### On the Simple Group of Order 25920

J. A. Todd
1947 Proceedings of the Royal Society A
On the simple group of order 25920 327 The 45 primes so arising will be called, following Baker, Jordan primes. W ith respect to any given one of the 45 nodes, A say, the remaining nodes fall into two sets, comprising 12 and 32 nodes respectively. The 12 nodes in the former of these two sets lie in the polar prime of A, and the fine joining any one of these to A contains no further node. Such lines.will be called e-lines. There are £.45.12 = 270 e-lines, each containing two of the nodes, 12 of
more » ... f the nodes, 12 of these lines passing through each node. The 32 nodes which do not he on e-lines through A lie in pairs on 16 lines through A. Such lines, which are called K-lines, each contain three nodes, and there are £.45.16 = 240 of them, sixteen passing through each node. The polar primes of on August 16, 2017 http://rspa.royalsocietypublishing.org/ Downloaded from on August 16, 2017 http://rspa.royalsocietypublishing.org/ Downloaded from