We show that the Morava K-theories of the groups of order 32 are concentrated in even degrees. Let G be a finite group and BG denote its classifying space. Determining the Morava K-theory of BG is generally difficult, mainly due to the weakness of existing methods of calculation, which all require knowledge of the cohomology of p-groups — in itself a notorious problem. Certain series of groups with particularly simple structure, such as wreath products, or groups having a cyclic maximal subgroup, or minimal non-abelian groups, are quite tractable, see e.g. the work of HopkinsKuhn-Ravenel [3], Hunton [4], and Yagita and his coauthors ([7], [10], [11], [12], [14]). A hard example is the 3-Sylow supgroup of GL4(F3): in [5], Kriz computes just enough of its 3-primary Morava K-theory to conclude that there are odd dimensional elements in it, thereby disproving a conjecture of Ravenel. A complete calculation however is still elusive. In later work by Kriz and Lee, this example was generalised to all n and all odd primes p [6]. In this note we shall consider the groups of order 32. In many cases the Morava K-theory is already known, or easily deduced from results in the literature. For the remaining groups, it was established in [8] that for n = 2 at least, their Morava K-theory K(n)∗(BG) is generated by transfers of Euler classes of complex representations. In other words, all groups of order 32 are “K(2)-good” in the sense of Hopkins-Kuhn-Ravenel. Some of the results however relied on computer calculations. This is to be remedied here, although we only prove a weaker statement: Theorem. Let G be a group of order 32. Then K(n)(BG) = 0. When starting this project, our objective of course was not to prove such a result, rather we hoped – rather naively, perhaps – that order 32 would be big enough to find a 2-primary counterexample to the even degree conjecture. In this we have failed and the problem remains open. We have not tried to determine ring structures. This should be possible in principle, using methods similar to those employed in [1], but since this paper is already so loaded with computations, we have refrained from doing so. The article is organised as follows. In Section 1, we recall a few old results used in the later calculations. Section 2 contains some technical lemmas. Section 3 collects all we need to know about the Morava K-theories of groups of smaller order. Section 4 lists the 51 groups of order 32 and disposes of those whose Morava Ktheory is either in the literature or can easily be read off from known computations. Finally, Section 5 contains the remaining calculations. Date: November 23, 2010. 2010 Mathematics Subject Classification. Primary 55R35, 55N20; Secondary 57T25.