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We describe a method to determine up to isomorphism the groups of order q n · p for a fixed prime-power q n and indeterminate prime p ≠ q. We report on the explicit construction of all groups of order 2 n · p for n ≤ 8 and 3 n · p for n ≤ 6. In particular, we show that there are 1 090 235 groups of order 768.
We thank E. A. O'Brien for helpful comments.
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