Well, my research is in

If the reader seeks a *representation* of a group, then he should refer to the
ATLAS of group representations
which is maintained by R.A.Wilson, S.J.Nickerson and me.

NB: This page was originally meant to focus on symmetric presentations, but the current page title seems to reflect the content more accurately. Also, these pages are somewhat neglected at present. Hopefully, this will not remain the case forever.

We shall give some presentations of groups (symmetric or otherwise). Firstly, choose a group. We have divided them into a number of classes to make location easier. Those groups that have just one (finite) non-abelian composition factor up to isomorphism are listed in the first seven sections according to the isomorphism type of this composition factor. Soluble groups and groups with at least two non-isomorphic non-abelian composition factors are listed under `other groups'.

Some of the presentations we list are standard Coxeter presentations. Click here for a list of these. Other sources of presentations include:

- Leonard Soicher, some Coxeter-type presentations given in the ATLAS and elsewhere. Labelled LHS.
- John Cannon, John McKay and Kiang-chuen Young, The non-abelian simple groups
*G*, |*G*| < 10^{5}-presentations, Communications in Algebra (1979). Labelled CMY. - Colin Cambell and Edmund Robertson, Presentations for simple groups
*G*, 10^{5}< |*G*| < 10^{6}, Communications in Algebra (1984). Labelled CR. - J.G.Sunday, the (2, 3,
*p*)- and (*p*, 2, 3)-presentations of L_{2}(*p*). Labelled JGS. - Robert Curtis, various symmetric presentations. Labelled RTC.
- His students, Ahmed Hammas and Abdul Jabbar. Labelled AH and AJ respectively.

- Alternating groups.
- Sporadic groups (including the JacquesTits group).
- Linear groups.
- Unitary groups.
- Symplectic groups.
- Orthogonal groups.
- Exceptional groups of Lie type (both twisted and untwisted).
- Other groups.

Each of the pages linked to below have a couple of sensitve images. Those like this:

return you to my homepage and those like this:

return you to this page.

A_{5} |
A_{6} |
A_{7} |
A_{8} |
A_{9} |
A_{10} |
A_{11} |
A_{12} |
A_{13} |

M_{11} |
M_{12} |
M_{22} |
M_{23} |
M_{24} |
J_{1} |
J_{2} |
J_{3} |
J_{4} |

HS | McL | Suz | Co_{3} |
Co_{2} |
Co_{1} |
Fi_{22} |
Fi_{23} |
Fi_{24}' |

He | HN | Th | B = BM | M = F_{1} |
Ru | O'N | Ly | T = ^{2}F_{4}(2)' |

L_{2}(4) = L_{2}(5) = A_{5} |
L_{3}(2) = L_{2}(7) |
L_{2}(9) = A_{6} = S_{4}(2)' = M_{10}' |
L_{4}(2) = A_{8} |

L_{2}(8) |
L_{2}(11) |
L_{2}(13) |
L_{2}(16) |
L_{2}(17) |
L_{2}(19) |
L_{2}(23) |
L_{2}(25) |
L_{2}(27) |
L_{2}(29) |
L_{2}(31) |
L_{2}(32) |

L_{3}(3) |
L_{3}(4) = M_{21} |
L_{3}(5) |
L_{3}(7) |
L_{3}(8) |
L_{3}(9) |
L_{3}(11) |
L_{4}(3) |
L_{5}(2) |

U_{3}(3) |
U_{3}(4) |
U_{3}(5) |
U_{3}(7) |
U_{3}(8) |
U_{3}(9) |
U_{3}(11) |

U_{4}(2) |
U_{4}(3) |
U_{5}(2) |
U_{6}(2) = Fi_{21} |

S_{4}(2) = S_{6} = A_{6}:2_{1} |
S_{4}(3) = U_{4}(2) |
S_{4}(4) |
S_{4}(5) |
S_{6}(2) |
S_{6}(3) |
S_{8}(2) |

O8^{+}(2) |
O8^{-}(2) |
O10^{+}(2) |
O10^{-}(2) |
O_{7}(3) |
O8^{+}(3) |
O8^{-}(3) |

G_{2}(2) = U_{3}(3):2 |
G_{2}(3) |
G_{2}(4) |
G_{2}(5) |
F_{4}(2) |
E_{6}(2) |
E_{7}(2) |
E_{8}(2) |
^{3}D_{4}(2) |
^{2}E_{6}(2) |

Sz(8) = ^{2}B_{2}(8) |
Sz(32) = ^{2}B_{2}(32) |
T.2 = ^{2}F_{4}(2) |
R(3) = ^{2}G_{2}(3) = L_{2}(8):3.
| R(27) = ^{2}G_{2}(27) |

Soluble groups (A_{4}, S_{4}, M_{9} etc.) |

A_{5} × L_{3}(2) |

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