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 J. J. CANNON, "A draft description of the group theory language Cayley," Proc. SYMSAC Symposium on Symbolic and Algebraic Computation (R. D. Jenks, Editor), ACM, New York, 1976.
- 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 S. S. MAGLIVERAS & L. C. YU, "On methods for determining subgroup structures of finite groups." (Unpublished.)
- 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 C. C. SIMS, "The primitive groups of degree not exceeding 20," Computational Problems in Abstract Algebra, (J. Leech, Editor), Pergamon Press, New York, 1970.
- 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 K. C. YOUNG, Computing with Finite Groups, Ph.D. Thesis, McGill Univ., Montreal, 1975.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Math. Comp. 32 (1978), 1293-1302
- MSC: Primary 20D05
- DOI: https://doi.org/10.1090/S0025-5718-1978-0498831-1
- MathSciNet review: 0498831