
 Standard generators for some of the covers of L3(4) defined and implemented.
 26th August 1997

 Programs to produce generators for all the maximal cyclic subgroups
(up to conjugacy) for all the sporadic groups
up to and including the O'Nan group.
 Representations of the O'Nan group on 122760 points,
and as 495 x 495 matrices over GF(3).
 21st August 1997

 Lots of representations of covers of U4(3).
 20th August 1997

 18th August 1997

 Generators for ^2F_4(2)
changed to standard generators defined by John Bray.
Standard generators for U4(2) also defined by John Bray.
 Some more representations of U4(2),
S4(4)
and U3(3).
 29th May 1997

 196882dimensional representation of the Monster.
(Not yet available on general release.)
 24th March 1997

 45dimensional representations of M24 over GF(7)
and GF(11).
 2dimensional representation of 2.A5 over GF(49) 
well, why not?
 7th March 1997

 Black box algorithms for finding standard generators of most of the
sporadic groups and their automorphism groups.
 6th March 1997

 Black box algorithms for finding standard generators of the
Held group and its automorphism group.
 3rd March 1997

 All the remaining modular irreducibles of
J1. Some new representations of
M23 in characteristics 3 and 7,
J3.2 in characteristics 5 and 19,
^3D4(2) in characteristics 2, 7 and 13,
S4(5).2 in characteristics 2 and 3,
O10(2).2 in characteristic 2 and permutations.
 19th February 1997

 Primitive permutation representations of
G2(5) on 3906, 7750 and 7875 points,
and of ^2F4(2)' on 1600 points.
 Standard generators of O8(2) and
O8(2):2, as well as
S6(3), defined
and implemented.
 Primitive permutation representations of
S8(2) on 120 and 136 points.
 Primitive permutation representations of
S6(2) on 28, 36, and 960 points  completing the
collection of all primitive permutation representations.
 Representations of
S4(5).2 over GF(2) and GF(5).
 7th February 1997

 1706dimensional representation of 2^2.
2E6(2) over GF(2).
 13th January 1997

 Orders and indices of maximal subgroups of the
Baby Monster.
 5th January 1997

 Some links on the 2E6(2) page corrected.
 9th December 1996

 Representations of 2.G2(4) over GF(5), GF(7) and GF(13).
 Some representations of covers of L3(4).
 5th December 1996

 Representations provided by John Bray: dimension 32 over GF(3) for
2.A13, dimension 6 over GF(7) for
6.A7, and dimension 133 over GF(9) for
the HaradaNorton group.
 15th November 1996

 Words for 2.U6(2), O7(3), S10, 2F4(2)', M12,
as maximal subgroups of the
Fischer group F22.
 13th November 1996

 Corrected generators for representations of
U3(5):2 and 3.U3(5):2 to agree
with the definition of standard generators.
 Words for L3(4).2, M22, S8, M11, and both classes of U3(5):2
as maximal subgroups of the
HigmanSims group.
 11th November 1996

 7th November 1996

 Some representations of
J2,
Sz(8),
L3(3) and
U3(3).
 Permutations on 8330 points for the Held group.
 Added some representations of double covers of alternating groups.
 Minor corrections to L5(2).
 1st November 1996

 Added words for the outer automorphism of the
Suzuki group, and for the maximal subgroup M12.2.
 25th October 1996

 Replaced second generator for 3McL over GF(4) by its inverse,
to make it agree with the description of standard generators.
 22nd October 1996

 Added Simon Norton's list of improvements to the Atlas of Finite groups,
in both dvi and PostScript
formats.
 Added a few representations to the Suzuki group,
and added definitions of standard generators for the covers (and corrected the
generators for the permutation representation of 3Suz2).
 14th October 1996

 Added some representations to the Held group.
 Added to M12 all faithful irreducibles in characteristic 2.
 Added to S6(2) all faithful irreducibles in characteristics 2 and 3,
as well as all irreducibles for the double cover in characteristic 3,
and some permutation representations.
 Added to G2(3) all faithful irreducibles in characteristic 3.
 11th October 1996

 Added to J1 all faithful irreducibles in characteristics 3, 5.
 10th October 1996

 Corrected definition of standard generators of 3McL.

Corrected word for class 2B in J4.
 Added to J1 all faithful irreducibles in characteristics 2 and 11.
 9th October 1996


Added to
M23 all but the largest
faithful irreducibles in characteristic 2,
and all except the largest primitive permutation representations.
 Added to
M11 all faithful irreducibles in characteristics 2, 3, 5, 11,
and all primitive permutation representations.
Last updated 07.01.98
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk