Geodesic
On the Maximum Order of the Group of a Tournament
Canadian mathematical bulletin, Tome 9 (1966) no. 5, pp. 563-569

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A (round-robin) tournament Tn consists of n nodes p1, p2, ..., Pn such that each pair of distinct nodes pi and pj is joined by one of the oriented arcs or . If the arc is in Tn, then we say that pi. dominates pj. The set of all dominance-preserving permutations a of the nodes T form a group, the automorphism group G(T ) of Tn. It is known (see [1]) that there exist tournaments Tn whose group n G(Tn) is abstractly isomorphic to a given group H if and only if the order g(H) of H is odd. 
Goldberg, Myron; Moon, J. W. On the Maximum Order of the Group of a Tournament. Canadian mathematical bulletin, Tome 9 (1966) no. 5, pp. 563-569. doi: 10.4153/CMB-1966-069-3
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     title = {On the {Maximum} {Order} of the {Group} of a {Tournament}},
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     year = {1966},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-069-3/}
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