# GAP:StructureDescription

## Definition

### Function type

This function takes as input a group and outputs a string that gives quick description of the group's structure.

### Behavior

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