# Groups of order 1320

## Contents

This article gives information about, and links to more details on, groups of order 1320
See pages on algebraic structures of order 1320| See pages on groups of a particular order

## GAP implementation

The order 1320 is part of GAP's SmallGroup library. Hence, any group of order 1320 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 1320 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:

```gap> SmallGroupsInformation(1320);

There are 181 groups of order 1320.
They are sorted by their Frattini factors.
1 has Frattini factor [ 330, 1 ].
2 has Frattini factor [ 330, 2 ].
3 has Frattini factor [ 330, 3 ].
4 has Frattini factor [ 330, 4 ].
5 has Frattini factor [ 330, 5 ].
6 has Frattini factor [ 330, 6 ].
7 has Frattini factor [ 330, 7 ].
8 has Frattini factor [ 330, 8 ].
9 has Frattini factor [ 330, 9 ].
10 has Frattini factor [ 330, 10 ].
11 has Frattini factor [ 330, 11 ].
12 has Frattini factor [ 330, 12 ].
13 has Frattini factor [ 660, 13 ].
14 has Frattini factor [ 660, 14 ].
15 - 21 have Frattini factor [ 660, 15 ].
22 has Frattini factor [ 660, 16 ].
23 - 27 have Frattini factor [ 660, 17 ].
28 - 32 have Frattini factor [ 660, 18 ].
33 - 37 have Frattini factor [ 660, 19 ].
38 - 40 have Frattini factor [ 660, 20 ].
41 has Frattini factor [ 660, 21 ].
42 has Frattini factor [ 660, 22 ].
43 has Frattini factor [ 660, 23 ].
44 has Frattini factor [ 660, 24 ].
45 - 51 have Frattini factor [ 660, 25 ].
52 - 58 have Frattini factor [ 660, 26 ].
59 - 65 have Frattini factor [ 660, 27 ].
66 - 72 have Frattini factor [ 660, 28 ].
73 - 79 have Frattini factor [ 660, 29 ].
80 - 86 have Frattini factor [ 660, 30 ].
87 - 93 have Frattini factor [ 660, 31 ].
94 has Frattini factor [ 660, 32 ].
95 - 99 have Frattini factor [ 660, 33 ].
100 - 104 have Frattini factor [ 660, 34 ].
105 - 109 have Frattini factor [ 660, 35 ].
110 - 114 have Frattini factor [ 660, 36 ].
115 - 119 have Frattini factor [ 660, 37 ].
120 - 124 have Frattini factor [ 660, 38 ].
125 - 129 have Frattini factor [ 660, 39 ].
130 - 132 have Frattini factor [ 660, 40 ].
133 - 181 have trivial Frattini subgroup.

For the selection functions the values of the following attributes
are precomputed and stored:
IsAbelian, IsNilpotentGroup, IsSupersolvableGroup, IsSolvableGroup,
LGLength, FrattinifactorSize and FrattinifactorId.

This size belongs to layer 5 of the SmallGroups library.
IdSmallGroup is available for this size.```