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group(deprecated)

  

transgroup

  

Look up information about transitive permutation groups

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

transgroup([deg, num], opts)

transgroup("degTnum", opts)

transgroup(deg, opts)

Parameters

deg

-

degree of a transitive permutation group

num

-

number of the group conjugacy class

opts

-

sequence of names specifying the information that is required

Description

• 

Important: The group package has been deprecated. Use the superseding command GroupTheory[TransitiveGroup] instead.

• 

The function looks up in tables the information specified in opts for the group or groups specified by deg and num.  The information is returned as a sequence, of which the ith element is the information specified by the ith element of opts.

• 

The first two forms of this function use both the degree and number, and hence return information about a specific conjugacy class of transitive groups in the symmetric group on {1,...,deg}.

  

The numbering of the classes used is described in "On Transitive Permutation Groups" by J.H. Conway, A. Hulpke, and J. McKay, LMS J. Comput. Math. 1 (1998), 1-8.

  

For instance, 9,15 is the 15-th class of degree 9 groups in the paper aforementioned. An alternative valid input for this class is the string 9T15.

• 

The available options are

  

'generators'     : set of group generators for a representative of the class,

  

'names'          : set of group names, using the notation of group[transnames]

  

'order'          : group order

  

'parity'         : parity of the group, given by 1 for even or -1 for odd

  

'SnConjugates'      : Array in which the ith element is the number of group elements with a cycle type given by the partition part = combinat[decodepart](deg, i)

  

'SnConjugates(part)': number of group elements with a cycle type given by the partition part

• 

The third form of this function specifies only a group degree. All of the above options can be used here, and for each option an Array is returned, of which the ith element corresponds to the option information for the ith group of degree deg.  In addition, the option 'number' can be used which returns an integer corresponding to the number of classes of degree deg.

• 

The command with(group,transgroup) allows the use of the abbreviated form of this command.

Examples

Important: The group package has been deprecated. Use the superseding command GroupTheory[TransitiveGroup] instead.

withgroup:

transgroup5T3,names

5:4,F(5)

(1)

transgroup5,3,names,parity

5:4,F(5),−1

(2)

transgroup6T12,order,parity,generators

60,1,1,2,3,4,6,5,6,1,4

(3)

transgroup10,number

45

(4)

transgroup5,number,order

5,5102060120

(5)

transgroup4,3,SnConjugates

12302

(6)

transgroup4,3,SnConjugates2,2

3

(7)

transgroup6,SnConjugates2,2,2

134031066070610015

(8)

See Also

combinat[decodepart]

combinat[partition]

group[permgroup]

group[SnConjugates]

GroupTheory

GroupTheory[TransitiveGroup]