This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
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This group, denoted or , is defined in the following equivalent ways:
- It is the automorphism group of the Leech lattice.
- It is the Schur covering group (specifically, it is a double cover) of Conway group:Co1.
Basic arithmetic functions
|order (number of elements, equivalently, cardinality or size of underlying set)||8315553613086720000||groups with same order||The order has factorization: .|
Arithmetic functions of a counting naturePLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]
|simple group||No||the center is nontrivial|
Linear representation theory
Further information: linear representation theory of Conway group:Co0
|degrees of irreducible representations over a splitting field (such as or )|| too long to list, see Linear representation theory of Conway group:Co0#GAP implementation|
number: 167, sum of squares: 8315553613086720000, maximum: 1021620600, quasirandom degree: 24
The group itself is too large to be constructed, stored and manipulated in GAP. However, information about its linear representation theory and character table is stored under the symbol "2.Co1" -- for more on this, see Linear representation theory of Conway group:Co0#GAP implementation.