ATLAS of Finite Group representations

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Contents

This ATLAS contains representations of many finite simple groups and related groups such as covering groups and automorphism groups of simple groups. To find a desired representation, first choose which of the following categories the group belongs to:

Alternating and symmetric groups.
Groups of Lie type.
- Classical groups.
- Exceptional groups. Please try Version 2 - beta test instead (exceptional groups only).
  - Untwisted groups.
  - Twisted groups.
Sporadic groups.
Miscellaneous groups.

You can also try our experimental generic group page maker.

NEW: A link to John Bray's presentations of groups.

NEW: Simon Norton's list of improvements to the Atlas of Finite Groups is available here in plain tex, and and dvi and PostScript formats.

Alternating groups

Alternating group A5.
Alternating group A6.
Alternating group A7.
Alternating group A8.
Alternating group A9.
Alternating group A10.
Alternating group A11.
Alternating group A12.
Alternating group A13.
Alternating group A14.
Generic alternating group.

Sporadic groups

Mathieu group M11.
Mathieu group M12.
Mathieu group M22.
Mathieu group M23.
Mathieu group M24.
Janko group J1.
Janko group J2.
Janko group J3.
Janko group J4.
Conway group Co1.
Conway group Co2.
Conway group Co3.
Fischer group F22.
Fischer group F23.
Fischer group F24.
Higman-Sims group.
McLaughlin group.
Held group.
Rudvalis group.
Suzuki sporadic group.
O'Nan group.
Harada-Norton group.
Lyons group.
Thompson group.
Baby Monster.
Monster.

Groups of Lie type

Classical groups

Linear groups

L2(4) = L2(5) = A5.
L2(7) = L3(2).
L2(8).
L2(9) = A6.
L2(11).
L2(13).
L2(16).
L2(17).
L2(19).
L2(23).
L2(25).
L2(27).
L2(29).
L2(31).
L2(32).
L2(49).
L2(81).
L3(3).
L3(4).
L3(5).
L3(7).
L3(8).
L3(9).
L3(11).
L4(2) = A8.
L4(3).
L5(2).
L6(2).
Generic linear group.

Unitary groups

U3(3).
U3(4).
U3(5).
U3(7).
U3(8).
U3(9).
U3(11).
U4(2).
U4(3).
U5(2).
U6(2).

Orthogonal groups

O7(3).
O8+(2).
O8-(2).
O8+(3).
O8-(3).
O9(3).
O10+(2).
O10-(2).

Symplectic groups

S4(4).
S4(5).
S4(7).
S6(2).
S6(3).
S8(2).
S10(2).

Exceptional groups

Untwisted groups

E6(2). Try also Version 2.
E6(4). Try also Version 2.
E7(2). Try also Version 2.
E7(4). Try also Version 2.
E8(2). Try also Version 2.
E8(5). Try also Version 2.
F4(2). Try also Version 2.
G2(3). Try also Version 2.
G2(4). Try also Version 2.
G2(5). Try also Version 2.

Twisted groups

Sz(8). Try also Version 2.
Sz(32). Try also Version 2.
R(27). Try also Version 2.
^3D4(2). Try also Version 2.
^2F4(2). Try also Version 2.
^2E6(2). Try also Version 2.

Miscellaneous groups

2³L₃(2).
M20.
W(F4)

Return to main ATLAS page.

Last updated 7th June 2000.

R.A.Wilson (R.A.Wilson@bham.ac.uk)

R.A.Parker (richard@ukonline.co.uk)

J.N.Bray (jnb@for.mat.bham.ac.uk)