This article is about a GAP function.
This function takes as input a group and outputs a string that gives quick description of the group's structure.
|Nature of input||Output||Example inputs and corresponding outputs||Additional comments|
|a finite group that GAP can recognize||a string giving a description of the group|| StructureDescription(SmallGroup(24,8)) gives "(C6 x C2) : C2"
StructureDescription(SmallGroup(16,8)) gives "QD16"
|Isomorphic groups always give the same structure description. However, it is possible to have non-isomorphic groups that give the same structure description.|
|an infinite group or some other input||a NoMethodFound error|
Aspects of structure description
|Letter/symbol||Number of parameters||Interpretation||Example|
|C||1 for size||cyclic group of size equal to the parameter||"C8" stands for the cyclic group of order eight.|
|A||1 for degree||alternating group of degree equal to the parameter||"A5" stands for the alternating group of degree five.|
|S||1 for degree||symmetric group of degree equal to the parameter||"S4" stands for the symmetric group of degree four.|
|D||1 for order||dihedral group of order equal to the parameter. Note that the order is twice the degree||"D8" stands for the dihedral group of order eight.|
|Q||1 for order||generalized quaternion group of order equal to the parameter.||"Q16" stands for generalized quaternion group:Q16|
|QD||1 for order||quasidihedral group (called semidihedral group on this wiki) of order equal to the parameter.||"QD16" stands for semidihedral group:SD16|
|PSL||2: 1 for degree (order of matrices), 1 for size of field||projective special linear group of given degree over field of given size||"PSL(2,11)" stands for projective special linear group:PSL(2,11): the projective special linear group of degree two over field:F11.|
|SL||2: 1 for degree (order of matrices), 1 for size of field||special linear group of given degree over field of given size||"SL(2,5)" stands for special linear group:SL(2,5): the special linear group of degree two over field:F5.|
|GL||2: 1 for degree (order of matrices), 1 for size of field|
The table needs to be completed