Classification of groups of order sixty-four times a prime

We split the classification of groups of order $64p$, $p$ prime into thirty-three cases. Some of these cases themselves have their own sub-cases, which you can see on their pages.

• Classification of groups of order 128 ($p=2$, which is also classified as a group of prime-seventh order.)

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Summary of results

Number of groups up to isomorphism

There are a few special cases to be dealt with manually:

• In the case $p=2$, that is, the groups of order 128, there are 2328 groups.
• In the case $p=3$, that is, the groups of order 192, there are 1543 groups.
• In the case $p=5$, that is, the groups of order 320, there are 1640 groups.
• In the case $p=7$, that is, the groups of order 448, there are 1396 groups.
• In the case $p=31$, that is, the groups of order 1984, there are 1388 groups.

All other cases depend only on the value of the prime modulo $64$, and the value is constant on the residue classes:

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List of groups

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See also

• Classification of groups of order a power of two times a prime