Groups of order 480

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This article gives information about, and links to more details on, groups of order 480
See pages on algebraic structures of order 480| See pages on groups of a particular order

GAP implementation

The order 840 is part of GAP's SmallGroup library. Hence, any group of order 840 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 840 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(480);

  There are 1213 groups of order 480.
  They are sorted by their Frattini factors.
     1 has Frattini factor [ 30, 1 ].
     2 has Frattini factor [ 30, 2 ].
     3 has Frattini factor [ 30, 3 ].
     4 has Frattini factor [ 30, 4 ].
     5 has Frattini factor [ 60, 6 ].
     6 has Frattini factor [ 60, 7 ].
     7 - 73 have Frattini factor [ 60, 8 ].
     74 has Frattini factor [ 60, 9 ].
     75 - 115 have Frattini factor [ 60, 10 ].
     116 - 156 have Frattini factor [ 60, 11 ].
     157 - 197 have Frattini factor [ 60, 12 ].
     198 - 216 have Frattini factor [ 60, 13 ].
     217 - 219 have Frattini factor [ 120, 34 ].
     220 - 222 have Frattini factor [ 120, 35 ].
     223 - 253 have Frattini factor [ 120, 36 ].
     254 - 257 have Frattini factor [ 120, 37 ].
     258 - 261 have Frattini factor [ 120, 38 ].
     262 - 268 have Frattini factor [ 120, 39 ].
     269 - 293 have Frattini factor [ 120, 40 ].
     294 - 318 have Frattini factor [ 120, 41 ].
     319 - 653 have Frattini factor [ 120, 42 ].
     654 - 660 have Frattini factor [ 120, 43 ].
     661 - 746 have Frattini factor [ 120, 44 ].
     747 - 832 have Frattini factor [ 120, 45 ].
     833 - 918 have Frattini factor [ 120, 46 ].
     919 - 942 have Frattini factor [ 120, 47 ].
     943 - 953 have Frattini factor [ 240, 189 ].
     954 - 960 have Frattini factor [ 240, 190 ].
     961 - 963 have Frattini factor [ 240, 192 ].
     964 - 966 have Frattini factor [ 240, 193 ].
     967 - 981 have Frattini factor [ 240, 194 ].
     982 - 1012 have Frattini factor [ 240, 195 ].
     1013 - 1023 have Frattini factor [ 240, 196 ].
     1024 - 1034 have Frattini factor [ 240, 197 ].
     1035 - 1045 have Frattini factor [ 240, 198 ].
     1046 has Frattini factor [ 240, 199 ].
     1047 - 1059 have Frattini factor [ 240, 200 ].
     1060 - 1072 have Frattini factor [ 240, 201 ].
     1073 - 1125 have Frattini factor [ 240, 202 ].
     1126 - 1132 have Frattini factor [ 240, 203 ].
     1133 - 1134 have Frattini factor [ 240, 204 ].
     1135 - 1149 have Frattini factor [ 240, 205 ].
     1150 - 1164 have Frattini factor [ 240, 206 ].
     1165 - 1179 have Frattini factor [ 240, 207 ].
     1180 - 1185 have Frattini factor [ 240, 208 ].
     1186 - 1213 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 2 of the SmallGroups library.
  IdSmallGroup is available for this size.