Groups of order 147

This article gives information about, and links to more details on, groups of order 147
See pages on algebraic structures of order 147 | See pages on groups of a particular order

This article gives basic information comparing and contrasting groups of order 147. The prime factorization of 147 is $147=3\cdot 7^{2}$.

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.

Statistics at a glance

Quantity	Value
Total number of groups	6
Number of abelian groups	2
Number of simple groups	0