This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A318895 #12 Sep 05 2018 11:50:21 %S A318895 1,1,1,2,3,8,27,115 %N A318895 Number of isoclinism classes of the groups of order 2^n. %C A318895 The concept of isoclinism was introduced in Hall (1940) and is crucial to enumerating the groups of order p^n where p is a prime. %C A318895 An isoclinism exists between two groups G1 and G2 if the following holds: There is an isomorphism f between their two inner automorphism groups G1/Z(G1) and G2/Z(G2). There is an isomorphism h between their two commutator groups [G1, G1] and [G2, G2]. Lastly, f and h commute with F1 and F2, where F1 is the mapping from G1/Z(G1) x G1/Z(G1) to [G1, G1], given by a, b -> ab(a^-1)(b^-1), and F2 is defined analogously. %H A318895 P. Hall, <a href="http://resolver.sub.uni-goettingen.de/purl?PPN243919689_0182">The classification of prime-power groups</a>, J. Reine Angew. Math. 182 (1940), 130-141. %H A318895 Rodney James, M. F. Newman and E. A. O'Brien, <a href="https://doi.org/10.1016/0021-8693(90)90244-I">The groups of order 128</a>, Journal of Algebra, Volume 129, Issue 1 (1990), 136-158. %H A318895 Vipul Naik, <a href="https://groupprops.subwiki.org/wiki/Arithmetic_functions_for_groups_of_order_2%5En#Up_to_isoclinism">This sequence, along with other properties of groups of order 2^n</a> %e A318895 There are 51 groups of order 32. These fall into 8 isoclinism classes. Therefore a(5) = 8. %Y A318895 Cf. A000001, A000679. A000041 has an interpretation as the number of Abelian groups with order 2^n. %K A318895 nonn,more %O A318895 0,4 %A A318895 _Jack W Grahl_, Sep 05 2018