Janko group

In mathematics, a Janko group is one of the four sporadic simple groups named for Zvonimir Janko. Janko constructed the first of these groups, J₁, in 1965 and predicted the existence of J₂ and J₃. In 1976, he suggested the existence of J₄. J₂, J₃ and J₄ were all later shown to exist.

Janko groups

• The Janko group J1 has order 175 560 = 2³ · 3 · 5 · 7 · 11 · 19. It is the only Janko group whose existence was proved by Janko himself.
• The Hall–Janko group has order 604 800 = 2⁷ · 3³ · 5² · 7. It is also known as J₂, HJ, or the Hall–Janko–Wales group. It was constructed by Marshall Hall, Jr. and David Wales.
• The Janko group J3 has order 50 232 960 = 2⁷ · 3⁵ · 5 · 17 · 19. It is also known as the Higman–Janko–McKay group. It was constructed by Graham Higman and John McKay.
• The Janko group J4 has order 86 775 571 046 077 562 880 = 2²¹ · 3³ · 5 · 7 · 11³ · 23 · 29 · 31 · 37 · 43. It was constructed by Simon P. Norton.

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