return a random group from the database of small groups
RandomSmallGroup( idopt, ordopt, formopt )
(optional) option of the form id = true (or just id) or id = false
(optional) option of the form maxorder = n, for a positive integer n
(optional) option of the form form = "permgroup" (default), form = "fpgroup" or form = "id"
The RandomSmallGroup() command returns a randomly selected group from the database of small groups, as a permutation group.
The id option controls how the group is selected. If the option id = true (or just id) is passed, then a randomly selected order in the range 1 .. 511 is first selected, and then, within the groups of that order, a random group is returned. If the id = false option is passed, then a truly (pseudo-)randomly selected group is returned from the database of small groups. Note that most groups in the small groups database have order equal to 256, so this is usually not what is wanted, which is why the default option is id = true.
The form option determines the form of what is returned. By default, a permutation group is returned. To have a finitely presented group returned, use the form = "fpgroup" option. Sometimes, only a valid small group ID is required, in which case, use the form = "id" option.
SEED = ,66302275552
< a permutation group on 256 letters with 8 generators >
G ≔ RandomSmallGroup⁡'id','maxorder'=200
G ≔ 1,23,84,75,106,911,2212,2413,2314,1915,2116,2017,2618,2527,4228,4129,4430,4331,3832,3733,4034,3935,4636,4547,6048,5949,6250,6151,5652,5553,5854,5763,7064,6965,6866,67,1,3,11,14,42,7,19,22,85,12,27,31,156,13,28,32,169,20,37,41,2310,21,38,42,2417,29,47,51,3318,30,48,52,3425,39,55,59,4326,40,56,60,4435,49,63,65,5336,50,64,66,5445,57,67,69,6146,58,68,70,62,1,5,17,35,36,18,62,9,25,45,46,26,103,12,29,49,50,30,134,15,33,53,54,34,167,20,39,57,58,40,218,23,43,61,62,44,2411,27,47,63,64,48,2814,31,51,65,66,52,3219,37,55,67,68,56,3822,41,59,69,70,60,42
G ≔ RandomSmallGroup⁡'form'=fpgroup
G ≔ ⁢a1⁢∣⁢a1484⁢
G ≔ RandomSmallGroup⁡'maxorder'=100,'form'=fpgroup
G ≔ ⁢_a,_b⁢∣⁢_b2,_a⁢_b⁢_a⁢_b,_a38⁢
id ≔ RandomSmallGroup⁡'form'='id','maxorder'=150
id ≔ 27,1
The GroupTheory[RandomSmallGroup] command was introduced in Maple 2017.
For more information on Maple 2017 changes, see Updates in Maple 2017.
Download Help Document