GroupOrder

GroupOrder[group]

returns the number of elements of group.

Details

  • GroupOrder works with PermutationGroup objects and named groups.
  • For permutation groups, the order is computed by constructing a strong generating set representation of the group.

Examples

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Basic Examples  (1)

Order of a group generated by two permutations:

Scope  (2)

Order of a group defined by generators:

Order of a named group:

Properties & Relations  (1)

The identity group has size 1, even if it is described with no generators:

Neat Examples  (1)

Compare orders of randomly generated permutation groups of increasing support with the symmetric group:

Wolfram Research (2010), GroupOrder, Wolfram Language function, https://reference.wolfram.com/language/ref/GroupOrder.html.

Text

Wolfram Research (2010), GroupOrder, Wolfram Language function, https://reference.wolfram.com/language/ref/GroupOrder.html.

BibTeX

@misc{reference.wolfram_2021_grouporder, author="Wolfram Research", title="{GroupOrder}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/GroupOrder.html}", note=[Accessed: 05-December-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_grouporder, organization={Wolfram Research}, title={GroupOrder}, year={2010}, url={https://reference.wolfram.com/language/ref/GroupOrder.html}, note=[Accessed: 05-December-2021 ]}

CMS

Wolfram Language. 2010. "GroupOrder." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GroupOrder.html.

APA

Wolfram Language. (2010). GroupOrder. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GroupOrder.html