Groups of order 1800

This article gives information about, and links to more details on, groups of order 1800
See pages on algebraic structures of order 1800 | See pages on groups of a particular order

Statistics at a glance

The number 1800 has prime factors 2, 3 and 5. The prime factorization is as follows:

$\!1800=2^{3}\cdot 3^{2}\cdot 5^{2}=8\cdot 9\cdot 25$

There are both solvable and non-solvable groups of this order.

GAP implementation

The order 1800 is part of GAP's SmallGroup library. Hence, any group of order 1800 can be constructed using the SmallGroup function by specifying its group ID. Also, IdGroup is available, so the group ID of any group of this order can be queried.

Further, the collection of all groups of order 1800 can be accessed as a list using GAP's AllSmallGroups function.

Here is GAP's summary information about how it stores groups of this order, accessed using GAP's SmallGroupsInformation function:

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