GAP:StructureDescription
From Groupprops
This article is about a GAP function.
Definition
Function type
This function takes as input a group and outputs a string that gives quick description of the group's structure.
Behavior
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
Basic constructions
Letter/symbol | Number of parameters | Interpretation | Example |
---|---|---|---|
1 | 0 | trivial group | |
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