Conway group:Co0
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Contents
Definition
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.
Its center is cyclic group:Z2 and the inner automorphism group is Conway group:Co1.
Arithmetic functions
Basic arithmetic functions
Function | Value | Similar groups | Explanation |
---|---|---|---|
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 nature
PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]Group properties
Property | Satisfied? | Explanation |
---|---|---|
simple group | No | the center is nontrivial |
perfect group | Yes | |
quasisimple group | Yes | |
solvable group | No |
Linear representation theory
Further information: linear representation theory of Conway group:Co0
Item | Value |
---|---|
degrees of irreducible representations over a splitting field (such as ![]() ![]() |
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 |
GAP implementation
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.