The nonabelian simple groups 𝐺, ∣𝐺∣<10⁶—maximal subgroups

Fischer, J.; McKay, J.

doi:10.1090/S0025-5718-1978-0498831-1

The nonabelian simple groups $G,$ $\mid G\mid <10^{6}$—maximal subgroups
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by J. Fischer and J. McKay PDF

Math. Comp. 32 (1978), 1293-1302 Request permission

Abstract:

The maximal subgroups of all the simple groups (except $L(2,q)$) of order up to one million are given to within conjugacy. Permutation characters on the cosets of the maximal subgroups are given, as are orbit lengths (whenever practical).

References

David M. Bloom, The subgroups of $\textrm {PSL}(3,\,q)$ for odd $q$, Trans. Amer. Math. Soc. 127 (1967), 150–178. MR 214671, DOI 10.1090/S0002-9947-1967-0214671-1

Proc. SYMSAC Symposium on Symbolic and Algebraic Computation

J. H. Conway, Three lectures on exceptional groups, Finite simple groups (Proc. Instructional Conf., Oxford, 1969) Academic Press, London, 1971, pp. 215–247. MR 0338152
H. S. M. Coxeter and W. O. J. Moser, Generators and relations for discrete groups, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 14, Springer-Verlag, Berlin-Göttingen-New York, 1965. MR 0174618
Walter Feit, The current situation in the theory of finite simple groups, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 55–93. MR 0427449
L. Finkelstein and A. Rudvalis, Maximal subgroups of the Hall-Janko-Wales group, J. Algebra 24 (1973), 486–493. MR 323889, DOI 10.1016/0021-8693(73)90122-1
David E. Flesner, Maximal subgroups of $\textrm {PSp}_{4}(2^{n})$ containing central elations or noncentered skew elations, Illinois J. Math. 19 (1975), 247–268. MR 382471
Marshall Hall Jr. and David Wales, The simple group of order $604,800$, J. Algebra 9 (1968), 417–450. MR 240192, DOI 10.1016/0021-8693(68)90014-8
R. W. Hartley, Determination of the ternary collineation groups whose coefficients lie in the $\textrm {GF}(2^n)$, Ann. of Math. (2) 27 (1925), no. 2, 140–158. MR 1502720, DOI 10.2307/1967970
B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703, DOI 10.1007/978-3-642-64981-3
Zvonimir Janko, A new finite simple group with abelian Sylow $2$-subgroups and its characterization, J. Algebra 3 (1966), 147–186. MR 193138, DOI 10.1016/0021-8693(66)90010-X
John McKay, The non-abelian simple groups $G,$ $G\ <\ 10^{6}$ — character tables, Comm. Algebra 7 (1979), no. 13, 1407–1445. MR 539357, DOI 10.1080/00927877908822410
Howard H. Mitchell, Determination of the ordinary and modular ternary linear groups, Trans. Amer. Math. Soc. 12 (1911), no. 2, 207–242. MR 1500887, DOI 10.1090/S0002-9947-1911-1500887-3
Howard H. Mitchell, The subgroups of the quaternary abelian linear group, Trans. Amer. Math. Soc. 15 (1914), no. 4, 379–396. MR 1500986, DOI 10.1090/S0002-9947-1914-1500986-9
Benjamin Mwene, On the subgroups of the group $PSL_{4}(2^{m}).$, J. Algebra 41 (1976), no. 1, 79–107. MR 409654, DOI 10.1016/0021-8693(76)90170-8

Computational Problems in Abstract Algebra

Michio Suzuki, On a class of doubly transitive groups, Ann. of Math. (2) 75 (1962), 105–145. MR 136646, DOI 10.2307/1970423
Helmut Wielandt, Finite permutation groups, Academic Press, New York-London, 1964. Translated from the German by R. Bercov. MR 0183775

Computing with Finite Groups