In the
mathematical field of
graph theory, the McLaughlin graph is a
strongly regular graph with parameters (275,112,30,56), and is the only such graph.
The
group theorist Jack McLaughlin discovered that the
automorphism group of this graph had a subgroup of index 2 which was a previously undiscovered
finite simple group, now called the
McLaughlin sporadic group
In the area of modern algebra known as group theory, the McLaughlin group McL is a sporadic simple group of order
: 27 ⋅ 36 ⋅ 53 ⋅ 7 ⋅ 11 = 898,128,000
: ≈ 9.
History and properties
McL is one of the 26 spo ...
.
The automorphism group has
rank 3, meaning that its
point stabilizer
In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism g ...
subgroup divides the remaining 274 vertices into two
orbits. Those orbits contain 112 and 162 vertices. The former is the
colinearity graph of the generalized quadrangle GQ(3,9). The latter is a strongly regular graph called the
local McLaughlin graph.
References
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External links
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Individual graphs
Regular graphs
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