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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 = 898128000 : ≈ 9. ==History and properties== ''McL'' is one of the 26 sporadic groups and was discovered by as an index 2 subgroup of a rank 3 permutation group acting on the McLaughlin graph with 275 = 1 + 112 + 162 vertices. It fixes a 2-2-3 triangle in the Leech lattice so is a subgroup of the Conway groups. Its Schur multiplier has order 3, and its outer automorphism group has order 2. The group 3.McL.2 is a maximal subgroup of the Lyons group. McL has one conjugacy class of involution (element of order 2), whose centralizer is a maximal subgroup of type 2.A8. This has a center of order 2; the quotient modulo the center is isomorphic to the alternating group A8. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「McLaughlin sporadic group」の詳細全文を読む スポンサード リンク
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