Groups of order 1120

This article gives information about, and links to more details on, groups of order 1120
See pages on algebraic structures of order 1120 | See pages on groups of a particular order

Statistics at a glance

The number 1120 has prime factors 2, 5, and 7. The prime factorization is as follows:

$\!1120=2^{5}\cdot 5^{1}\cdot 7^{1}=32\cdot 5\cdot 7$

All groups of this order are solvable groups, and in particular, finite solvable groups.

GAP implementation

The order 1120 is part of GAP's SmallGroup library. Hence, any group of order 1120 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 1120 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(1120);

  There are 1092 groups of order 1120.
  They are sorted by their Frattini factors.
     1 has Frattini factor [ 70, 1 ].
     2 has Frattini factor [ 70, 2 ].
     3 has Frattini factor [ 70, 3 ].
     4 has Frattini factor [ 70, 4 ].
     5 has Frattini factor [ 140, 5 ].
     6 has Frattini factor [ 140, 6 ].
     7 - 73 have Frattini factor [ 140, 7 ].
     74 - 114 have Frattini factor [ 140, 8 ].
     115 - 155 have Frattini factor [ 140, 9 ].
     156 - 196 have Frattini factor [ 140, 10 ].
     197 - 215 have Frattini factor [ 140, 11 ].
     216 - 246 have Frattini factor [ 280, 32 ].
     247 - 271 have Frattini factor [ 280, 34 ].
     272 - 296 have Frattini factor [ 280, 35 ].
     297 - 631 have Frattini factor [ 280, 36 ].
     632 - 717 have Frattini factor [ 280, 37 ].
     718 - 803 have Frattini factor [ 280, 38 ].
     804 - 889 have Frattini factor [ 280, 39 ].
     890 - 913 have Frattini factor [ 280, 40 ].
     914 has Frattini factor [ 560, 170 ].
     915 - 945 have Frattini factor [ 560, 171 ].
     946 has Frattini factor [ 560, 172 ].
     947 has Frattini factor [ 560, 173 ].
     948 - 960 have Frattini factor [ 560, 174 ].
     961 - 973 have Frattini factor [ 560, 175 ].
     974 - 1026 have Frattini factor [ 560, 176 ].
     1027 - 1041 have Frattini factor [ 560, 177 ].
     1042 - 1056 have Frattini factor [ 560, 178 ].
     1057 - 1071 have Frattini factor [ 560, 179 ].
     1072 - 1077 have Frattini factor [ 560, 180 ].
     1078 - 1092 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.