Groups of order 1029

This article gives information about, and links to more details on, groups of order 1029
See pages on algebraic structures of order 1029 | See pages on groups of a particular order

Statistics at a glance

The number 675 has 3, 7 as its only prime factors. The prime factorization is as follows:

$\!675=3\cdot 7^{3}$

There are only two prime factors of this number. Order has only two prime factors implies solvable (by Burnside's $p^{a}q^{b}$-theorem) and hence all groups of this order are solvable groups (specifically, finite solvable groups). Another way of putting this is that the order is a solvability-forcing number. In particular, there is no simple non-abelian group of this order.

Quantity	Value
Total number of groups up to isomorphism	19

Minimal order attaining number

$1029$ is the smallest number such that there are precisely $19$ groups of that order up to isomorphism. That is, the value of the minimal order attaining function at $19$ is $1029$.